MOPAC MANUAL (Fifth Edition) A GENERAL MOLECULAR ORBITAL PACKAGE Written by James J. P. Stewart, Frank J. Seiler Research Laboratory United States Air Force Academy Colorado Springs, CO 80840 1 CONTENTS 1 FORWARD BY PROF. MICHAEL J. S. DEWAR . . . . . . . . i 2 UPDATES FROM VERSION 4.00 . . . . . . . . . . . . iii 3 ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . vi CHAPTER 1 DESCRIPTION OF MOPAC 1.1 SUMMARY OF MOPAC CAPABILITIES . . . . . . . . . . 1-2 1.2 COPYRIGHT STATUS OF MOPAC . . . . . . . . . . . . 1-3 1.3 RELATIONSHIP OF AMPAC AND MOPAC . . . . . . . . . 1-3 1.4 PROGRAMS RECOMMENDED FOR USE WITH MOPAC . . . . . 1-4 1.5 THE DATA-FILE . . . . . . . . . . . . . . . . . . 1-5 1.5.1 Example Of Data For Ethylene . . . . . . . . . . 1-6 1.5.2 Example Of Data For Polytetrahydrofuran . . . . 1-7 CHAPTER 2 KEYWORDS 2.1 SPECIFICATION OF KEYWORDS . . . . . . . . . . . . 2-1 2.2 FULL LIST OF KEYWORDS USED IN MOPAC . . . . . . . 2-2 2.3 DEFINITIONS OF KEYWORDS . . . . . . . . . . . . . 2-4 CHAPTER 3 GEOMETRY SPECIFICATION 3.1 CONSTRAINTS . . . . . . . . . . . . . . . . . . . 3-2 3.2 DEFINITION OF ELEMENTS AND ISOTOPES . . . . . . . 3-3 3.3 EXAMPLES OF COORDINATE DEFINITIONS. . . . . . . . 3-6 CHAPTER 4 EXAMPLES 4.1 MNRSD1 TEST DATA FILE FOR FORMALDEHYDE . . . . . . 4-1 4.2 MOPAC OUTPUT FOR TEST-DATA FILE MNRSD1 . . . . . . 4-2 CHAPTER 5 TESTDATA 5.1 DATA FILE FOR A FORCE CALCULATION . . . . . . . . 5-1 5.2 RESULTS FILE FOR THE FORCE CALCULATION . . . . . . 5-1 5.3 EXAMPLE OF REACTION PATH WITH SYMMETRY . . . . . 5-11 CHAPTER 6 BACKGROUND 6.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . 6-1 6.2 CORRECTION TO THE PEPTIDE LINKAGE . . . . . . . . 6-1 6.3 LEVEL OF PRECISION WITHIN MOPAC . . . . . . . . . 6-3 6.4 CONVERGENCE TESTS IN SUBROUTINE ITER . . . . . . . 6-5 6.5 CONVERGENCE IN SCF CALCULATION . . . . . . . . . . 6-6 6.6 CAUSES OF FAILURE TO ACHIEVE AN SCF . . . . . . . 6-7 6.7 TORSION OR DIHEDRAL ANGLE COHERENCY . . . . . . . 6-8 6.8 VIBRATIONAL ANALYSIS . . . . . . . . . . . . . . . 6-8 Page 2 6.9 A NOTE ON THERMOCHEMISTRY . . . . . . . . . . . . 6-9 6.10 REACTION COORDINATES . . . . . . . . . . . . . . 6-16 6.11 SPARKLES . . . . . . . . . . . . . . . . . . . . 6-29 6.12 MECHANISM OF THE FRAME IN THE FORCE CALCULATION 6-31 6.13 PSEUDODIAGONALIZATION -SUBROUTINE DIAG . . . . . 6-31 6.14 DYNAMIC REACTION COORDINATE . . . . . . . . . . 6-34 6.15 CONFIGURATION INTERACTION . . . . . . . . . . . 6-35 6.16 REDUCED MASSES IN A FORCE CALCULATION . . . . . 6-43 6.17 USE OF SADDLE CALCULATION . . . . . . . . . . . 6-43 6.18 HOW TO ESCAPE FROM A HILLTOP . . . . . . . . . . 6-45 6.19 POLARIZABILITY CALCULATION . . . . . . . . . . . 6-47 6.20 SOLID STATE CAPABILITY . . . . . . . . . . . . . 6-49 CHAPTER 7 PROGRAM 7.1 MAIN GEOMETRIC SEQUENCE . . . . . . . . . . . . . 7-2 7.2 MAIN ELECTRONIC FLOW . . . . . . . . . . . . . . . 7-3 7.3 CONTROL WITHIN MOPAC . . . . . . . . . . . . . . . 7-4 CHAPTER 8 ERROR MESSAGES PRODUCED BY MOPAC CHAPTER 9 CRITERIA 9.1 SCF CRITERION . . . . . . . . . . . . . . . . . . 9-1 9.2 GEOMETRIC OPTIMIZATION CRITERIA . . . . . . . . . 9-2 CHAPTER 10 DEBUGGING 10.1 DEBUGGING KEYWORDS . . . . . . . . . . . . . . . 10-1 CHAPTER 11 INSTALLING MOPAC APPENDIX A FORTRAN FILES APPENDIX B SUBROUTINE CALLS IN MOPAC APPENDIX C DESCRIPTION OF SUBROUTINES IN MOPAC APPENDIX D HEATS OF FORMATION OF SOME MNDO, PM3 AND AM1 COMPOUNDS APPENDIX E REFERENCES 1 FORWARD BY PROF. MICHAEL J. S. DEWAR "MOPAC is the present culmination of a continuing project that started twenty years ago, directed to the development of quantum mechanical procedures simple enough, and accurate enough, to be useful to chemists as an aid in their own research. A historical account of this development, with references, has appeared [1]. The first really effective treatment was MINDO/3 [2], which is still useful in various areas of hydrocarbon chemistry but ran into problems with heteroatoms. This was succeeded by MNDO [3] and more recently by AM1 [4] which seems to have overcome most of the deficiencies of its predecessors at no cost in computing time. Our computer programs steadily evolved with the development of new algorithms. In addition to the basic programs for the SCF calculations and geometry optimization, programs were developed for calculating vibration frequencies [5], thermodynamic parameters [6], kinetic isotope effects [7], linear polymers [8], polarizabilities and hyperpolarizabilities [9,10], and SCF-CI calculations [11]. While this disjointed collection of programs served its purpose, it was inconvenient and time consuming to use. A major step was the integration [12] of most of these into a single unified program [MOPAC] with a greatly simplified input. The individual programs were also rewritten in a more efficient form so that the computing time reported for most calculations has now been halved. In its present form MOPAC is impressively easy to use and it contains options for nearly all the applications where our procedures have been found useful." Michael J.S. Dewar, January 1987 i REFERENCES (1) Dewar, M.J.S., J. Mol. Struct., 100, 41 (1983). (2) Dewar, M.J.S.; Bingham, R.C.; Lo, D.H., J. Am. Chem. Soc., 97, 1285 (1975). (3) Dewar, M.J.S.; Thiel, W., J. Am. Chem. Soc., 99, 4899 (1977). (4) Dewar, M.J.S.; Zoebisch, E.G.; Healy, E.F.; Stewart, J.J.P., J. Am. Chem. Soc.; 107, 3902 (1985). (5) Dewar, M.J.S.; Ford, G.P., J. Am. Chem. Soc., 99, 1685 (1977); Dewar, M.J.S.; Ford, G.; McKee, M.; Rzepa, H.S.; Yamaguchi, Y., J. Mol. Struct., 43, 135 (1978). (6) Dewar, M.J.S.; Ford, G., J. Am. Chem. Soc., 99, 7822 (1977). (7) Dewar, M.J.S.; Brown, S.B.; Ford, G.P.; Nelson, D.J.; Rzepa, H.S., J. Am. Chem. Soc., 100, 7832 (1978). (8) Dewar, M.J.S.; Yamaguchi, Y.; Suck, S.H., Chem. Phys. Lett., 50,175,279 (1977). (9) Dewar, M.J.S.; Bergman, J.G.; Suck, S.H.; Weiner, P.K., Chem. Phys. Lett., 38,226,(1976); Dewar, M.J.S.; Yamaguchi, Y.; Suck, S.H., Chem. Phys. Lett., 59, 541 (1978). (10) Dewar, M.J.S.; Stewart, J.J.P., Chem. Phys. Lett., 111,416 (1984). (11) Dewar, M.J.S.; Doubleday, C., J. Am. Chem. Soc., 100, 4935 (1978). (12) Stewart, J.J.P. QCPE # 455. ii | 2 UPDATES FROM VERSION 4.00 | | | MOPAC is updated once a year. This is the best compromise | between staying current and asking users to continuously change | their software. Updates may be obtained from QCPE at the same cost | as the original, or from sites that have a current copy. All VAX | versions of MOPAC have the same QCPE number - 455; they are | distinguished by version numbers. Users are recommended to update | their programs at least once every two years, and preferably every | year. | | New Features of Version 5.0 | | 1. A new method, MNDO-PM3, has been added. This method allows | hypervalent systems to be calculated with accuracies comparable | with non-hypervalent compounds. | | 2. In the DRC the option has been provided for the user to supply | initial velocity vectors from the data-file. See keyword | VELOCITY. | | 3. Time can now be specified as seconds (the default), minutes, | hours, or days. See keyword T=. | | 4. The energy partition output has been rewritten so that each type | of interaction is printed in matrix form. The code for this was | written by Prof Tsuneo Hirano. | | 5. Hyperpolarizabilities can be calculated by invoking the keyword | POLAR. The POLAR routine was completely rewritten by Dr. Henry | Kurtz of Memphis State University. | | 6. The SHIFT option is now used by default. To prevent it being | used, add the keyword SHIFT=0.0. The SHIFT option has been | extensively re-written to allow the amount of damping of the SCF | iterations to be determined by the rate of convergence. The | basic methodology was described by A. V. Mitin -- see | references. The effect of this is to allow systems that | previously failed to go SCF to now converge. | | 7. Notwithstanding the improved SHIFT option, some systems still | persist in failing to go SCF. If this is in a non-FORCE | calculation, then if an SCF is almost achieved a warning will be | printed and the calculation will continue. In a FORCE | calculation the SCF must be completed to the precision selected, | otherwise the second derivatives will not be sufficiently | accurate. | | 8. The keyword GNORM now applies to both gradient minimizations as | well as to the geometry optimization. | | 9. The meaning of LET has been generalized to now mean override | default safety features. iii | 10. Boron has been added to the AM1 set of elements: see | references. | | 11. Zinc has been added to the MNDO set of elements: see | references. | | 12. Some more warning messages are produced. In MECI, for example, | if you specify the second triplet when a C.I.=2 is used, you | will be told that the allowed states are three singlets and one | triplet. | | 13. REPP and ROTATE have been completely re-written by Prof. Ernest | R. Davidson of Indiana University. The new routines are easier | to read and faster on a vector machine. | | 14. In a THERMO calculation, the heat of formation of the system | relative to its elements in their standard state at 298K is | printed. | | | | ERRORS CORRECTED IN VERSION 5.0 | | 1. Sometimes the geometry optimization routine would call for a sudden | large change in the geometry. This would result in a nonsensical | geometry, and the failure to achieve an SCF. All steps are now | conservative. | | 2. In COMPFG some coordinates are printed if DEBUG and COMPFG are used. | When the calculation was run in cartesian coordinates the output was | incorrectly multiplied by 180/pi. This has been corrected. | | 3. Even when analytic derivatives were not used, channel 2 was touched | (rewound). This gave rise to a spurious file FOR002.DAT. This file is | now not created unless ANALYT is specified. | | 4. Systems of zero electrons are now allowed. | | 5. In a SADDLE calculation, if the number of atoms in the reactants is | different from that in the products, the calculation is stopped. | | 6. In forming the inverse square root of the overlap matrix in the | Mulliken population, a crash sometimes occurred due to the existence of | negative molecular overlap integrals -- theoretically they cannot occur, | but sometimes result due to round-off. This has been corrected. | | 7. All variables should now be initialized before use. The lack of | initialization caused difficulties with certain computers. | | 8. In certain instances the bugfix to DIAG made in Version 4.0 slowed | down the rate at which an SCF was achieved. This has been corrected by | going back to the original formulation, but limiting the cosine to the | range 1.0 to -1.0. iv | 9. Under certain circumstances the "THREE ATOMS IN A STRAIGHT LINE" | error message would be generated spuriously, and the calculation stopped. | This has been corrected. | | 10. When PULAY is used in a FORCE calculation of an excited state, the | SCF would sometimes lock onto the excited state. This was a result of | FORCE needing the excited density matrix for the I.R. transition dipole | calculation. Later on, when ITER is called, the density matrix is that | of the excited state, and as PULAY is similar to the gradient | minimization in that it converges on the nearest stationary point, the | SCF that results is an excited state. This really messes up the FORCE | calculation. To correct this, the old density matrix is reformed in ITER | before the SCF is done. | | | | | Help with MOPAC | | ------------------------------------------------- | | Telephone and mail support is given by the | | | Frank J. Seiler Research Laboratory on a time | | | permitting basis. If you need help, call | | | the Seiler MOPAC Consultant at | | | | | | (719) 472-2655 | | | | | | Similarly, mail should be addressed to | | | | | | MOPAC Consultant | | | FJSRL/NC | | | U.S. Air Force Academy CO 80840-6528 | | | | | ------------------------------------------------- v 3 ACKNOWLEDGEMENTS Acknowledgements The initial writing of MOPAC took about six months, with the | current version incorporating five more years of effort. During this time several co-workers provided invaluable assistance. Some contributed code, some ideas, and some identified bugs. Of those who helped, I would like to recognize the following people for their assistance during the writing of MOPAC. Major Donn Storch, at the Air Force Academy, has been involved during the entire development of MOPAC, taking a professional interest in its design and structure. Many improvements are due to his practical suggestions. | | Major Kenneth (Skip) Dieter, for endeavoring, sometimes | unsuccessfully, to keep me completely honest in defining the | capabilities of MOPAC. For her unflagging patience in checking the manual for clarity of expression, and for drawing to my attention innumerable spelling and grammatical errors, I thank my wife, Anna. | | Over the years a large amount of advice, ideas and code has | been contributed by various people in order to improve MOPAC. The | following incomplete list recognises various contributors: | Prof. Santiago Olivella: Critical analysis of Versions 1 to 3. | Prof. Tsuneo Hirano: Rewrite of the Energy Partition. | Prof. Peter Pulay: Designing the rapid pseudodiagonalization. | Prof. Mark Gordon: Critical comments on the IRC. | Prof. Henry Kurtz: Writing the polarizability and hyperpolarizability. | Prof. Henry Rzepa: Providing the code for the BFGS optimizer | Major Larry Davis and Lt. Col. Larry Burggraf: Designed the form | of the DRC and IRC. | Dr. John McKelvey: Numerous suggestions for improving output. | Dr. Erich Wimmer: Suggestions for imcreasing the speed of calculation. | Dr. James Friedheim: Testing of Versions 1 and 2. | Dr. Eamonn Healy: Critical evaluation of Versions 1-4. | | This list does not include the large number of people who | developed methods which are used in MOPAC. The more important | contributions are given in the References at the end of this | Manual I wish to thank Prof. Michael J.S. Dewar for providing the facilities and funds during the initial development of the MOPAC program, the staff of the Frank J. Seiler Research Laboratory and the Chemistry Department at the Air Force Academy for their support. vi CHAPTER 1 DESCRIPTION OF MOPAC MOPAC is a general-purpose semi-empirical molecular orbital package for the study of chemical structures and reactions. The semi-empirical Hamiltonians MNDO, MINDO/3, AM1, and PM3 are used in the electronic part of the calculation to obtain molecular orbitals, the heat of formation and its derivative with respect to molecular geometry. Using these results MOPAC calculates the vibrational spectra, thermodynamic quantities, isotopic substitution effects and force constants for molecules, radicals, ions, and polymers. For studying chemical reactions, a transition-state location routine and two transition state optimizing routines are available. For users to get the most out of the program, they must understand how the program works, how to enter data, how to interpret the results, and what to do when things go wrong. While MOPAC calls upon many concepts in quantum theory and thermodynamics and uses some fairly advanced mathematics, the user need not be familiar with these specialized topics. MOPAC is written with the non-theoretician in mind. The input data are kept as simple as possible so users can give their attention to the chemistry involved and not concern themselves with quantum and thermodynamic exotica. The simplest description of how MOPAC works is that the user creates a data-file which describes a molecular system and specifies what kind of calculations and output are desired. The user then commands MOPAC to carry out the calculation using that data-file. Finally the user extracts the desired output on the system from the output files created by MOPAC. NOTES (1) This is the "fifth edition". MOPAC has undergone a steady expansion since its first release, and users of the earlier editions are recommended to familiarize themselves with the changes which are described in this manual. If any errors are found, or if MOPAC does not perform as described, please contact Dr. James J. P. Stewart, Frank J. Seiler Research Laboratory, U.S. Air Force Academy, Colorado Springs, CO 80840-6528. (2) MOPAC runs successfully on normal CDC, Data General, Gould, and Digital computers, and also on the CDC 205 and CRAY-XMP "supercomputers". The CRAY version has been partly optimized to take advantage of the CRAY architecture. Several versions exist for microcomputers such as the IBM PC-AT and XT, Zenith, etc. 1-1 DESCRIPTION OF MOPAC Page 1-2 1.1 SUMMARY OF MOPAC CAPABILITIES 1. MNDO, MINDO/3, AM1, and PM3 Hamiltonians. 2. Restricted Hartree-Fock (RHF) and Unrestricted Hartree-Fock (UHF) methods. 3. Extensive Configuration Interaction 1. 100 configurations 2. Singlets, Doublets, Triplets, Quartets, Quintets, and Sextets 3. Excited states 4. Geometry optimizations, etc., on specified states 4. Single SCF calculation 5. Geometry optimization 6. Gradient minimization 7. Transition state location 8. Reaction path coordinate calculation 9. Force constant calculation 10. Normal coordinate analysis 11. Transition dipole calculation 12. Thermodynamic properties calculation 13. Localized orbitals 14. Covalent bond orders 15. Bond analysis into sigma and pi contributions 16. One dimensional polymer calculation 17. Dynamic Reaction Coordinate calculation 18. Intrinsic Reaction Coordinate calculation - 2 - DESCRIPTION OF MOPAC Page 1-3 | 1.2 COPYRIGHT STATUS OF MOPAC | | At the request of the Air Force Academy Law Department the following | notice has been placed in MOPAC. | | Notice of Public Domain nature of MOPAC | | 'This computer program is a work of the United States | Government and as such is not subject to protection by | copyright (17 U.S.C. # 105.) Any person who fraudulently | places a copyright notice or does any other act contrary | to the provisions of 17 U.S. Code 506(c) shall be subject | to the penalties provided therein. This notice shall not | be altered or removed from this software and is to be on | all reproductions.' | | I recommend that a user obtain a copy by either copying it from an | existing site or ordering an 'official' copy from the Quantum Chemistry | Program Exchange, (QCPE), Department of Chemistry, Indiana University, | Bloomington, Indiana, 47405. The cost covers handling only. Contact the | Editor, Richard Counts at (812) 335-4784 for further details. | | | | | | 1.3 RELATIONSHIP OF AMPAC AND MOPAC | | | In 1985 MOPAC 3.0 and AMPAC 1.0 were submitted to QCPE for | distribution. At that time, AMPAC differed from MOPAC in that it had the | AM1 algorithm. Additionally, changes in some MNDO parameters in AMPAC | made AMPAC results incompatable with MOPAC Versions 1-3. Subsequent | versions of MOPAC, in addition to being more highly debugged than Version | 3.0, also had the AM1 method. Such versions were compatable with AMPAC | and with versions 1-3 of MOPAC. | | In order to avoid confusion, all versions of MOPAC after 3.0 include | journal references so that the user knows unambiguously which parameter | sets were used in any given job. | | Since 1985 AMPAC and MOPAC have evolved along different lines. In | MOPAC I have endeavoured to provide a highly robust program, one with | only a few new features, but which is easily portable and which can be | relied upon to give precise, if not very exciting, answers. At Austin, | the functionality of AMPAC has been enhanced by the research work of | Prof. Dewar's group. AMPAC thus has functionalities not present in | MOPAC. In publications, users should cite not only the program name but | also the version number. | | Commercial concerns have optimized both MOPAC and AMPAC for use on | supercomputers. The quality of optimization and the degree to which the | parent algorithm has been preserved differs between MOPAC and AMPAC and | also between some machine specific versions. Different users may prefer | one program to the other, based on considerations such as speed. Some - 3 - DESCRIPTION OF MOPAC Page 1-4 | modifications of AMPAC run faster than some modifications of MOPAC, and | vice versa, but if these are modified versions of MOPAC 3.0 or AMPAC 1.0, | they represent the programming prowess of the companies doing the | conversion, and not any intrinsic difference between the two programs. | | Testing of these large algorithms is difficult, and several times | users have reported bugs in MOPAC or AMPAC which were introduced after | they were supplied by QCPE. | | Cooperative Development of MOPAC | | MOPAC has developed, and hopefully will continue to develop, by the | addition of contributed code. As a policy, any supplied code which is | incorporated into MOPAC will be described in the next release of the | Manual, and the author or supplier acknowledged. In the following | release only journal references will be retained. The objective is to | produce a good program. This is obviously not a one-person undertaking, | if it was, then the product would be poor indeed. Instead, as we are in | a time of rapid change in computational chemistry, a time characterized | by a very free exchange of ideas and code, MOPAC has been evolving by | accretion. The unstinting and generous donation of intellectual effort | speaks highly of the donors, however, with the rapid commercialization of | computational chemistry software in the past few years, it is unfortunate | but it seems unlikely that this idyllic state will continue. 1.4 PROGRAMS RECOMMENDED FOR USE WITH MOPAC MOPAC is the core program of a series of programs for the theoretical study of chemical phenomena. This version is the third in an on-going development, and efforts are being made to continue its further evolution. In order to make using MOPAC easier, four other programs have also been written. Users of MOPAC are recommended to use all four programs. Efforts will be made to continue the development of these programs. DRAW DRAW, written by Maj. Donn Storch, USAF, and available through QCPE, is a powerful editing program specifically written to interface with MOPAC. Among the various facilities it offers are: 1. The on-line editing and analysis of a data file, starting from scratch or from an existing data file, an archive file, or from a results file. 2. The option of continuous graphical representation of the system being studied. Several types of terminals are supported, including DIGITAL, TEKTRONIX, and TERAK terminals. - 4 - DESCRIPTION OF MOPAC Page 1-5 3. The drawing of electron density contour maps generated by DENSITY on graphical devices. 4. The drawing of solid-state band structures generated by MOSOL. 5. The sketching of molecular vibrations, generated by a normal coordinate analysis. DENSITY DENSITY, written by Dr. James J. P. Stewart, and available through QCPE, is an electron-density plotting program. It accepts data-files directly from MOPAC, and is intended to be used for the graphical representation of electron density distribution, individual M.O.'s, and difference maps. MOHELP MOHELP, also available through QCPE, is an on-line help facility, written by Maj. Donn Storch and Dr. James J. P. Stewart, to allow non-VAX users access to the VAX HELP libraries for MOPAC, DRAW, and DENSITY. MOSOL MOSOL (Distributed by QCPE) is a full solid-state MNDO program written by Dr. James J. P. Stewart. In comparison with MOPAC, MOSOL is extremely slow. As a result, while geometry optimization, force constants, and other functions can be carried out by MOSOL, these slow calculations are best done using the solid-state facility within MOPAC. MOSOL should only be used for generating band-structures and densities of states, a task that MOPAC cannot perform. 1.5 THE DATA-FILE This section is aimed at the complete novice -- someone who knows nothing at all about the structure of a MOPAC data-file. First of all, there are at most four possible types of data-files for MOPAC, but the simplest data-file is the most commonly used. Rather than define it, two examples are shown below. An explanation of the geometry definitions shown in the examples is given in the chapter "GEOMETRY SPECIFICATION". - 5 - DESCRIPTION OF MOPAC Page 1-6 1.5.1 Example Of Data For Ethylene Line 1 : UHF PULAY MINDO3 VECTORS DENSITY LOCAL T=300 Line 2 : EXAMPLE OF DATA FOR MOPAC Line 3 : MINDO/3 UHF CLOSED-SHELL D2D ETHYLENE Line 4a: C Line 4b: C 1.400118 1 Line 4c: H 1.098326 1 123.572063 1 Line 4d: H 1.098326 1 123.572063 1 180.000000 0 2 1 3 Line 4e: H 1.098326 1 123.572063 1 90.000000 0 1 2 3 Line 4f: H 1.098326 1 123.572063 1 270.000000 0 1 2 3 Line 5 : As can be seen, the first three lines are textual. The first line consists of keywords (here seven keywords are shown). These control the calculation. The next two lines are comments or titles. The user might want to put the name of the molecule and why it is being run on these two lines. These three lines are obligatory. If no name or comment is wanted, leave blank lines. If no keywords are specified, leave a blank line. A common error is to have a blank line before the keyword line: this error is quite tricky to find, so be careful not to have four lines before the start of the geometric data (lines 4a-4f in the example). Whatever is decided, the three lines, blank or otherwise, are obligatory. The next set of lines defines the geometry. In the example, the numbers are all neatly lined up; this is not necessary, but does make it easier when looking for errors in the data. The geometry is defined in lines 4a to 4f; line 5 terminates both the geometry and the data-file. Any additional data, for example symmetry data, would follow line 5. Summarizing, then, the structure for a MOPAC data-file is: Line 1: Keywords. (See chapter 2 on definitions of keywords) Line 2: Title of the calculation, e.g. the name of the molecule or ion. Line 3: Other information describing the calculation. Lines 4: Internal or cartesian coordinates (See chapter on specification of geometry) Line 5: Blank line to terminate the geometry definition. Other layouts for data-files involve additions to the simple layout. These additions occur at the end of the data-file, after line 5. The three most common additions are: (a) Symmetry data: This follows the geometric data, and is ended by a blank line. (b) Reaction path: After all geometry and symmetry data (if any) are read in, points on the reaction coordinate are defined. (c) Saddle data: A complete second geometry is input. The second geometry follows the first geometry and symmetry data (if any). - 6 - DESCRIPTION OF MOPAC Page 1-7 1.5.2 Example Of Data For Polytetrahydrofuran The following example illustrates the data file for a four hour polytetrahydrofuran calculation. As you can see the layout of the data is almost the same as that for a molecule, the main difference is in the presence of the translation vector atom "Tv". Line 1 :T=4H Line 2 : POLY-TETRAHYDROFURAN (C4 H8 O)2 Line 3 : Line 4a: C 0.000000 0 0.000000 0 0.000000 0 0 0 0 Line 4b: C 1.551261 1 0.000000 0 0.000000 0 1 0 0 Line 4c: O 1.401861 1 108.919034 1 0.000000 0 2 1 0 Line 4d: C 1.401958 1 119.302489 1 -179.392581 1 3 2 1 Line 4e: C 1.551074 1 108.956238 1 179.014664 1 4 3 2 Line 4f: C 1.541928 1 113.074843 1 179.724877 1 5 4 3 Line 4g: C 1.551502 1 113.039652 1 179.525806 1 6 5 4 Line 4h: O 1.402677 1 108.663575 1 179.855864 1 7 6 5 Line 4i: C 1.402671 1 119.250433 1 -179.637345 1 8 7 6 Line 4j: C 1.552020 1 108.665746 1 -179.161900 1 9 8 7 Line 4k: XX 1.552507 1 112.659354 1 -178.914985 1 10 9 8 Line 4l: XX 1.547723 1 113.375266 1 -179.924995 1 11 10 9 Line 4m: H 1.114250 1 89.824605 1 126.911018 1 1 3 2 Line 4n: H 1.114708 1 89.909148 1 -126.650667 1 1 3 2 Line 4o: H 1.123297 1 93.602831 1 127.182594 1 2 4 3 Line 4p: H 1.123640 1 93.853406 1 -126.320187 1 2 4 3 Line 4q: H 1.123549 1 90.682924 1 126.763659 1 4 6 5 Line 4r: H 1.123417 1 90.679889 1 -127.033695 1 4 6 5 Line 4s: H 1.114352 1 90.239157 1 126.447043 1 5 7 6 Line 4t: H 1.114462 1 89.842852 1 -127.140168 1 5 7 6 Line 4u: H 1.114340 1 89.831790 1 126.653999 1 6 8 7 Line 4v: H 1.114433 1 89.753913 1 -126.926618 1 6 8 7 Line 4w: H 1.123126 1 93.644744 1 127.030541 1 7 9 8 Line 4x: H 1.123225 1 93.880969 1 -126.380511 1 7 9 8 Line 4y: H 1.123328 1 90.261019 1 127.815464 1 9 11 10 Line 4z: H 1.123227 1 91.051403 1 -125.914234 1 9 11 10 Line 4A: H 1.113970 1 90.374545 1 126.799259 1 10 12 11 Line 4B: H 1.114347 1 90.255788 1 -126.709810 1 10 12 11 Line 4C: Tv 12.299490 1 0.000000 0 0.000000 0 1 11 10 Line 5 : 0 0.000000 0 0.000000 0 0.000000 0 0 0 0 Polytetrahydrofuran has a repeat unit of (C4 H8 O)2; i.e., twice the monomer unit. This is necessary in order to allow the lattice to repeat after a translation through 12.3 Angstroms. See the section on Solid State Capability for further details. Note the two dummy atoms on lines 4k and 4l. These are useful, but not essential, for defining the geometry. The atoms on lines 4y to 4B use these dummy atoms, as does the translation vector on line 4C. The translation vector has only the length marked for optimization. The reason for this is also explained in the Background chapter. - 7 - CHAPTER 2 KEYWORDS 2.1 SPECIFICATION OF KEYWORDS All control data are entered in the form of keywords, which form the first line of a data-file. A description of what each keyword does is given in Section 2-3. The order in which keywords appear is not important although they must be separated by a space. Some keywords can be abbreviated, allowed abbreviations are noted in Section 2-3 (for example 1ELECTRON can be entered as 1ELECT). However the full keyword is preferred in order to more clearly document the calculation and to obviate the possibility that an abbreviated keyword might not be recognized. If there is insufficient space in the first line for all the keywords needed, then consider abbreviating the longer words. One type of keyword, those with an equal sign, such as, BAR=0.05, may not be abbreviated, and the full word needs to be supplied. Most keywords which involve an equal sign, such as SCFCRT=1.D-12 can, at the user's discretion, be written with spaces before and after the equal sign. Thus all permutations of SCFCRT=1.D-12, such as SCFCRT =1.D-12, SCFCRT = 1.D-12, SCFCRT= 1.D-12, SCFCRT = 1.D-12, etc. are allowed. Exceptions to this are T=, T-PRIORITY=, H-PRIORITY=, X-PRIORITY=, IRC=, DRC= and TRANS=. ' T=' cannot be abbreviated to ' T ' as many keywords start or end with a 'T'; for the other keywords the associated abbreviated keywords have specific meanings. If two keywords which are incompatible, like UHF and C.I., are supplied, or a keyword which is incompatible with the species supplied, for instance TRIPLET and a methyl radical, then error trapping will normally occur, and an error message will be printed. This usually takes an insignificant time, so data are quickly checked for obvious errors. - 8 - KEYWORDS Page 2-2 2.2 FULL LIST OF KEYWORDS USED IN MOPAC 0SCF - READ IN DATA, THEN STOP 1ELECTRON- PRINT FINAL ONE-ELECTRON MATRIX 1SCF - DO ONE SCF AND THEN STOP ANALYT - USE ANALYTICAL DERIVATIVES OF ENERGY W.R.T. GEOMETRY AM1 - USE THE AM1 HAMILTONIAN BAR=n.n - REDUCE BAR LENGTH BY A MAXIMUM OF n.n BIRADICAL- SYSTEM HAS TWO UNPAIRED ELECTRONS BONDS - PRINT FINAL BOND-ORDER MATRIX C.I. - A MULTI-ELECTRON CONFIGURATION INTERACTION SPECIFIED CHARGE=n - CHARGE ON SYSTEM = n (e.g. NH4 => CHARGE=1) COMPFG - PRINT HEAT OF FORMATION CALCULATED IN COMPFG CYCLES - PERFORM MAXIMUM NUMBER OF CYCLES IN NLLSQ DCART - PRINT DETAILS OF WORKING IN DCART DEBUG - DEBUG OPTION TURNED ON DEBUGPULAY PRINT DETAILS OF WORKING IN PULAY DENOUT - DENSITY MATRIX OUTPUT (CHANNEL 10) DENSITY - PRINT FINAL DENSITY MATRIX DEP - GENERATE FORTRAN CODE FOR PARAMETERS FOR NEW ELEMENTS DEPVAR=n - TRANSLATION VECTOR IS A MULTIPLE OF BOND-LENGTH DERIV - PRINT PART OF WORKING IN DERIV DFORCE - FORCE CALCULATION SPECIFIED, ALSO PRINT FORCE MATRIX. DFP - USE DAVIDON-FLETCHER-POWELL METHOD TO OPTIMIZE GEOMETRIES DOUBLET - RHF DOUBLET STATE REQUIRED DRC - DYNAMIC REACTION COORDINATE CALCULATION DUMP=n - WRITE RESTART FILES EVERY n SECONDS ECHO - DATA ARE ECHOED BACK BEFORE CALCULATION STARTS EIGS - PRINT ALL EIGENVALUES IN ITER ENPART - PARTITION ENERGY INTO COMPONENTS ESR - CALCULATE RHF UNPAIRED SPIN DENSITY EXCITED - OPTIMIZE FIRST EXCITED SINGLET STATE EXTERNAL - READ MNDO OR AM1 PARAMETERS OFF DISK FILL=n - IN RHF OPEN AND CLOSED SHELL, FORCE M.O. n TO BE FILLED FLEPO - PRINT DETAILS OF GEOMETRY OPTIMIZATION FMAT - PRINT DETAILS OF WORKING IN FMAT FOCK - PRINT LAST FOCK MATRIX FORCE - FORCE CALCULATION SPECIFIED FULSCF - FULL SCF CALCN'S TO BE DONE IN SEARCHES, AND DERIVATIVES WHEN NON-VARIATIONALLY OPTIMIZED WAVEFUNCTIONS USED GEO-OK - OVERRIDE INTERATOMIC DISTANCE CHECK GNORM=n.n- EXIT WHEN GRADIENT NORM DROPS BELOW n.n GRADIENTS- PRINT ALL GRADIENTS GRAPH - GENERATE FILE FOR GRAPHICS HCORE - PRINT DETAILS OF WORKING IN HCORE H-PRIO - HEAT OF FORMATION TAKES PRIORITY IN DRC IRC - INTRINSIC REACTION COORDINATE CALCULATION ISOTOPE - FORCE MATRIX WRITTEN TO DISK (CHANNEL 9 ) ITER - PRINT DETAILS OF WORKING IN ITER ITRY=N - SET LIMIT OF NUMBER OF SCF ITERATIONS TO N. KINETIC - EXCESS KINETIC ENERGY ADDED TO DRC CALCULATION - 9 - KEYWORDS Page 2-3 LINMIN - PRINT DETAILS OF LINE MINIMIZATION LARGE - PRINT EXPANDED OUTPUT LET - OVERRIDE CERTAIN SAFETY CHECKS LOCALIZE - PRINT LOCALIZED ORBITALS MINDO/3 - USE THE MINDO/3 HAMILTONIAN MECI - PRINT DETAILS OF MECI CALCULATION MICROS - USE SPECIFIC MICROSTATES IN THE C.I. | MMOK - USE MOLECULAR MECHANICS CORRECTION TO CONH BONDS MOLDAT - PRINT DETAILS OF WORKING IN MOLDAT MULLIK - PRINT THE MULLIKEN POPULATION ANALYSIS NLLSQ - MINIMIZE GRADIENTS USING NLLSQ NOINTER - DO NOT PRINT INTERATOMIC DISTANCES | NOMM - DO NOT USE MOLECULAR MECHANICS CORRECTION TO CONH BONDS NOXYZ - DO NOT PRINT CARTESIAN COORDINATES OLDENS - READ INITIAL DENSITY MATRIX OFF DISK OPEN - OPEN-SHELL RHF CALCULATION REQUESTED PI - RESOLVE DENSITY MATRIX INTO SIGMA AND PI BONDS PL - MONITOR CONVERGENCE OF DENSITY MATRIX IN ITER | PM3 - USE THE MNDO-PM3 HAMILTONIAN | POLAR - CALCULATE FIRST, SECOND AND THIRD ORDER POLARIZABILITIES POWSQ - PRINT DETAILS OF WORKING IN POWSQ PRECISE - CRITERIA TO BE INCREASED BY 100 TIMES PULAY - USE PULAY'S CONVERGER TO OBTAIN A SCF QUARTET - RHF QUARTET STATE REQUIRED QUINTET - RHF QUINTET STATE REQUIRED RESTART - CALCULATION RESTARTED ROOT=n - ROOT n TO BE OPTIMIZED IN A C.I. CALCULATION ROT=n - THE SYMMETRY NUMBER OF THE SYSTEM IS n. SADDLE - OPTIMIZE TRANSITION STATE SCFCRT=n - DEFAULT SCF CRITERION REPLACED BY THE VALUE SUPPLIED SEARCH - Use LINMIN instead of this keyword SEXTET - RHF SEXTET STATE REQUIRED | SHIFT=n - A DAMPING FACTOR OF n DEFINED TO START SCF SIGMA - MINIMIZE GRADIENTS USING SIGMA SINGLET - RHF SINGLET STATE REQUIRED SPIN - PRINT FINAL UHF SPIN MATRIX STEP1=n - STEP SIZE n FOR FIRST COORDINATE IN GRID CALCULATION STEP2=n - STEP SIZE n FOR SECOND COORDINATE IN GRID CALCULATION SYMMETRY - IMPOSE SYMMETRY CONDITIONS T=n - A TIME OF n SECONDS REQUESTED THERMO - PERFORM A THERMODYNAMICS CALCULATION TIMES - PRINT TIMES OF VARIOUS STAGES T-PRIO - TIME TAKES PRIORITY IN DRC TRANS - THE SYSTEM IS A TRANSITION STATE (USED IN THERMODYNAMICS CALCULATION) TRIPLET - TRIPLET STATE REQUIRED UHF - UNRESTRICTED HARTREE-FOCK CALCULATION VECTORS - PRINT FINAL EIGENVECTORS | VELOCITY - SUPPLY THE INITIAL VELOCITY VECTOR IN A DRC CALCULATION X-PRIO - GEOMETRY CHANGES TAKE PRIORITY IN DRC XYZ - DO ALL GEOMETRIC OPERATIONS IN CARTESIAN COORDINATES. - 10 - KEYWORDS Page 2-4 2.3 DEFINITIONS OF KEYWORDS The definitions below are given with some technical expressions which are not further defined. Interested users are referred to Appendix E of this manual to locate appropriate references which will provide further clarification. There are three classes of keywords: (1) those which CONTROL substantial aspects of the calculation, i.e., those which affect the final heat of formation, (2) those which determine which OUTPUT will be calculated and printed, and (3) those which dictate the WORKING of the calculation, but which do not affect the heat of formation. The assignment to one of these classes is designated by a (C), (O) or (W), respectively, following each keyword in the list below. 0SCF (O) The data can be read in and output, but no actual calculation is performed when this keyword is used. This is useful as a check on the input data to rule out errors introduced in transmission (usually a very last resort). 1ELECTRON (O) The final one-electron matrix is printed out. This matrix is composed of atomic orbitals; the array element between orbitals i and j on different atoms is given by H(i,j) = 0.5 x (beta(i) +beta(j)) x overlap(i,j) The matrix elements between orbitals i and j on the same atom are calculated from the electron-nuclear attraction energy, and also from the U(i) value if i=j. The one-electron matrix is unaffected by (a) the charge and (b) the electron density. It is only a function of the geometry. Abbreviation: 1ELEC. 1SCF (C) When users want to examine the results of a single SCF calculation of a geometry, 1SCF should be used. All the keywords relevant to output can be used. If the gradients are to be calculated, then GRADIENTS should be specified as they are not calculated by default. If the keyword RESTART is also present, then the geometric parameters which were being optimized will be used in the gradient calculation. 1SCF is helpful in a learning situation. MOPAC normally performs many SCF calculations, and in order to minimize output when following the working of the SCF calculation, 1SCF is very useful. - 11 - KEYWORDS Page 2-5 ANALYT (W) By default, finite difference derivatives of energy with respect to geometry are used. If ANALYT is specified, then analytical derivatives are used instead. Since the analytical derivatives are over Gaussian functions -- a STO-6G basis set is used -- the overlaps are also over Gaussian functions. This will result in a very small (less than 0.1 Kcal/mole) change in heat of formation. Use analytical derivatives (a) when the mantissa used is less than about 51-53 bits, or (b) when comparison with finite difference is desired. Finite difference derivatives are still used when non-variationally optimized wavefunctions are present. AM1 (C) The new AM1 method is to be used. By default MNDO is run. BAR=n.nn (W) In the SADDLE calculation the distance between the two geometries is steadily reduced until the transition state is located. Sometimes, however, the user may want to alter the maximum rate at which the distance between the two geometries reduces. BAR is a ratio, normally 0.15, or 15 percent. This represents a maximum rate of reduction of the bar of 15 percent per step. Alternative values that might be considered are BAR=0.05 or BAR=0.10, although other values may be used. See also SADDLE. BIRADICAL (C) NOTE: BIRADICAL is a redundant keyword, and represents a particular configuration interaction calculation. Experienced users of MECI (q.v.) can duplicate the effect of the keyword BIRADICAL by using the MECI keywords OPEN(2,2) and SINGLET. For molecules which are believed to have biradicaloid character the option exists to optimize the lowest singlet energy state which results from the mixing of three states. These states are, in order, (1) the (micro)state arising from a one electron excitation from the HOMO to the LUMO, which is combined with the microstate resulting from the time-reversal operator acting on the parent microstate, the result being a full singlet state; (2) the state resulting from de-excitation from the formal LUMO to the HOMO; and (3) the state resulting from the single electron in the formal HOMO being excited into the LUMO. - 12 - KEYWORDS Page 2-6 Microstate 1 Microstate 2 Microstate 3 Alpha Beta Alpha Beta Alpha Beta Alpha Beta LUMO * * * * --- --- --- --- --- --- --- --- + HOMO * * * * --- --- --- --- --- --- --- --- A configuration interaction calculation is involved here. A biradical calculation done without C.I. at the RHF level would be meaningless. Either rotational invariance would be lost, as in the D2d form of ethylene, or very artificial barriers to rotations would be found, such as in a methane molecule "orbiting" a D2d ethylene. In both cases the inclusion of limited configuration interaction corrects the error. BIRADICAL should not be used if either the HOMO or LUMO is degenerate; in this case, the full manifold of HOMO x LUMO should be included in the C.I., using MECI options. The user should be aware of this situation. When the biradical calculation is performed correctly, the result is normally a net stabilization. However, if the first singlet excited state is much higher in energy than the closed-shell ground state, BIRADICAL can lead to a destabilization. Abbreviation: BIRAD. See also MECI, C.I., OPEN, SINGLET. BONDS (O) The rotationally invariant bond order between all pairs of atoms is printed. In this context a bond is defined as the sum of the squares of the density matrix elements connecting any two atoms. For ethane, ethylene, and acetylene the carbon-carbon bond orders are roughly 1.00, 2.00, and 3.00 respectively. The diagonal terms are the valencies calculated from the atomic terms only and are defined as the sum of the bonds the atom makes with other atoms. In UHF and non-variationally optimized wavefunctions the calculated valency will be incorrect, the degree of error being proportional to the non-duodempotency of the density matrix. For an RHF wavefunction the square of the density matrix is equal to twice the density matrix. The bonding contributions of all M.O.'s in the system are printed immediately before the bonds matrix. The idea of molecular orbital valency was developed by Gopinathan, Siddarth, and Ravimohan. Just as an atomic orbital has a 'valency', so has a molecular orbital. This leads to the following relations: The sum of the bonding contributions of all occupied M.O.'s is the same as the sum of all valencies which, in turn is equal to two times the sum of all bonds. The sum of the bonding contributions of all M.O.'s is zero. - 13 - KEYWORDS Page 2-7 C.I. (C) Normally configuration interaction is invoked if any of the keywords which imply a C.I. calculation are used, such as BIRADICAL, TRIPLET or QUARTET. Note that ROOT= does not imply a C.I. calculation: ROOT= is only used when a C.I. calculation is done. However, as these implied C.I.'s involve the minimum number of configurations practical, the user may want to define a larger than minimum C.I., in which case the keyword C.I.=n can be used. When C.I.=n is specified, the n M.O.'s which "bracket" the occupied- virtual energy levels will be used. Thus, C.I.=2 will include both the HOMO and the LUMO, while C.I.=1 (implied for odd-electron systems) will only include the HOMO (This will do nothing for a closed-shell system, and leads to Dewar's half-electron correction for odd-electron systems). Users should be aware of the rapid increase in the size of the C.I. with increasing numbers of M.O.'s being used. Numbers of microstates implied by the use of the keyword C.I.=n on its own are as follows: Keyword Even-electron systems Odd-electron systems No. of electrons, configs No. of electrons, configs Alpha Beta Alpha Beta C.I.=1 1 1 1 1 0 1 C.I.=2 1 1 4 1 0 2 C.I.=3 2 2 9 2 1 9 C.I.=4 2 2 36 2 1 24 C.I.=5 3 3 100 3 2 100 C.I.=6 3 3 400 3 2 300 C.I.=7 4 4 1225 4 3 1225 C.I.=8 (Do not use unless other keywords also used, see below) If a change of spin is defined, then larger numbers of M.O.'s can be used up to a maximum of 10. The C.I. matrix is of size 100 x 100. For calculations involving up to 100 configurations, the spin-states are exact eigenstates of the spin operators. For systems with more than 100 configurations, the 100 configurations of lowest energy are used. See also MICROS and the keywords defining spin-states. Note that for any system, use of C.I.=5 or higher normally implies the diagonalization of a 100 by 100 matrix. As a geometry optimization using a C.I. requires the derivatives to be calculated using full SCF calculations, geometry optimization with large C.I.'s will require a considerable amount of time. Associated keywords: MECI, ROOT=, SINGLET, DOUBLET, etc. - 14 - KEYWORDS Page 2-8 CHARGE=n (C) When the system being studied is an ion, the charge, n, on the ion must be supplied by CHARGE=n. For cations n can be 1 or 2 or 3, etc, for anions -1 or -2 or -3, etc. EXAMPLES ION KEYWORD ION KEYWORD NH4(+) CHARGE=1 CH3COO(-) CHARGE=-1 C2H5(+) CHARGE=1 (COO)(=) CHARGE=-2 SO4(=) CHARGE=-2 PO4(3-) CHARGE=-3 HSO4(-) CHARGE=-1 H2PO4(-) CHARGE=-1 CYCLES=n (C) In Bartel's method of gradient norm minimization, NLLSQ, the default number of cycles (100) is replaced by the number n specified by CYCLES=n. DCART (O) The cartesian derivatives which are calculated in DCART for variationally optimized systems are printed if the keyword DCART is present. The derivatives are in units of kcals/Angstrom, and the coordinates are displacements in x, y, and z. DEBUG (O) Certain keywords have specific output control meanings, such as FOCK, VECTORS and DENSITY. If they are used, only the final arrays of the relevant type are printed. If DEBUG is supplied, then all arrays are printed. This is useful in debugging ITER. DEBUG can also increase the amount of output produced when certain output keywords are used, e.g. COMPFG. DENOUT (O) The density matrix at the end of the calculation is to be output in a form suitable for input in another job. If an automatic dump due to the time being exceeded occurs during the current run then DENOUT is invoked automatically. (see RESTART) - 15 - KEYWORDS Page 2-9 DENSITY (O) At the end of a job, when the results are being printed, the density matrix is also printed. For RHF the normal density matrix is printed. For UHF the sum of the alpha and beta density matrices is printed. If density is not requested, then the diagonal of the density matrix, i.e., the electron density on the atomic orbitals, will be printed. DEP (O) For use only with EXTERNAL=. When new parameters are published, they can be entered at run-time by using EXTERNAL=, but as this is somewhat clumsy, a permanent change can be made by use of DEP. If DEP is invoked, a complete block of FORTRAN code will be generated, and this can be inserted directly into the BLOCK DATA file. Note that this is designed only for use with MNDO or AM1 parameters. Only code for AM1 will be generated. To convert the FORTRAN code to define MNDO parameters, insert the letter M before every left parenthesis; thus, convert "(" to read "M(". DEPVAR=n.nn (C) In polymers the translation vector is frequently a multiple of some internal distance. For example, in polythene it is the C1-C3 distance. If a cluster unit cell of C6H12 is used, then symmetry can be used to tie together all the carbon atom coordinates and the translation vector distance. In this example DEPVAR=3.0 would be suitable. DFP (W) By default the Broyden-Fletcher-Goldfarb-Shanno method will be used to optimize geometries. The older Davidon-Fletcher-Powell method can be invoked by specifying DFP. This is intended to be used for comparison of the two methods. - 16 - KEYWORDS Page 2-10 DOUBLET (C) When a configuration interaction calculation is done, all spin states are calculated simultaneously, either for component of spin = 0 or 1/2. When only doublet states are of interest, then DOUBLET can be specified, and all other spin states, while calculated, are ignored in the choice of root to be used. Note that while almost every odd-electron system will have a doublet ground state, DOUBLET should still be specified if the desired state must be a doublet. DOUBLET has no meaning in a UHF calculation. DRC (C) A Dynamic Reaction Coordinate calculation is to be run. By default, total energy is conserved, so that as the "reaction" proceeds in time, energy is transferred between kinetic and potential forms. DRC=n.nnn (C) In a DRC calculation, the "half-life" for loss of kinetic energy is defined as n.nnn x 10 femtoseconds. If n.nnn is set to zero, infinite damping simulating a very condensed phase is obtained. This keyword cannot be written with spaces around the '=' sign. DUMP (W) Restart files are written automatically at one hour cpu time intervals to allow a long job to be restarted if the job is terminated catastrophically. To change the frequency of dump, set DUMP=nn to request a dump every nn seconds. Alternative form, DUMP=nnM for a dump every nn minutes. DUMP only works with geometry optimization, gradient minimization, and FORCE calculations. It does not (yet) work with a path or SADDLE calculation. ECHO (O) Data are echoed back if ECHO is specified. Only useful if data are suspected to be corrupt. - 17 - KEYWORDS Page 2-11 ENPART (O) This is a very useful tool for analyzing the energy terms within a system. The total energy, in eV, obtained by the addition of the electronic and nuclear terms, is partitioned into mono- and bi-centric contributions, and these contributions in turn are divided into nuclear and one- and two-electron terms. ESR (O) The unpaired spin density arising from an odd-electron system can be calculated both RHF and UHF. In a UHF calculation the alpha and beta M.O.'s have different spatial forms, so unpaired spin density can naturally be present on in-plane hydrogen atoms such as in the phenoxy radical. In the RHF formalism a MECI calculation is performed. If the keywords OPEN and C.I.= are both absent then only a single state is calculated. The unpaired spin density is then calculated from the state function. In order to have unpaired spin density on the hydrogens in, for example, the phenoxy radical, several states should be mixed. EXCITED (C) The state to be calculated is the first excited open-shell singlet state. If the ground state is a singlet, then the state calculated will be S(1); if the ground state is a triplet, then S(2). This state would normally be the state resulting from a one-electron excitation from the HOMO to the LUMO. Exceptions would be if the lowest singlet state were a biradical, in which case the EXCITED state could be a closed shell. The EXCITED state will be calculated from a BIRADICAL calculation in which the second root of the C.I. matrix is selected. Note that the eigenvector of the C.I. matrix is not used in the current formalism. Abbreviation: EXCI. NOTE: EXCITED is a redundant keyword, and represents a particular configuration interaction calculation. Experienced users of MECI can duplicate the effect of the keyword EXCITED by using the MECI keywords OPEN(2,2), SINGLET, and ROOT=2. - 18 - KEYWORDS Page 2-12 EXTERNAL=name (C) Normally, AM1 and MNDO parameters are taken from the BLOCK DATA files within MOPAC. When the supplied parameters are not suitable, as in an element recently parameterized, and the parameters not yet installed in the user's copy of MOPAC, then the new parameters can be inserted at run time by use of EXTERNAL=, where is the name of the file which contains the new parameters. consists of a series of parameter definitions in the format where the possible parameters are USS, UPP, UDD, ZS, ZP, ZD, BETAS, BETAP, BETAD, GSS, GSP, GPP, GP2, HSP, ALP, FNnm, n=1,2, or 3, and m=1 to 10, and the elements are defined by their chemical symbols, such as Si or SI. When new parameters for elements are published, they can be typed in as shown. This file is ended by a blank line, the word END or nothing, i.e., no end-of-file delimiter. An example of a parameter data file would be: Start of line| (Put at least 2 spaces before and after parameter name) Line 1: USS Si -34.08201495 Line 2: UPP Si -28.03211675 Line 3: BETAS Si -5.01104521 Line 4: BETAP Si -2.23153969 Line 5: ZS Si 1.28184511 Line 6: ZP Si 1.84073175 Line 7: ALP Si 2.18688712 Line 8: GSS Si 9.82 Line 9: GPP Si 7.31 Line 10: GSP Si 8.36 Line 11: GP2 Si 6.54 Line 12: HSP Si 1.32 Derived parameters do no need to be entered; they will be calculated from the optimized parameters. All "constants" such as the experimental heat of atomization are already inserted for all elements. NOTE: EXTERNAL can only be used to input parameters for MNDO or AM1. It is unlikely, however, that any more MINDO/3 parameters will be published. See also DEP to make a permanent change. - 19 - KEYWORDS Page 2-13 FILL=n (C) The n'th M.O. in an RHF calculation is constrained to be filled. It has no effect on a UHF calculation. After the first iteration (NOTE: not after the first SCF calculation, but after the first iteration within the first SCF calculation) the n'th M.O. is stored, and, if occupied, no further action is taken at that time. If unoccupied, then the HOMO and the n'th M.O.'s are swapped around, so that the n'th M.O. is now filled. On all subsequent iterations the M.O. nearest in character to the stored M.O. is forced to be filled, and the stored M.O. replaced by that M.O. This is necessitated by the fact that in a reaction a particular M.O. may change its character very considerably. A useful procedure is to run 1SCF and DENOUT first, in order to identify the M.O.'s; the complete job is then run with OLDENS and FILL=nn, so that the eigenvectors at the first iteration are fully known. As FILL is known to give difficulty at times, consider also using C.I.=n and ROOT=m. FLEPO (O) The predicted and actual changes in the geometry, the derivatives, and search direction for each geometry optimization cycle are printed. This is useful if there is any question regarding the efficiency of the geometry optimizer. FMAT Details of the construction of the Hessian matrix for the force calculation are to be printed. - 20 - KEYWORDS Page 2-14 FORCE (C) A force-calculation is to be run. The Hessian, that is the matrix (in millidynes per Angstrom) of second derivatives of the energy with respect to displacements of all pairs of atoms in x, y, and z, is calculated. On diagonalization this gives the force constants for the molecule. The force matrix, weighted for isotopic masses, is then used for calculating the vibrational frequencies. The system can be characterized as a ground state or a transition state by the presence of five (for a linear system) or six eigenvalues which are very small (less than about 30 reciprocal centimeters). A transition state is further characterized by one, and exactly one, negative force constant. A FORCE calculation is a prerequisite for a THERMO calculation. Before a FORCE calculation is started, a check is made to ensure that a stationary point is being used. This check involves calculating the gradient norm (GNORM) and if it is significant, the GNORM will be reduced using NLLSQ (Bartel's method). All internal coordinates are optimized, and any symmetry constraints are ignored at this point. An implication of this is that if the specification of the geometry relies on any angles being exactly 180 or zero degrees, the calculation may fail. The geometric definition supplied to FORCE should not rely on angles or dihedrals assuming exact values. (The test of exact linearity is sufficiently slack that most molecules that are linear, such as acetylene and but-2-yne, should not be stopped.) See also THERMO, LET, TRANS, ISOTOPE. FULSCF (W) In line-searches the option exists to require all energy evaluations to be done using full SCF calculations. Normally full SCF calculations are not carried out during a line search as the density matrix is normally not changing very fast. The only important exception is in non-variationally optimized wavefunctions, such as occur in half-electron or C.I. calculations. Note: FULSCF will cause all derivatives to be calculated by explicit SCF calculations when non-variationally optimized wavefunctions are used. (This was in earlier copies of MOPAC but not documented.) - 21 - KEYWORDS Page 2-15 GEO-OK (W) Normally the program will stop with a warning message if two atoms are within 0.8 Angstroms of each other, or, more rarely, the BFGS routine has difficulty optimizing the geometry. GEO-OK will over-ride the job termination sequence, and allow the calculation to proceed. In practice, most jobs that terminate due to these checks contain errors in data, so caution should be exercised if GEO-OK is used. An important exception to this warning is when the system contains, or may give rise to, a Hydrogen molecule. GEO-OK will override other geometric safety checks such as the unstable gradient in a geometry optimization preventing reliable optimization. See also the message "GRADIENTS OF OLD GEOMETRY, GNORM= nn.nnnn" GNORM=n.nn (W) The geometry optimization termination criteria in both gradient minimization and energy minimization can be over-ridden by specifying a gradient norm requirement. For example, GNORM=20 would allow the geometry optimization to exit as soon as the gradient norm dropped below 20.0, the default being 1.0. A GNORM=0.01 could be used to refine a geometry beyond the normal limits. WARNING: If a very small value is chosen, the geometry optimization procedures may not terminate in a reasonable time. A reasonable lower bound for GNORM is about 0.1. GRADIENTS (O) In a 1SCF calculation gradients are not calculated by default: in non-variationally optimized systems this would take an excessive time. GRADIENTS allows the gradients to be calculated. All gradients are then calculated, whether marked for calculation or not, and printed. An exception is when the 1SCF was used in conjunction with the keyword RESTART, in which case only the coordinates being optimized would have their gradients printed. Abbreviation: GRAD. GRAPH (O) Information needed to generate electron density contour maps can be written to a file by calling GRAPH. GRAPH first calls MULLIK in order to generate the inverse-square-root of the overlap matrix, which is required for the re-normalization of the eigenvectors. All data essential for the graphics package DENSITY are then output. H-PRIORITY (O) In a DRC calculation, results will be printed whenever the calculated heat of formation changes by 0.1 Kcal/mole. Abbreviation: H-PRIO. - 22 - KEYWORDS Page 2-16 H-PRIORITY=n.nn (O) In a DRC calculation, results will be printed whenever the calculated heat of formation changes by n.nn Kcal/mole. IRC (C) An Intrinsic Reaction Coordinate calculation is to be run. All kinetic energy is shed at every point in the calculation. See Background. IRC=n (C) An Intrinsic Reaction Coordinate calculation to be run; an initial perturbation in the direction of normal coordinate n to be applied. If n is negative, then perturbation is reversed, i.e., initial motion is in the opposite direction to the normal coordinate. This keyword cannot be written with spaces around the '=' sign. ISOTOPE (O) Generation of the FORCE matrix is very time-consuming, and in isotopic substitution studies several vibrational calculations may be needed. To allow the frequencies to be calculated from the (constant) force matrix, ISOTOPE is used. When a FORCE calculation is completed, ISOTOPE will cause the force matrix to be stored, regardless of whether or not any intervening restarts have been made. To re-calculate the frequencies, etc. starting at the end of the force matrix calculation, specify RESTART. The two keywords RESTART and ISOTOPE can be used together. For example, if a normal FORCE calculation runs for a long time, the user may want to divide it up into stages and save the final force matrix. Once ISOTOPE has been used, it does not need to be used on subsequent RESTART runs. ITRY=NN (W) The default maximum number of SCF iterations is 200. When this limit presents difficulty, ITRY=nn can be used to re-define it. For example, if ITRY=400 is used, the maximum number of iterations will be set to 400. ITRY should normally not be changed until all other means of obtaining a SCF have been exhausted, e.g. PULAY CAMP-KING etc. KINETIC=n.nnn (C) In a DRC calculation n.nnn Kcals/mole of excess kinetic energy is added to the system as soon as the kinetic energy builds up to 0.2 Kcal/mole. The excess energy is added to the velocity vector, without change of direction. - 23 - KEYWORDS Page 2-17 | LINMIN (O) | | There are two line-minimization routines in MOPAC, an energy | minimization and a gradient norm minimization. LINMIN will output | details of the line minimization used in a given job. LARGE (O) Most of the time the output invoked by keywords is sufficient. LARGE will cause less-commonly wanted, but still useful, output to be printed. Currently LARGE only applies to the MECI. LET (W) | | As MOPAC evolves, the meaning of LET is changing. | | Now LET means essentially "I know what I'm doing, override safety | checks". | | Currently, LET has the following meanings | | 1. In a FORCE calculation, it means that the supplied geometry is | to be used, even if the gradients are large. | | 2. In a geometry optimization, the specified GNORM is to be used, | even if it is less than 0.0001. | | 3. In a POLAR calculation, the molecule is to be orientated along | its principal moments of inertia before the calculation starts. | LET will prevent this step being done. | LOCALIZE (O) The occupied eigenvectors are transformed into a localized set of M.O.'s by a series of 2 by 2 rotations which maximize . The value of 1/ is a direct measure of the number of centers involved in the M.O.. Thus the value of 1/ is 2.0 for H2, 3.0 for a three-center bond and 1.0 for a lone pair. Higher degeneracies than allowed by point group theory are readily obtained. For example, benzene would give rise to a 6-fold degenerate C-H bond, a 6-fold degenerate C-C sigma bond and a three-fold degenerate C-C pi bond. In principle, there is no single step method to unambiguously obtain the most localized set of M.O.'s in systems where several canonical structures are possible, just as no simple method exists for finding the most stable conformer of some large compound. However, the localized bonds generated will normally be quite acceptable for routine applications. Abbreviation: LOCAL. - 24 - KEYWORDS Page 2-18 MECI (O) At the end of the calculation details of the Multi Electron Configuration Interaction calculation are printed if MECI is specified. The state vectors can be printed by specifying VECTORS. The MECI calculation is either invoked automatically, or explicitly invoked by the use of the C.I.=n keyword. MICROS=n (C) The microstates used by MECI are normally generated by use of a permutation operator. When individually defined microstates are desired, then MICROS=n can be used, where n defines the number of microstates to be read in. Format for Microstates After the geometry data plus any symmetry data are read in, data defining each microstate is read in, using format 20I1, one microstate per line. The microstate data is preceded by the word "MICROS" on a line by itself. There is at present no mechanism for using MICROS with a reaction path. For a system with n M.O.'s in the C.I. (use OPEN=(n1,n) or C.I.=n to do this), the populations of the n alpha M.O.'s are defined, followed by the n beta M.O.'s. Allowed occupancies are zero and one. For n=6 the closed-shell ground state would be defined as 111000111000, meaning one electron in each of the first three alpha M.O.'s, and one electron in each of the first three beta M.O.'s. Users are warned that they are responsible for completing any spin manifolds. Thus while the state 111100110000 is a triplet state with component of spin = 1, the state 111000110100, while having a component of spin = 0 is neither a singlet nor a triplet. In order to complete the spin manifold the microstate 110100111000 must also be included. If a manifold of spin states is not complete, then the eigenstates of the spin operator will not be quantized. When and only when 100 or fewer microstates are supplied, loss of spin quantization occurs. There are two other limitations on possible microstates. First, the number of electrons in every microstate should be the same. If they differ, a warning message will be printed, and the calculation continued (but the results will almost certainly be nonsense). Second, the component of spin for every microstate must be the same, except for teaching purposes. Two microstates of different components of spin will have a zero matrix element connecting them. No warning will be given as this is a reasonable operation in a teaching situation. For example, if all states arising from two electrons in two levels are to be calculated, say for teaching Russel-Saunders coupling, then the following microstates would be used: - 25 - KEYWORDS Page 2-19 Microstate No. of alpha, beta electrons Ms State 1100 2 0 1 Triplet 1010 1 1 0 Singlet 1001 1 1 0 Mixed 0110 1 1 0 Mixed 0101 1 1 0 Singlet 0011 0 2 -1 Triplet Constraints on the space manifold are just as rigorous, but much easier to satisfy. If the energy levels are degenerate, then all components of a manifold of degenerate M.O.'s should be either included or excluded. If only some, but not all, components are used, the required degeneracy of the states will be missing. As an example, for the tetrahedral methane cation, if the user supplies the microstates corresponding to a component of spin = 3/2, neglecting Jahn-Teller distortion, the minimum number of states that can be supplied is 90 = (6!/(1!*5!))*(6!/(4!*2!)). While the total number of electrons should be the same for all microstates, this number does not need to be the same as the number of electrons supplied to the C.I.; thus in the example above, a cationic state could be 110000111000. The format is defined as 20I1 so that spaces can be used for empty M.O.'s. MINDO/3 (C) The default Hamiltonian within MOPAC is MNDO, with the alternatives of AM1 and MINDO/3. To use the MINDO/3 Hamiltonian the keyword MINDO/3 should be used. Acceptable alternatives to the keyword MINDO/3 are MINDO and MINDO3. | MMOK (C) | | If the system contains a peptide linkage, then MMOK will allow a | molecular mechanics correction to be applied so that the barrier to | rotation is increased (to 14.00 Kcal/mole in N-methyl acetamide). MULLIK (O) A full Mulliken Population analysis is to be done on the final RHF wavefunction. This involves the following steps: (1) The eigenvector matrix is divided by the square root of the overlap matrix, S. (2) The Coulson-type density matrix, P, is formed. (3) The overlap population is formed from P(i,j)*S(i,j). (4) Half the off-diagonals are added onto the diagonals. - 26 - KEYWORDS Page 2-20 NLLSQ (C) The gradient norm is to be minimized by Bartel's method. This is a Non-Linear Least Squares gradient minimization routine. Gradient minimization will locate one of three possible points: (a) A minimum in the energy surface. The gradient norm will go to zero, and the lowest five or six eigenvalues resulting from a FORCE calculation will be approximately zero. (b) A transition state. The gradient norm will vanish, as in (a), but in this case the system is characterized by one, and only one, negative force constant. (c) A local minimum in the gradient norm space. In this (normally unwanted) case the gradient norm is minimized, but does not go to zero. A FORCE calculation will not give the five or six zero eigenvalues characteristic of a stationary point. While normally undesirable, this is sometimes the only way to obtain a geometry. For instance, if a system is formed which cannot be characterized as an intermediate, and at the same time is not a transition state, but nonetheless has some chemical significance, then that state can be refined using NLLSQ. NOINTER (O) The interatomic distances are printed by default. If you do not want them to be printed, specify NOINTER. For big jobs this reduces the output file considerably. | NOMM (C) | All four semi-empirical methods underestimate the barrier to rotation of | a peptide bond. A Molecular Mechanics correction has been added which | increases the barrier in N-methyl acetamide to 14 Kcal/mole. If you do | not want this correction, specify NOMM (NO Molecular Mechanics). NOXYZ (O) The cartesian coordinates are printed by default. If you do not want them to be printed, specify NOXYZ. For big jobs this reduces the output file considerably. OLDENS (W) A density matrix produced by an earlier run of MOPAC is to be used to start the current calculation. This can be used in attempts to obtain an SCF when a previous calculation ended successfully but a subsequent run failed to go SCF. - 27 - KEYWORDS Page 2-21 OPEN(n1,n2) (C) The M.O. occupancy during the SCF calculation can be defined in terms of doubly occupied, empty, and fractionally occupied M.O.'s. The fractionally occupied M.O.'s are defined by OPEN(n1,n2), where n1 = number of electrons in the open-shell manifold, and n2 = number of open-shell M.O.'s; n1 must be in the range 0 to 2. OPEN(1,1) will be assumed for odd-electron systems unless an OPEN keyword is used. Errors introduced by use of fractional occupancy are automatically corrected in a MECI calculation when OPEN(n1,n2) is used. PI (O) The normal density matrix is composed of atomic orbitals, that is s, px, py and pz. PI allows the user to see how each atom-atom interaction is split into sigma and pi bonds. The resulting "density matrix" is composed of the following basis-functions:- s-sigma, p-sigma, p-pi, d-sigma, d-pi, d-dell. The on-diagonal terms give the hybridization state, so that an sp2 hybridized system would be represented as s-sigma 1.0, p-sigma 2.0, p-pi 1.0 | PM3 | | The PM3 method is to be used. PM3 is still very new, and users are | cautioned that as yet we do not know how well it works for transition | states or for vibrational frequencies. | | | POLAR | | The polarizability and first and second hyperpolarizabilities are to | be calculated. At present this calculation does not work for polymers, | but should work for all other systems. POWSQ (C) Details of the working of POWSQ are printed out. This is only useful in debugging. PRECISE (W) The criteria for terminating all optimizations, electronic and geometric, are to be increased by a factor, normally, 100. This can be used where more precise results are wanted. If the results are going to be used in a FORCE calculation, where the geometry needs to be known quite precisely, then PRECISE is recommended; for small systems the extra cost in CPU time is minimal. - 28 - KEYWORDS Page 2-22 PULAY (W) The default converger in the SCF calculation is to be replaced by Pulay's procedure as soon as the density matrix is sufficiently stable. A considerable improvement in speed can be achieved by the use of PULAY. If a large number of SCF calculations are envisaged, a sample calculation using 1SCF and PULAY should be compared with using 1SCF on its own, and if a saving in time results, then PULAY should be used in the full calculation. PULAY should be used with care in that its use will prevent the combined package of convergers (SHIFT, PULAY and the CAMP-KING convergers) from automatically being used in the event that the system fails to go SCF in (ITRY-10) iterations. The combined set of convergers very seldom fails. QUARTET (C) The desired spin-state is a quartet, i.e., the state with component of spin = 1/2 and spin = 3/2. When a configuration interaction calculation is done, all spin states of spin equal to, or greater than 1/2 are calculated simultaneously, for component of spin = 1/2. From these states the quartet states are selected when QUARTET is specified, and all other spin states, while calculated, are ignored in the choice of root to be used. If QUARTET is used on its own, then a single state, corresponding to an alpha electron in each of three M.O.'s is calculated. QUARTET has no meaning in a UHF calculation. QUINTET (C) The desired spin-state is a quintet, that is, the state with component of spin = 0 and spin = 2. When a configuration interaction calculation is done, all spin states of spin equal to, or greater than 0 are calculated simultaneously, for component of spin = 0. From these states the quintet states are selected when QUINTET is specified, and the septet states, while calculated, will be ignored in the choice of root to be used. If QUINTET is used on its own, then a single state, corresponding to an alpha electron in each of four M.O.'s is calculated. QUINTET has no meaning in a UHF calculation. - 29 - KEYWORDS Page 2-23 RESTART (W) When a job has been stopped, for whatever reason, and intermediate results have been stored, then the calculation can be restarted at the point where it stopped by specifying RESTART. The most common cause of a job stopping before completion is its exceeding the time allocated. A saddle-point calculation has no restart, but the output file contains information which can easily be used to start the calculation from a point near to where it stopped. It is not necessary to change the geometric data to reflect the new geometry, as a result the geometry printed at the start of a restarted job will be that of the original data, not that of the restarted file. A convenient way to monitor a long run is to specify 1SCF and RESTART; this will give a normal output file at very little cost. NOTE 1: In the FORCE calculation two restarts are possible. These are (a) a restart in FLEPO if the geometry was not optimized fully before FORCE was called, and (b) the normal restart in the construction of the force matrix. If the restart is in FLEPO within FORCE then the keyword FORCE should be deleted, and the keyword RESTART used on its own. Forgetting this point is a frequent cause of failed jobs. NOTE 2: Two restarts also exist in the IRC calculation. If an IRC calculation stops while in the FORCE calculation, then a normal restart can be done. If the job stops while doing the IRC calculation itself then the keyword IRC=n should be changed to IRC, or it can be omitted if DRC is also specified. The absence of the string "IRC=" is used to indicate that the FORCE calculation was completed before the restart files were written. ROOT=n (C) The n'th root of a C.I. calculation is to be used in the calculation. If a keyword specifying the spin-state is also present, e.g. SINGLET or TRIPLET, then the n'th root of that state will be selected. Thus ROOT=3 and SINGLET will select the third singlet root. If ROOT=3 is used on its own, then the third root will be used, which may be a triplet, the third singlet, or the second singlet (the second root might be a triplet). In normal use, this keyword would not be used. It is retained for educational and research purposes. Unusual care should be exercised when ROOT= is specified. - 30 - KEYWORDS Page 2-24 ROT=n (C) In the calculation of the rotational contributions to the thermodynamic quantities the symmetry number of the molecule must be supplied. The symmetry number of a point group is the number of equivalent positions attainable by pure rotations. No reflections or improper rotations are allowed. This number cannot be assumed by default, and may be affected by subtle modifications to the molecule, such as isotopic substitution. A list of the most important symmetry numbers follows: ---- TABLE OF SYMMETRY NUMBERS ---- C1 CI CS 1 D2 D2D D2H 4 C(INF)V 1 C2 C2V C2H 2 D3 D3D D3H 6 D(INF)H 2 C3 C3V C3H 3 D4 D4D D4H 8 T TD 12 C4 C4V C4H 4 D6 D6D D6H 12 OH 24 C6 C6V C6H 6 S6 3 SADDLE (C) The transition state in a simple chemical reaction is to be optimized. Extra data are required. After the first geometry, specifying the reactants, and any symmetry functions have been defined, the second geometry, specifying the products, is defined, using the same format as that of the first geometry. SADDLE often fails to work successfully. Frequently this is due to equivalent dihedral angles in the reactant and product differing by about 360 degrees rather than zero degrees. As the choice of dihedral can be difficult, users should consider running this calculation with the keyword XYZ. There is normally no ambiguity in the definition of cartesian coordinates. See also BAR=. Many of the bugs in SADDLE have been removed in this version. Use of the XYZ option is strongly recommended. SCFCRT=n.nn (W) The default SCF criterion is to be replaced by that defined by SCFCRT=. The SCF criterion can be varied from about 0.001 to 1.D-25, although numbers in the range 0.0001 to 1.D-14 will suffice for most applications. To find a suitable value 1SCF and various values of SCFCRT=n.nnn should be used; a SCFCRT which allows evaluation of the heat of formation to an acceptable precision can thus be found rapidly. An overly tight criterion can lead to failure to achieve a SCF, and consequent failure of the run. - 31 - KEYWORDS Page 2-25 SEXTET (C) The desired spin-state is a sextet: the state with component of spin = 1/2 and spin = 5/2. The sextet states are the highest spin states normally calculable using MOPAC in its unmodified form. If SEXTET is used on its own, then a single state, corresponding to one alpha electron in each of five M.O.'s, is calculated. If several sextets are to be calculated, say the second or third, then OPEN(n1,n2) should be used. SEXTET has no meaning in a UHF calculation. | SHIFT=n.nn (W) | | In an attempt to obtain an SCF by damping oscillations which slow | down the convergence or prevent an SCF being achieved, the virtual M.O. | energy levels are shifted up or down in energy by a shift technique. The | principle is that if the virtual M.O.'s are changed in energy relative to | the occupied set, then the polarizability of the occupied M.O.'s will | change pro rata. Normally, oscillations are due to autoregenerative | charge fluctuations. | | The SHIFT method has been re-written so that the value of SHIFT | changes automatically to give a critically-damped system. This can | result in a positive or negative shift of the virtual M.O. energy | levels. If a non-zero SHIFT is specified, it will be used to start the | SHIFT technique, rather than the default 15eV. If SHIFT=0 is specified, | the SHIFT technique will not be used unless normal convergence techniques | fail and the automatic "ALL CONVERGERS..." message is produced. SIGMA (C) The McIver-Komornicki gradient norm minimization routines, POWSQ and SEARCH are to be used. These are very rapid routines, but do not work for all species. If the gradient norm is low, i.e., less than about 5 units, then SIGMA will probably work; in most cases, NLLSQ is recommended. SIGMA first calculates a quite accurate Hessian matrix, a slow step, then works out the direction of fastest decent, and searches along that direction until the gradient norm is minimized. The Hessian is then partially updated in light of the new gradients, and a fresh search direction found. Clearly, if the Hessian changes markedly as a result of the line-search, the update done will be inaccurate, and the new search direction will be faulty. SIGMA should be avoided if at all possible when non-variationally optimized calculations are being done. | | If the Hessian is suspected to be corrupt within SIGMA it will be | automatically recalculated. This frequently speeds up the rate at which | the transition state is located. If you do not want the Hessian to be | reinitialized -- it is costly in CPU time -- specify LET on the keyword | line. - 32 - KEYWORDS Page 2-26 SINGLET (C) When a configuration interaction calculation is done, all spin states are calculated simultaneously, either for component of spin = 0 or 1/2. When only singlet states are of interest, then SINGLET can be specified, and all other spin states, while calculated, are ignored in the choice of root to be used. Note that while almost every even-electron system will have a singlet ground state, SINGLET should still be specified if the desired state must be a singlet. SINGLET has no meaning in a UHF calculation, but see also TRIPLET. SPIN (O) The spin matrix, defined as the difference between the alpha and beta density matrices, is to be printed. If the system has a closed-shell ground state, e.g. methane run UHF, the spin matrix will be null. If SPIN is not requested in a UHF calculation, then the diagonal of the spin matrix, that is the spin density on the atomic orbitals, will be printed. STEP1=n.nnn (C) In a grid calculation the step size in degrees or Angstroms for the first of the two parameters is given by n.nnn. 11 steps in each direction are calculated, giving a total of 121 steps. The origin is in the center at position (6,6). STEP2=n.nnn (C) In a grid calculation the step size in degrees or Angstroms for the second of the two parameters is given by n.nnn. SYMMETRY (C) Symmetry data defining related bond lengths, angles and dihedrals can be included by supplying additional data after the geometry has been entered. If there are any other data, such as values for the reaction coordinates, or a second geometry, as required by SADDLE, then it would follow the symmetry data. Symmetry data are terminated by one blank line. For non-variationally optimized systems symmetry constraints can save a lot of time because many derivatives do not need to be calculated. At the same time, there is a risk that the geometry may be wrongly specified, e.g. if methane radical cation is defined as being tetrahedral, no indication that this is faulty will be given until a FORCE calculation is run. (This system undergoes spontaneous Jahn-Teller distortion.) - 33 - KEYWORDS Page 2-27 Usually a lower heat of formation can be obtained when SYMMETRY is specified. To see why, consider the geometry of benzene. If no assumptions are made regarding the geometry, then all the C-C bond lengths will be very slightly different, and the angles will be almost, but not quite 120 degrees. Fixing all angles at 120 degrees, dihedrals at 180 or 0 degrees, and only optimizing one C-C and one C-H bond-length will result in a 2-D optimization, and exact D6h symmetry. Any deformation from this symmetry must involve error, so by imposing symmetry some error is removed. The layout of the symmetry data is: ,... where the numerical code for is given in the table of SYMMETRY FUNCTIONS below. For example, ethane, with three independent variables, can be defined as SYMMETRY ETHANE, D3D NA NB NC C 0.000000 0 0.000000 0 0.000000 0 0 0 0 C 1.528853 1 0.000000 0 0.000000 0 1 0 0 H 1.105161 1 110.240079 1 0.000000 0 2 1 0 H 1.105161 0 110.240079 0 120.000000 0 2 1 3 H 1.105161 0 110.240079 0 240.000000 0 2 1 3 H 1.105161 0 110.240079 0 60.000000 0 1 2 3 H 1.105161 0 110.240079 0 180.000000 0 1 2 3 H 1.105161 0 110.240079 0 300.000000 0 1 2 3 0 0.000000 0 0.000000 0 0.000000 0 0 0 0 3, 1, 4, 5, 6, 7, 8, 3, 2, 4, 5, 6, 7, 8, Here atom 3, a hydrogen, is used to define the bond lengths (symmetry relation 1) of atoms 4,5,6,7 and 8 with the atoms they are specified to bond with in the NA column of the data file; similarly, its angle (symmetry relation 2) is used to define the bond-angle of atoms 4,5,6,7 and 8 with the two atoms specified in the NA and NB columns of the data file. The other angles are point-group symmetry defined as a multiple of 60 degrees. Spaces, tabs or commas can be used to separate data. Note that only three parameters are marked to be optimized. The symmetry data can be the last line of the data file unless more data follows, in which case a blank line must be inserted after the symmetry data. - 34 - KEYWORDS Page 2-28 The full list of available symmetry relations is as follows: SYMMETRY FUNCTIONS 1 BOND LENGTH IS SET EQUAL TO THE REFERENCE BOND LENGTH 2 BOND ANGLE IS SET EQUAL TO THE REFERENCE BOND ANGLE 3 DIHEDRAL ANGLE IS SET EQUAL TO THE REFERENCE DIHEDRAL ANGLE 4 DIHEDRAL ANGLE VARIES AS 90 DEGREES - REFERENCE DIHEDRAL 5 DIHEDRAL ANGLE VARIES AS 90 DEGREES + REFERENCE DIHEDRAL 6 DIHEDRAL ANGLE VARIES AS 120 DEGREES - REFERENCE DIHEDRAL 7 DIHEDRAL ANGLE VARIES AS 120 DEGREES + REFERENCE DIHEDRAL 8 DIHEDRAL ANGLE VARIES AS 180 DEGREES - REFERENCE DIHEDRAL 9 DIHEDRAL ANGLE VARIES AS 180 DEGREES + REFERENCE DIHEDRAL 10 DIHEDRAL ANGLE VARIES AS 240 DEGREES - REFERENCE DIHEDRAL 11 DIHEDRAL ANGLE VARIES AS 240 DEGREES + REFERENCE DIHEDRAL 12 DIHEDRAL ANGLE VARIES AS 270 DEGREES - REFERENCE DIHEDRAL 13 DIHEDRAL ANGLE VARIES AS 270 DEGREES + REFERENCE DIHEDRAL 14 DIHEDRAL ANGLE VARIES AS THE NEGATIVE OF THE REFERENCE DIHEDRAL 15 BOND LENGTH VARIES AS HALF THE REFERENCE BOND LENGTH 16 BOND ANGLE VARIES AS HALF THE REFERENCE BOND ANGLE 17 BOND ANGLE VARIES AS 180 DEGREES - REFERENCE BOND ANGLE 18 BOND LENGTH IS A MULTIPLE OF REFERENCE BOND-LENGTH Function 18 is intended for use in polymers, in which the translation vector may be a multiple of some bond-length. 1,2,3 and 14 are most commonly used. Abbreviation: SYM. SYMMETRY is not available for use with cartesian coordinates. T= (W) This is a facility to allow the program to shut down in an orderly manner on computers with execution time C.P.U. limits. The total C.P.U. time allowed for the current job is limited to nn.nn seconds; by default this is one hour, i.e., 3600 seconds. If the next cycle of the calculation cannot be completed without running a risk of exceeding the assigned time the calculation will write a restart file and then stop. The safety margin is 100 percent; that is, to do another cycle, enough time to do at least two full cycles must remain. | | Alternative specifications of the time are T=nn.nnM, this defines | the time in minutes, T=nn.nnH, in hours, and T=nn.nnD, in days, for very | long jobs. This keyword cannot be written with spaces around the '=' sign. - 35 - KEYWORDS Page 2-29 THERMO (O) The thermodynamic quantities, internal energy, heat capacity, partition function, and entropy can be calculated for translation, rotation and vibrational degrees of freedom for a single temperature, or a range of temperatures. Special situations such as linear systems and transition states are accommodated. The approximations used in the THERMO calculation are invalid below 100K, and checking of the lower bound of the temperature range is done to prevent temperatures of less than 100K being used. Another limitation, for which no checking is done, is that there should be no internal rotations. If any exist, they will not be recognized as such, and the calculated quantities will be too low as a result. In order to use THERMO the keyword FORCE must also be specified, as well as the value for the symmetry number; this is given by ROT=n. If THERMO is specified on its own, then the default values of the temperature range are assumed. This starts at 200K and increases in steps of 10 degrees to 400K. Three options exist for overriding the default temperature range. These are: THERMO(nnn) (O) The thermodynamic quantities for a 200 degree range of temperatures, starting at nnnK and with an interval of 10 degrees are to be calculated. THERMO(nnn,mmm) (O) The thermodynamic quantities for the temperature range limited by a lower bound of nnn Kelvin and an upper bound of mmm Kelvin, the step size being calculated in order to give approximately 20 points, and a reasonable value for the step. The size of the step in Kelvin degrees will be 1, 2, or 5, or a power of 10 times these numbers. THERMO(nnn,mmm,lll) (O) Same as for THERMO(nnn,mmm), only now the user can explicitly define the step size. The step size cannot be less than 1K. T-PRIORITY (O) In a DRC calculation, results will be printed whenever the calculated time changes by 0.1 femtoseconds. Abbreviation, T-PRIO. - 36 - KEYWORDS Page 2-30 T-PRIORITY=n.nn (O) In a DRC calculation, results will be printed whenever the calculated time changes by n.nn femtoseconds. TRANS (C) The imaginary frequency due to the reaction vector in a transition state calculation must not be included in the thermochemical calculation. The number of genuine vibrations considered can be: 3N-5 for a linear ground state system, 3N-6 for a non-linear ground state system, or 3N-6 for a linear transition-state complex, 3N-7 for a non-linear transition-state complex. This keyword must be used in conjunction with THERMO if a transition state is being calculated. TRANS=n (C) The facility exists to allow the THERMO calculation to handle systems with internal rotations. TRANS=n will remove the n lowest vibrations. Note that TRANS=1 is equivalent to TRANS on its own. For xylene, for example, TRANS=2 would be suitable. This keyword cannot be written with spaces around the '=' sign. TRIPLET (C) The triplet state is defined. If the system has an odd number of electrons, an error message will be printed. UHF interpretation. The number of alpha electrons exceeds that of the beta electrons by 2. If TRIPLET is not specified, then the numbers of alpha and beta electrons are set equal. This does not necessarily correspond to a singlet. RHF interpretation. An RHF MECI calculation is performed to calculate the triplet state. If no other C.I. keywords are used, then only one state is calculated by default. The occupancy of the M.O.'s in the SCF calculation is defined as (...2,1,1,0,..), that is, one electron is put in each of the two highest occupied M.O.'s. - 37 - KEYWORDS Page 2-31 See keywords C.I.=n and OPEN(n1,n2). UHF (C) The unrestricted Hartree-Fock Hamiltonian is to be used. VECTORS (O) The eigenvectors are to be printed. In UHF calculations both alpha and beta eigenvectors are printed; in all cases the full set, occupied and virtual, are output. The eigenvectors are normalized to unity, that is the sum of the squares of the coefficients is exactly one. If DEBUG is specified, then ALL eigenvectors on every iteration of every SCF calculation will be printed. This is useful in a learning context, but would normally be very undesirable. | VELOCITY (C) | | The user can supply the initial velocity vector to start a DRC | calculation. Limitations have to be imposed on the geometry in order for | this keyword to work. These are (a) the input geometry must be in | cartesian coordinates, (b) the first three atoms must not be coaxial, (c) | triatomic systems are not allowed (See geometry specification - triatomic | systems are in internal coordinates, by definition.) | | Put the velocity vector after the geometry as three data per line, | representing the x, y, and z components of velocity for each atom. The | units of velocity are centimeters per second. | | The velocity vector will be rotated so as to suit the final | cartesian coordinate orientation of the molecule. X-PRIORITY (O) In a DRC calculation, results will be printed whenever the calculated geometry changes by 0.05 Angstroms. The geometry change is defined as the linear sum of the translation vectors of motion for all atoms in the system. Abbreviation, X-PRIO. X-PRIORITY=n.nn (O) In a DRC calculation, results will be printed whenever the calculated geometry changes by n.nn Angstroms. - 38 - KEYWORDS Page 2-32 XYZ (W) The SADDLE calculation quite often fails due to faulty definition of the second geometry because the dihedrals give a lot of difficulty. To make this option easier to use, XYZ was developed. A calculation using XYZ runs entirely in cartesian coordinates, thus eliminating the problems associated with dihedrals. The connectivity of the two systems can be different, but the numbering must be the same. Dummy atoms can be used; these will be removed at the start of the run. A new numbering system will be generated by the program, when necessary. | | XYZ is also useful for removing dummy atoms from an internal | coordinate file; use XYZ and 1SCF. | | If a large ring system is being optimized, sometimes the closure is | difficult, in which case XYZ will normally work. | | Except for SADDLE, do not use XYZ by default: use it only when | something goes wrong! - 39 - CHAPTER 3 GEOMETRY SPECIFICATION FORMAT: The geometry is read in using essentially "Free-Format" of FORTRAN-77. In fact, a character input is used in order to accommodate the chemical symbols, but the numeric data can be regarded as "free-format". This means that integers and real numbers can be interspersed, numbers can be separated by one or more spaces, a tab and/or by one comma. If a number is not specified, its value is set to zero. The geometry can be defined in terms of either internal or cartesian coordinates. INTERNAL COORDINATE DEFINITION For any one atom (i) this consists of an interatomic distance in Angstroms from an already-defined atom (j), an interatomic angle in degrees between atoms i and j and an already defined k, (k and j must be different atoms), and finally a torsional angle in degrees between atoms i, j, k, and an already defined atom l (l cannot be the same as k or j). See also dihedral angle coherency. Exceptions: 1. Atom 1 has no coordinates at all: this is the origin. 2. Atom 2 must be connected to atom 1 by an interatomic distance only. 3. Atom 3 can be connected to atom 1 or 2, and must make an angle with atom 2 or 1 (thus - 3-2-1 or 3-1-2); no dihedral is possible for atom 3. By default, atom 3 is connected to atom 2. - 40 - GEOMETRY SPECIFICATION Page 3-2 3.1 CONSTRAINTS 1. Interatomic distances must be greater than zero. Zero Angstroms is acceptable only if the parameter is symmetry-related to another atom, and is the dependent function. 2. Angles must be in the range 0.0 to 180.0, inclusive. This constraint is for the benefit of the user only; negative angles are the result of errors in the construction of the geometry, and angles greater than 180 degrees are fruitful sources of errors in the dihedrals. 3. Dihedrals angles must be definable. If atom i makes a dihedral with atoms j, k, and l, and the three atoms j, k, and l are in a straight line, then the dihedral has no definable angle. During the calculation this constraint is checked continuously, and if atoms j, k, and l lie within