Features of MOPAC2016

Relationship to MOPAC2012

MOPAC2016 is best regarded as MOPAC2012 with improved transition-state location and improved biochemistry modeling.

Relationship to MOPAC2009

MOPAC2012 is best regarded as MOPAC2009 plus PM7 and PM7-TS

Relationship to MOPAC2007

MOPAC2009 is best regarded as MOPAC2007 plus the MOZYME function.

Relationship to MOPAC6

MOPAC2007 is an updated version of MOPAC6, the last public domain version of MOPAC.  MOPAC6 had been written in FORTRAN-77, and had become unwieldy.  Maintenance had become increasingly difficult, and the decision was made to completely re-write the program in FORTRAN-90/95.  During this process several major changes were made.  The method MINDO/3 was deleted as were several infrequently-used functionalitiess.  The structure of the program was reorganized, so that maintenance and debugging would be easier.  A consistent style was imposed on the whole code.  This meant that once the overall structure was understood, individual routines could be read by developers with relative ease.

Reliability

Despite all the work that has gone into MOPAC2007, it has relatively few features that were not present in MOPAC6; the focus of the effort has not been to add new features, rather it has been to produce a highly-debugged, robust program.  The goal is that all the functions implied by the keywords should work as described.  During the beta-test, from September 2006 to the end of January 2007, several hundred bugs were found and fixed. Towards the end of the beta-test the rate at which bugs were being found dropped to about two to three a day, and most of those that were reported were not too serious.  After MOPAC2007 was released in late January, over 500 licenses were issued and, as a result of this large number of users/groups all busily using the new program, the steady trickle of bug-reports continued. The policy is that whenever a bug is reported all work stops until the fault in corrected.  In practice, this meant that bugs were fixed with about two days, so MOPAC2007 is constantly being maintained in a state of "No Known Bugs" (NKB). It is expected that this trickle of bug reports will continue for several months, during which time the program will get steadily more robust. 

New features in MOPAC2007

PM6:  At the time, this was the most recent NDDO method in MOPAC.

 

Features of MOPAC6

  Geometry optimization
  Methods
  SCF Procedures
  Derived Properties
  Types of Species
  Symmetry theory
  Electric fields
  Electrostatic Potential
  Solvent effects
  Electronic Excited states
  Vibrations
  Thermodynamics
  Dynamics
  Intrinsic Reaction Coordinate
  Reaction Paths
  Saddle-Point Location
   

Geometry Optimization - General

One of the commonest operations in computational chemistry is optimizing the geometry. This involves modifying the geometry until the energy is a minimum. At that point, the net forces acting on every atom vanish. Over the years, various methods for optimizing geometries have been developed. One of these, Baker's EigenFollowing procedure, has proven to be very robust, and this is now used as the default. If, for any reason, the EF method is not wanted, other methods are available.

Constrained by definition

When only part of a system is to be optimized, options are provided to constrain other parts of the system. For example, a bond length, angle, or dihedral for one or more atoms can be defined as fixed at some initial value, or the x or y or z coordinate can be defined as unchanging.

Constrained by symmetry

Some systems have symmetry that can be used to accelerate geometric operations. Thus in Fullerene, C60, all atoms are in the same environment, and there are exactly two unique bond-lengths. The geometry optimization calculation can be reduced from order 174 (3$\times$60-6) to order two by use of symmetry. Symmetry can also be used in unsymmetric systems. For example, in determining the transition state for the SN2 reaction Br- + CH4 $\rightarrow$ CH3Br + H-, the C-Br and C-H distances can be set equal, and the geometry optimized. After releasing the symmetry constraint, the transition state geometry is determined in one step by use of Baker's EigenFollowing method.

Energy Minimization

The degree to which geometries can be optimized can be varied according to the user's need: from the default, which is the best compromise between precision and speed, to high precision for publication work, to low precision for rapid screening. Unconditionally, the degree of optimization can be displayed, although the default is for this information to be suppressed unless problems are encountered.

Unless special action is taken, only local minima are located. Thus optimization of the geometry of dimethyl ether would not yield ethanol, nor would optimization of gauche butane yield trans butane.

Transition State location

Several methods are provided for refining transition states. One, Baker's EigenFollowing, is usually sufficient for most systems; the others are provided for the rare instances when the default TS does not work.

NDDO Methods

The following NDDO methods are supported: MNDO, AM1, PM3, RM1, and PM6. For a list of elements available, see Elements available.

SCF Procedures

Restricted Hartree Fock

The default self-consistent method is restricted Hartree-Fock. This allows both closed shell and open shell systems. For open shell systems, errors due to the half electron approximation are automatically corrected.

Unrestricted Hartree Fock

At user's choice, unrestricted Hartree-Fock SCF calculations can be run. In these, the α and β spin molecular orbitals have different spatial forms. When UHF is used, the expectation values of the S and S2 operators are printed. In addition to printing the α and β spin molecular orbitals, the associated α and β spin density matrices can be printed, as can the α - β spin density matrix.

Derived Properties

Bond orders

Several types of bond orders can be displayed. The simplest is the Wyberg indices, which mirror the simple ideas of single, double, and triple bonds. More complicated representations include Mulliken populations, delocalizability, superdelocalizability, free valence, and spin density.

Charges

By default, the net charge on each atom is printed. These are the Coulson charges, although if requested, Mulliken charges can also be printed.

Dipole moment

By default, the dipole vector (calculated from atomic charges and the lone pairs) is calculated and printed, along with the net dipole moment, in Debye.

Static (zero frequency) Polarizability

The polarizability of a system is a measure of the response of the electron density distribution to a static electric field . This can be calculated two ways, by the application of electric fields (the static method) and by direct analysis of the wavefunction (the sum over states method). For large systems, the application of electric fields method is faster, although the sum over states method is more precise for all systems. Because of the limited precision of the static method, a way has to be provided to allow the user to determine the precision. Static polarizability (and first and second non-linear optical responses) can be determined from the changing dipole or from the changing heat of formation. By printing the results of the calculation based on both dipole and ΔHf, side by side, the user can get an estimate of the precision.

Frequency dependent Non-Linear Optics

In addition to the polarizability, the following non-linear optical properties can be calculated: first and second order properties (β and γ), Electric Field Second Harmonic Generation (EFISH), optical rectification, electrooptic Pockel's Effect, second and third harmonic generation. Where appropriate, averages are printed.

Types of Species

Atoms

Simple calculations on atoms yield conventional heats of formation. These are the heats of atomization of the elements. Most atoms have open shells in the ground state, and these can be allowed for by use of appropriate keywords. By default, the electronic state of the system will be printed. Excited states can be readily calculated, and the transition dipole for photoexcitation can be printed. If, as is common, the originating state (usually the ground state) or the terminating state (usually an excited state) is degenerate, the degeneracy is taken into account in the calculation of transition dipole. The conventional selection rules can be derived by an analysis of the states and transition dipoles.

Molecules

The commonest type of system calculated consists of neutral, polyatomic molecules. These can be simple, closed shell species, such as benzene, to radicals, e.g. nitric oxide, to zwitterions, to multiple open shell radicals, such as NH4., to excited electronic states, e.g. n-π* pyridine.

Ions

Calculations can be performed on ionized species, both isolated and with counterions, in both gas phase and solvated. All degrees of ionization are allowed.

Polymers

Regular polymer systems for which periodic boundary conditions can be imposed can be calculated. The time for such calculations is about 30% greater than for a discrete molecule of the same size as the unit cell used. Geometries, including unit cell length, can be optimized.

Effect of Stretching

In polymers, a reaction can be set up, in which the translation vector distance can be steadily increased. The effect of this is to steadily increase the distance between the repeat units of the polymer. Initially, the energy would not change significantly, as any conformational flexibility in the polymer is used up, but once that is done, the energy of the system (a measure of the stress) would rise parabolically with increased strain. From an analysis of this parabola, and given the density of the polymer, the Young's modulus (the degree of elastic behavior) can readily be calculated. If the strain is increased without limit, a point would be reached at which the weakest bond in the polymer would break, and the stress would immediately drop to zero. From this, and the experimental density, the tensile strength can be calculated.

Vibrations (Phonon Spectrum)

As with molecules, the vibrational spectrum of polymers can be calculated. However, unlike molecular normal modes, which have quantized vibrational frequencies, polymers give rise to bands of frequencies, defined by the associated wave-vector k in the Brillouin zone. At k=0, four of these bands have zero frequency, corresponding to the four trivial vibrations of a polymer.

Defect polymers (solitons)

Excitations can occur in some polymers, to give rise to ion pairs, isolated electronic excited states, and other electronic defects. These can be modeled using oligomers. A simple excited state would be in polyacetylene, for example, in which one carbon atom was singly bonded or doubly bonded to two other carbon atoms. The effect of an applied electric field to induce hopping of solitons can be modeled.

Layer Systems

By using the Born-von Kármán periodic boundary conditions, layer systems can be modeled. Geometry optimization, including optimizing the unit cell dimensions, can be carried out.

Solids

By using the Born-von Kármán periodic boundary conditions, regular solid systems can be modeled. Geometry optimization, including optimizing the unit cell dimensions, can be carried out.

Compressivity

For cubic systems, the compressivity of the crystal can be deduced by calculating the ΔHf  in a reaction in which the unit cell dimension is systematically varied.

Electronic Structure (Brillouin Zone)

A utility program for analyzing the electronic structure of polymers, layer systems, and solids is provided. This uses output from MOPAC, the space-group symmetry operations, and interactive user input to generate the Little groups for points in k-space, band structures, and cross-sections through k-space for selected bands. The first step in this analysis is to symmetrize the energy matrix for the solid. After this is done, the resulting structures in k-space are fully symmetry adapted.

Symmetry theory

Symmetry is very important in chemistry, and, in recognition of this, MOPAC makes extensive use of symmetry theory. Most of the symmetry theory is done automatically, without any user action being necessary. The simplest operation is the recognition of the point-group of a molecule. All non-magnetic single point groups up to order 7 and most of the groups up to order 8 are recognized. This set includes the three infinite groups (R3, the order of the sphere, C $_{infty v}$, and D $_{infty h}$) for all chemically realizable representations, and the seven cubic point-groups. There is an ambiguity in the definition of some irreducible representations of some groups, such as b1 and b2 in C2v. This ambiguity is resolved using the conventional definition for orienting molecules. To allow for the fact that molecular geometries might not be completely precise, a certain tolerance is built in to the test for point-groups. Sometimes, a user might wish to use a sub-group of the full point-group. This can be done by using NOREOR, or, if symmetry theory is not wanted at all NOSYM can be specified.

Symmetry Labels

Symmetry labels are automatically assigned to molecular orbitals, vibrations, and electronic states. These labels are of the form nR, where R is the irreducible representation and n is the nth occurrence of that representation. For each eigenfunction, the symmetry label is unique, and for this and other reasons, the symmetry labels are true quantum numbers. This is particularly evident in electronic states, where the symmetry label includes information on the spin state.

Symmetrizing vibrations

To facilitate vibrational analysis of high-symmetry systems, symmetry theory is used to symmetrize the force matrix. This has the side effect of reducing any errors introduced by finite precision mathematics. The resulting normal modes are completely symmetry adapted, and subsequent analysis of these modes is made much easier.

Accelerating Calculation of Vibrations

For molecules that have symmetry, symmetry theory is automatically used to accelerate the construction of the force matrix. This reduces the time needed for the calculation of normal modes. For C60, the increase in speed is a factor of about 40.

Electric Fields

The effect of applied external electric fields can be modeled. The fields are uniform, and the orientation and intensity of the field is under user control. The applied fields cannot be used in the translation directions of infinite systems.

Electrostatic Potential

Four electrostatic potential methods are available, of which two can generate data for use by graphics programs. These are the Wang-Ford Parametric Electrostatic Potential (PMEP) and the Merz-Bessler ESP methods. The PMEP method gives results similar to those from ab initio 6-31G calculations, but is limited in the range of atoms allowed. In contrast, the ESP method is quite general.

Solvent effects

 The effect of solvents can be modeled by Andreas Klamt's COSMO technique.  In the COSMO method, both ground and excited state systems in solution can be modeled, and the geometries of solvated systems optimized.

Electronic Excited states

MOPAC contains an extensive configuration interaction package. This allows a wide range of open and closed shell ground and excited state phenomena to be modeled. Examples of the types of systems that can be modeled include: methane, stabilized by mixing in excited states; oxygen, with an open shell ground state; methane cation, with and without Jahn Teller effects, and high spin systems (up to nonet). Keywords are provided for the commonest types of C.I. (single electron excitation, single plus double, single plus paired double, single, double, and triple excitations). All other types of C.I. can be defined explicitly, under keyword control.

Internal checks are automatically carried out to ensure that the calculations do not violate any theoretical rules, although these constraints can be relaxed, at user discretion. State spin and symmetries are automatically assigned.

The effect of C.I. on electron density distributions can be modeled, both in ground and excited states, and for ground state and vibrational states.

Vibrations

The normal modes of vibration of a stationary system can be calculated. For ground states, this consists of the 3N-6 or 3N-5 non-zero modes, while for simple transition states, the 3N-7 real modes and 1 imaginary mode are reported. If desired, the force constants for the system can be printed.

Description of Vibrations

Because of the complexity of normal modes, an analysis of these modes is printed. This analysis allows the nature of the normal mode (i.e., X-Y stretch, A-B-C bend, etc) to be rapidly described. The normal coordinates are printed. However these are of limited use because they are velocity vectors and do not indicate the energy carried by each atom. An additional display shows the effect of mass-weighting the normal modes; this gives an alternative view of the molecular vibrations.

Effective Mass and Travel

To the degree to which normal modes can be described as a simple harmonic oscillator, the effective mass involved can be calculated. For a homonuclear diatomic, this is half the atomic mass; if one of the atoms is extremely massive, the mass is approximately that of the other atom.

From quantum theory, the energy of vibration is quantized. Therefore, given a knowledge of the force constant for the vibration, and the effective mass, the excursion distance (in mass weighted space) can readily be calculated. By default, when normal modes are calculated, these two quantities are printed.

Transition Dipole

The relative intensity of an infra-red active band is a simple function of the transition dipole. This quantity is printed whenever the vibrational analysis is printed in a FORCE calculation

Internal Coordinate Force Constants

Although not an observable, the internal coordinate force constants are often of interest. These quantities are printed at the end of a normal coordinate calculation.

Isotopic Substitution

Although calculating the force matrix in a normal coordinate analysis is often lengthy, the final stage, mass weighting and generating normal modes, is very rapid. To allow different isotopic masses to be used in a single normal coordinate analysis, the option exists to save the force matrix. The isotopic masses can then be changed, and the old force matrix used again. Such calculations are very rapid.

Trivial Modes, projecting out

A minor increase in precision is achieved by projecting out the six trivial modes. These can subsequently be printed out. The order of the modes is then defined as x, then y, then z translation, followed by the three rotations, about the moments of inertia.

Thermodynamics

Various thermodynamic quantities (Partition function, enthalpy, heat capacity, and entropy) can be calculated for any temperature, or range of temperatures. These quantities can be decomposed into vibrational, rotational, internal, and translational contributions. The effect of changing temperature on the ΔHf can be monitored.

Dynamics

Conservation of Energy

The time evolution of a system can be investigated. The starting point can be either a stationary point (optimized geometry or a transition state) or a non-stationary point, and the initial velocity vector can be zero, or determined by one of the normal modes, or an arbitrary (user supplied) vector. At each step, the position of each atom is modified by (a) the forces acting on it and its isotopic mass, (b) the velocity vector of the atom, and (c) information on the acceleration, and rate of acceleration, of the atom. During the course of the molecular dynamics, the total energy (kinetic plus potential) is constant as the system moves down a potential energy surface, the velocity increases, and vice versa.

Simulated Annealing

Although the default is to conserve energy, the option exists to allow kinetic energy to be reduced, with the rate of reduction being a function of time, by specifying a half-life in femtoseconds. The effect of this option is to simulate cooling of the system, analogous to the molecular mechanics method of simulated annealing.

Simulated heating

No constraint is placed on the sign of the half-life, consequently, a negative half life can be used. This simulates heating of the system. Invariably, unlimited heating results in atomization of any compound.

By an appropriate choice of keywords, any combination of heating and cooling, including conserving energy, can be modeled in a single run.

Sampling

Sampling of the state of the system can be done several ways: each point calculated can be printed, or constant steps in time, energy, or position can be chosen. At each point printed, the amount of information printed is determined by keywords, from a single line giving simple energetics, to the energetics plus geometry plus velocity vector.

Simulated vibrations

The easiest way to calculate vibrational frequencies is to calculate the force matrix and perform a normal mode analysis. While this is acceptable most of the time, in some systems the normal modes are sufficiently non-simple-harmonic that these vibrational frequencies are unacceptable.

An alternative is to set the system in motion, using the normal modes calculated conventionally, and to determine directly the period of vibration. For well behaved systems, this is almost exactly the same as that given from the force matrix, verifying the internal consistency of the various methods.

For very simple systems, e.g. diatomics, a second alternative is to plot the energy coordinate graph, and determine the vibrational period from either the energies or the gradients.

Intrinsic Reaction Coordinate

The time-independent behavior of a system can be modeled using the IRC option. In this, the atoms in a system move in response to the forces acting on them, moderated by their isotopic masses, however, at each step all kinetic energy is annihilated. The effect is to produce a time-independent trajectory, the steepest decent from the starting geometry to a stationary point.

Reaction Paths

Where a definable reaction coordinate can be identified, this can be used to drive a chemical reaction. For example, in a bond-breaking bond-making reaction, the bond being made can be used as the reaction coordinate. Several options are provided for specifying reaction paths, the three most common of which are: (a) to supply the various values of the reaction coordinate as extra data (at each point on the reaction path, the gradient of the path is calculated); (b) to define a step size and number of point to be calculated (at the end of the calculation, the ΔHf  are printed in a form suitable for plotting); and (c) to give two step sizes and numbers of points in two directions. This option is useful in mapping out a potential energy surfaces.

Saddle-Point Location

The geometry of the transition state is not always easy to define. The option exists to allow the reactants and the products to be defined, and to allow the saddle or transition state between these two systems to be calculated. Recent changes in this function have made it more robust, so that now the failure rate in locating transition states is very low. (In practice, transition states have been located for all reactions investigated.)