Optimization

Selecting the Optimization Goal

By default, optimizations search for a local minimum.

QST2

Search for a transition structure using the STQN method. This option requires the reactant and product structures as input, specified in two consecutive groups of title and molecule specification sections. Note that the atoms must be specified in the same order in the two structures. TS should not be specified with QST2.

QST3

Search for a transition structure using the STQN method. This option requires the reactant, product, and initial TS structures as input, specified in three consecutive groups of title and molecule specification sections. Note that the atoms must be specified in the same order within the three structures. TS should not be specified with QST3.

TS

Requests optimization to a transition state rather than a local minimum, using the Berny algorithm.

Saddle=N

Requests optimization to a saddle point of order N using the Berny algorithm.

Conical

Search for a conical intersection or avoided crossing using the state-averaged CASSCF method. Avoided is a synonym for Conical. Note that CASSCF=SlaterDet is needed in order to locate a conical intersection between a singlet state and a triplet state.

Options

Options to Modify the Initial Geometry

ModRedundant

Except for any case when it is combined with the GIC option (see below), the ModRedundant option will add, delete, or modify redundant internal coordinate definitions (including scan and constraint information) before performing the calculation. This option requires a separate input section following the geometry specification; when used in conjunction with QST2 or QST3, a ModRedundant input section must follow each geometry specification. AddRedundant is synonymous with ModRedundant.

[Type] N1 [N2 [N3 [N4]]] [A | F]
[Type] N1 [N2 [N3 [N4]]] B 
[Type] N1 [N2 [N3 [N4]]] K | R 
[Type] N1 [N2 [N3 [N4]]] D 
[Type] N1 [N2 [N3 [N4]]] H diag-elem 
[Type] N1 [N2 [N3 [N4]]] S nsteps stepsize 

See the examples for illustrations of the use of ModRedundant.

ReadOptimize

Read an input section modifying which atoms are to be optimized. The atom list is specified in a separate input section (terminated by a blank line). By default, the atom list contains all atoms in the molecule, unless any atoms are designated as frozen within the molecule specification, in which case the initial atom list excludes them. If the structure is being read in from the checkpoint file, then the list of atoms to be optimized matches that in the checkpoint file. ReadOpt and RdOpt are synonyms for this option. ReadFreeze and RdFreeze are deprecated synonyms.

The input section uses the following format:

atoms=list [notatoms=list]

where each list is a comma or space-separated list of atom numbers, atom number ranges and/or atom types. Keywords are applied in succession. Here are some examples:

Bare integers without a keyword are interpreted as atom numbers:

1,3,5 7        Adds atoms 1, 3, 5 and 7.

For ONIOM optimizations only, block and notblock can be similarly used to include/not include rigid blocks defined in ONIOM molecule specifications. If there are contradictions between atoms specified as atoms and within blocks—e.g., an atom is included within a block but excluded by atom type—Gaussian 16 generates an error.

You can start from an empty atom list by placing noatoms as the first item in the input section. For example, the following input optimizes all non-hydrogen atoms within atoms 1-100 and freezes all other atoms in the molecule:

noatoms atoms=1-100 notatoms=H

Atoms can also be specified by ONIOM layer via the [not]layer keywords, which accept these values: real for the real system, model for the model system in a 2-layer ONIOM, middle for the middle layer in a 3-layer ONIOM, and small for the model layer of a 3-layer ONIOM. Atoms may be similarly included/excluded by residue with residue and notresidue, which accept lists of residue names. Both keyword pairs function as shorthand forms for atom lists.

Separate sections are read for each geometry for transition state optimizations using QST2 or QST3. Be aware that providing contradictory input—e.g., different frozen atoms for the reactants and products—will produce unpredictable results.

NoFreeze

Activates (unfreezes) all variables, in other words freeze nothing and optimize all atoms. This option is useful when reading in a structure from a checkpoint file that contains frozen atoms (i.e. with Geom=Check). This option should not be used with GICs; use UnFreezeAll in the GIC input section instead.

General Procedural Options

MaxCycles=N

Sets the maximum number of optimization steps to N. The default is the maximum of 20 and twice the number of redundant internal coordinates in use (for the default procedure) or twice the number of variables to be optimized (for other procedures).

MaxStep=N

Sets the maximum size for an optimization step (the initial trust radius) to 0.01N Bohr or radians. The default value for N is 30.

Restart

Restarts a geometry optimization from the checkpoint file. In this case, the entire route section will consist of the Opt keyword and the same options to it as specified for the original job (along with Restart). No other input is needed (see the examples).

InitialHarmonic=N

Add harmonic constraints to the initial structure with force constant N/1000000 Hartree/Bohr². IHarmonic is a synonym for this option.

ChkHarmonic=N

Add harmonic constraints to the initial structure saved on the chk file with force constant N/1000000 Hartree/Bohr². CHarmonic is a synonym for this option.

ReadHarmonic=N

Add harmonic constraints to a structure read in the input stream (in the input orientation), with force constant N/1000000 Hartree/Bohr². RHarmonic is a synonym for this option.

MaxMicroiterations=N

Allow up to N microiterations. The default is based on NAtoms but is at least 5000. MaxMicro is a synonym for this option.

NGoUp=N

Opt=NGoUp=N allows the energy to increase N times before the algorithm switches to doing only linear searches. The default is 1, meaning that only linear searches are performed after the second time in row that the energy increases. N=-1 forces only linear searches whenever the energy rises.

NGoDown=N

When near a saddle point, mix at most N eigenvectors of the Hessian with negative eigenvalues to form a step away from the saddle point. The default is 3. N=-1 turns this feature off, and the algorithm takes only the regular RFO step. NoDownHill is equivalent to NGoDown=-1.

MaxEStep=N

Take a step of length N/1000 (Bohr or radians) when moving away from a saddle point. The default is N=600 (0.6) for regular optimizations and N=100 (0.1) for ONIOM Opt=Quadmac calculations.

Options Related to Initial Force Constants

Unless you specify otherwise, a Berny geometry optimization starts with an initial guess for the second derivative matrix—also known as the Hessian—which is determined using connectivity derived from atomic radii and a simple valence force field [Schlegel84a, Peng96]. The approximate matrix is improved at each point using the computed first derivatives. This scheme usually works fine, but for some cases the initial guess may be so poor that the optimization fails to start off properly or spends many early steps improving the Hessian without nearing the optimized structure. In addition, for optimizations to transition states, some knowledge of the curvature around the saddle point is essential, and the default approximate Hessian must always be improved.

There are a variety of options which retrieve or compute improved force constants for a geometry optimization. They are listed following this preliminary discussion.

There are two other approaches to providing the initial Hessian which are sometimes useful:

• Input new guesses: The default approximate matrix can be used, but with new guesses read in for some or all of the diagonal elements of the Hessian. This is specified in the ModRedundant input or on the variable definition lines in the Z-matrix. For example:

  1 2 H 0.55
  

  The letter H indicates that a diagonal force constant is being specified for this coordinate and that its value is 0.55 Hartree/au².

• Compute some or all of the Hessian numerically: You can ask the optimization program to compute part of the second derivative matrix numerically. In this case each specified variable will be stepped in only one direction, not both up and down as would be required for an accurate determination of force constants. The resulting second-derivatives are not as good as those determined by a frequency calculation but are fine for starting an optimization. Of course, this requires that the program do an extra gradient calculation for each specified variable. This procedure is requested by a flag (D) on the variable definition lines:

  1 2 D
  1 2 3 D 

  This input tells the program to do three points before taking the first optimization step: the usual first point, a geometry with the bond between atoms 1 and 2 incremented slightly, and a geometry with the angle between atoms 1, 2 and 3 incremented slightly. The program will estimate all force constants (on and off diagonal) for bond(1,2) and angle(1,2,3) from the three points. This option is only available with the Berny and EF algorithms.

The following options select methods for providing improved force constants:

ReadFC

Extract force constants from a checkpoint file. These will typically be the final approximate force constants from an optimization at a lower level, or (much better) the force constants computed correctly by a lower-level frequency calculation (the latter are greatly preferable to the former).

CalcFC

Specifies that the force constants be computed at the first point using the current method (available for the HF, CIS, MP2, CASSCF, DFT, and semi-empirical methods only).

RCFC

Specifies that the computed force constants in Cartesian coordinates (as opposed to internal) from a frequency calculation are to be read from the checkpoint file. Normally it is preferable to pick up the force constants already converted to internal coordinates as described above (ReadFC). However, a frequency calculation occasionally reveals that a molecule needs to distort to lower symmetry. In this case, the computed force constants in terms of the old internal coordinates cannot be used, and instead Opt=RCFC is used to read the Cartesian force constants and transform them. Note that Cartesian force constants are only available on the checkpoint file after a frequency calculation. You cannot use this option after an optimization dies because of a wrong number of negative eigenvalues in the approximate second derivative matrix. In the latter case, you may want to start from the most recent geometry and compute some derivatives numerically (see below). ReadCartesianFC is a synonym for RCFC.

CalcHFFC

Specifies that the analytic HF force constants are to be computed at the first point. CalcHFFC is used with MP2 optimizations, and it is equivalent to CalcFC for DFT methods, AM1, PM3, PM3MM, PM6 and PDDG.

CalcAll

Specifies that the force constants are to be computed at every point using the current method (available for the HF,CIS, MP2, CASSCF, DFT, and semi-empirical methods only). Note that vibrational frequency analysis is automatically done at the converged structure and the results of the calculation are archived as a frequency job.

RecalcFC=N

Do analytic second derivatives at step 1 and every N^th step thereafter during an optimization.

VCD

Calculate VCD intensities at each point of a Hartree-Fock or DFT Opt=CalcAll optimization.

NoRaman

Specifies that Raman intensities are not to be calculated at each point of a Hartree-Fock Opt=CalcAll job (since it includes a frequency analysis using the results of the final point of the optimization). The Raman intensities add 10-20% to the cost of each intermediate second derivative point. NoRaman is the default for methods other than Hartree-Fock.

StarOnly

Specifies that the specified force constants are to be estimated numerically but that no optimization is to be done. Note that this has nothing to do with computation of vibrational frequencies.

NewEstmFC

Estimate the force constants using a valence force field. This is the default.

EstmFC

Estimate the force constants using the old diagonal guesses. Only available for the Berny algorithm.

FCCards

Requests that read the energy (although value is not used), cartesian forces and force constants from the input stream, as written out by Punch=Derivatives. The format for this input is:

The force constants are in lower triangular form: ((F(J,I),J=1,I),I=1,3N_atoms), where 3N_atoms is the number of Cartesian coordinates.

Convergence-Related Options

These options are available for the Berny algorithm only.

Tight

This option tightens the cutoffs on forces and step size that are used to determine convergence. An optimization with Opt=Tight will take several more steps than with the default cutoffs. For molecular systems with very small force constants (low frequency vibrational modes), this may be necessary to ensure adequate convergence and reliability of frequencies computed in a subsequent job step. This option can only be used with Berny optimizations. For DFT calculations, Int=UltraFine should be specified as well.

VeryTight

Extremely tight optimization convergence criteria. VTight is a synonym for VeryTight. For DFT calculations, Int=UltraFine should be specified as well.

EigenTest

EigenTest requests and NoEigenTest suppresses testing the curvature in Berny optimizations. The test is on by default only for transition states in internal (Z-matrix) or Cartesian coordinates, for which it is recommended. Occasionally, transition state optimizations converge even if the test is not passed, but NoEigenTest is only recommended for those with large computing budgets.

Expert

Relaxes various limits on maximum and minimum force constants and step sizes enforced by the Berny program. This option can lead to faster convergence but is quite dangerous. It is used by experts in cases where the forces and force constants are very different from typical molecules and Z-matrices, and sometimes in conjunction with Opt=CalcFC or Opt=CalcAll. NoExpert enforces the default limits and is the default.

Loose

Sets the optimization convergence criteria to a maximum step size of 0.01 au and an RMS force of 0.0017 au. These values are consistent with the Int(Grid=SG1) keyword, and may be appropriate for initial optimizations of large molecules using DFT methods which are intended to be followed by a full convergence optimization using the default (Fine) grid. It is not recommended for use by itself.

Algorithm-Related Options

GEDIIS

Use GEDIIS optimization algorithm. This is the default for minimizations when gradients are available.

RFO

Requests the Rational Function Optimization [Simons83] step during Berny optimizations. It is the default for transition state optimizations (Opt=TS). This was also the default algorithm for minimizations using gradients in Gaussian 03.

EF

Requests an eigenvalue-following algorithm [Simons83, Cerjan81, Banerjee85], which is useful only for methods without derivatives (for which it is the default). Available for both minima and transition states. and EigenvalueFollow are all synonyms for EF. When used with Opt=Z-Matrix, a maximum of 50 variables may be optimized.

ONIOM-Related Options

Micro

Use microiterations in ONIOM(MO:MM) optimizations. This is the default, with selection of L120 or L103 for the microiterations depending on whether electronic embedding is on or off. NoMicro forbids microiterations during ONIOM(MO:MM) optimizations. Mic120 says to use microiterations in L120 for ONIOM(MO:MM), even for mechanical embedding. This is the default for electronic embedding. Mic103 says to perform microiterations in L103 for ONIOM(MO:MM). It is the default for mechanical embedding, and it cannot be used with electronic embedding.

QuadMacro

Controls whether the coupled, quadratic macro step is used during ONIOM(MO:MM) geometry optimizations [Vreven06a]. NoQuadMacro is the default.

Coordinate System Selection Options

Redundant

Build an automatic set of redundant internal coordinates such as bonds, angles, and dihedrals from the current Cartesian coordinates or Z-Matrix values, using the old algorithm available in Gaussian 16. Perform the optimization using the Berny algorithm in these redundant internal coordinates. This is the default for methods for which analytic gradients are available.

Z-matrix

Perform the optimization with the Berny algorithm using internal coordinates [Schlegel82, Schlegel89, Schlegel95]. In this case, the keyword FOpt rather than Opt requests that the program verify that a full optimization is being done (i.e., that the variables including inactive variables are linearly independent and span the degrees of freedom allowed by the molecular symmetry). The POpt form requests a partial optimization in internal coordinates. It also suppresses the frequency analysis at the end of optimizations which include second derivatives at every point (via the CalcAll option). See Appendix C for details and examples of Z-matrix molecule specifications.

Cartesian

Requests that the optimization be performed in Cartesian coordinates, using the Berny algorithm. Note that the initial structure may be input using any coordinate system. No partial optimization or freezing of variables can be done with purely Cartesian optimizations; the mixed optimization format with all atoms specified via Cartesian lines in the Z-matrix can be used along with Opt=Z-matrix if these features are needed. When a Z-matrix without any variables is used for the molecule specification, and Opt=Z-matrix is specified, then the optimization will actually be performed in Cartesian coordinates. Note that a variety of other coordinate systems, such as distance matrix coordinates, can be constructed using the ModRedundant option.

Generalized Internal Coordinate (GIC) Options

GIC

Build an automatic set of redundant internal coordinates using the new GIC algorithm. Perform the optimization using the Berny algorithm in the GIC-type internal coordinates. Note that the coordinates generated with this option can be the same bonds, angles, and dihedrals generated by the default algorithm. However, these coordinates are internally stored and manipulated as the generalized ones (e.g., relevant analytical derivatives with respect to Cartesian coordinates displacements can be calculated automatically via an auto differentiation engine). The GICs are more flexible and, in principle, can be any combination of standard mathematical functions. Note that Geom=Checkpoint Opt=GIC option is equivalent to Geom=(Checkpoint,GIC).

AddGIC

Add, delete, or modify GIC-type internal coordinate definitions (including scan and constraint information) before performing the calculation using the new GIC algorithm. This option requires a separate input section following the geometry specification. When used in conjunction with QST2 or QST3, a GIC input section must follow each geometry specification. The syntax of the GIC input section is described in GIC Info. Note that Opt=(ModRedundant,GIC) is equivalent to Opt=AddGIC. Note that Geom=Checkpoint Opt=ReadAllGIC is equivalent to Geom=(Checkpoint, ReadAllGIC).

GICOld

Build an automatic set of redundant internal coordinates using the current default algorithm (as with the option Redundant) and then convert the coordinates into the GICs and treat them as such. Perform the optimization using the Berny algorithm in the GIC-type internal coordinates.

ReadAllGIC

Do not build any redundant internal coordinates by default. Instead, read the input stream for user-provided GIC definitions and create the coordinates. Perform the optimization using the Berny algorithm in the GIC-type internal coordinates. This option requires a separate GIC input section following the geometry specification. When used in conjunction with QST2 or QST3, a GIC input section must follow each geometry specification. The syntax of the GIC input section is described in the GIC Considerations tab.

Rarely Used Options

Path=M

In combination with either the QST2 or the QST3 option, requests the simultaneous optimization of a transition state and an M-point reaction path in redundant internal coordinates [Ayala97]. No coordinate may be frozen during this type of calculation.

If QST2 is specified, the title and molecule specification sections for both reactant and product structures are required as input as usual. The remaining M-2 points on the path are then generated by linear interpolation between the reactant and product input structures. The highest energy structure becomes the initial guess for the transition structure. Each point is optimized to lie in the reaction path and the highest point is optimized toward the transition structure.

If QST3 is specified, a third set of title and molecule specification sections must be included in the input as a guess for the transition state as usual. The remaining M-3 points on the path are generated by two successive linear interpolations, first between the reactant and transition structure and then between the transition structure and product. By default, the central point is optimized to the transition structure, regardless of the ordering of the energies. In this case, M must be an odd number so that the points on the path may be distributed evenly between the two sides of the transition structure.

In the output for a simultaneous optimization calculation, the predicted geometry for the optimized transition structure is followed by a list of all M converged reaction path structures.

The treatment of the input reactant and product structures is controlled by other options: OptReactant, OptProduct, BiMolecular.

Note that the SCF wavefunction for structures in the reactant valley may be quite different from that of structures in the product valley. Guess=Always can be used to prevent the wavefunction of a reactant-like structure from being used as a guess for the wavefunction of a product-like structure.

OptReactant

Specifies that the input structure for the reactant in a path optimization calculation (Opt=Path) should be optimized to a local minimum. This is the default. NoOptReactant retains the input structure as a point that is already on the reaction path (which generally means that it should have been previously optimized to a minimum). OptReactant may not be combined with BiMolecular.

BiMolecular

Specifies that the reactants or products are bimolecular and that the input structure will be used as an anchor point in an Opt=Path optimization. This anchor point will not appear as one of the M points on the path. Instead, it will be used to control how far the reactant side spreads out from the transition state. By default, this option is off.

OptProduct

Specifies that the input structure for the product in a path optimization calculation (Opt=Path) should be optimized to a local minimum. This is the default. NoOptProduct retains the input structure as a point that is already on the reaction path (which generally means that it should have been previously optimized to a minimum). OptProduct may not be combined with BiMolecular.

Linear

Linear requests and NoLinear suppresses the linear search in Berny optimizations. The default is to use the linear search whenever possible.

TrustUpdate

TrustUpdate requests and NoTrustUpdate suppresses dynamic update of the trust radius in Berny optimizations. The default is to update for minima.

Newton

Use the Newton-Raphson step rather than the RFO step during Berny optimizations.

NRScale

NRScale requests that if the step size in the Newton-Raphson step in Berny optimizations exceeds the maximum, then it is to be scaled back. NoNRScale causes a minimization on the surface of the sphere of maximum step size [Golab83]. Scaling is the default for transition state optimizations and minimizing on the sphere is the default for minimizations.

Steep

Requests steepest descent instead of Newton-Raphson steps during Berny optimizations. This is only compatible with Berny local minimum optimizations. It may be useful when starting far from the minimum, but is unlikely to reach full convergence.

UpdateMethod=keyword

Specifies the Hessian update method. Keyword is one of: Powell, BFGS, PDBFGS, ND2Corr, OD2Corr, D2CorrBFGS, Bofill, D2CMix and None.

HFError

Assume that numerical errors in the energy and forces are those appropriate for HF and post-SCF calculations (1.0D-07 and 1.0D-07, respectively). This is the default for optimizations using those methods and also for semi-empirical methods.

FineGridError

Assume that numerical errors in the energy and forces are those appropriate for DFT calculations using the default grid (1.0D-07 and 1.0D-06, respectively). This is the default for optimizations using a DFT method and using the default grid (or specifying Int=FineGrid).

SG1Error

Assume that numerical errors in the energy and forces are those appropriate for DFT calculations using the SG-1 grid (1.0D-07 and 1.0D-05, respectively). This is the default for optimizations using a DFT method and Int(Grid=SG1Grid).

Availability

Analytic gradients are available for the HF, all DFT methods, CIS, MP2, MP3, MP4(SDQ), CID, CISD, CCD, CCSD, QCISD, CASSCF, and all semi-empirical methods.

The Tight, VeryTight, Expert, Eigentest and EstmFC options are available for the Berny algorithm only.

Optimizations of large molecules which have many very low frequency vibrational modes with DFT will often proceed more reliably when a larger DFT integration grid is requested (Int=UltraFine).

Related Keywords

IRC, IRCMax, Scan, Force, Frequency, Geom

Examples

Output from Optimization Jobs. The string GradGradGrad… delimits the output from the Berny optimization procedures. On the first, initialization pass, the program prints a table giving the initial values of the variables to be optimized. For optimizations in redundant internal coordinates, all coordinates in use are displayed in the table (not merely those present in the molecule specification section):

 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
 Berny optimization.    The opt. algorithm is identified by the header format & this line.
 Initialization pass.
                   ----------------------------
                   !    Initial Parameters    !
                   ! (Angstroms and Degrees)  !
--------------------                          ----------------------
! Name  Definition              Value          Derivative Info.    !
--------------------------------------------------------------------
! R1    R(2,1)                  1.             estimate D2E/DX2   !
! R2    R(3,1)                  1.             estimate D2E/DX2   !
! A1    A(2,1,3)              104.5            estimate D2E/DX2   !
--------------------------------------------------------------------

The manner in which the initial second derivative are provided is indicated under the heading Derivative Info. In this case the second derivatives will be estimated.

Each subsequent step of the optimization is delimited by lines like these:

GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
Berny optimization.
Search for a local minimum.
Step number   4 out of a maximum of  20

Once the optimization completes, the final structure is displayed:

Optimization completed.
   -- Stationary point found.
                    ----------------------------
                    !   Optimized Parameters   !
                    ! (Angstroms and Degrees)  !
--------------------                            --------------------
! Name  Definition              Value          Derivative Info.    !
--------------------------------------------------------------------
! R1    R(2,1)                  0.9892         -DE/DX =    0.0002 !
! R2    R(3,1)                  0.9892         -DE/DX =    0.0002 !
! A1    A(2,1,3)              100.004          -DE/DX =    0.0001 !
--------------------------------------------------------------------

The redundant internal coordinate definitions are given in the second column of the table. The numbers in parentheses refer to the atoms within the molecule specification. For example, the variable R1, defined as R(2,1), specifies the bond length between atoms 1 and 2. The energy for the optimized structure will be found in the output from the final optimization step, which precedes this table in the output file.

Compound Jobs. Optimizations are commonly followed by frequency calculations at the optimized structure. To facilitate this procedure, the Opt keyword may be combined with Freq in the route section of an input file, and this combination will automatically generate a two-step job.

It is also common to follow an optimization with a single point energy calculation at a higher level of theory. The following route section automatically performs an HF/6-31G(d,p) optimization followed by an MP4/6-31G(d,p) single point energy calculation :

# MP4/6-31G(d,p)//HF/6-31G(d,p) Test

Note that the Opt keyword is not required in this case. However, it may be included if setting any of its options is desired.

This structure is acetaldehyde with an OH substituted for one of the hydrogens in the methyl group; the first input line for ModRedundant creates a hydrogen bond between that hydrogen atom and the oxygen atom in the carbonyl group. Note that this adds only the bond between these two atoms The associated angles and dihedral angles could be added as well using the B action code:

3  8  B

Displaying the Value of a Desired Coordinate. The second input line for ModRedundant specifies the C-C=O bond angle, ensuring that its value will be displayed in the summary structure table for each optimization step.

Using Wildcards in Redundant Internal Coordinates. A distance matrix coordinate system can be activated using the following input:

The following input defines partial distance matrix coordinates to connect only the closest layers of atoms:

The following input sets up an optimization in redundant internal coordinates in which atoms N1 through Nn are frozen (such jobs may require the NoSymm keyword). Note that the lines containing the B action code will generate Cartesian coordinates for all of the coordinates involving the specified atom since only one atom number is specified:

The following input defines special “spherical” internal coordinates appropriate for molecules like C₆₀ by removing all dihedral angles from the redundant internal coordinates:

Additional examples are found in the section on relaxed PES scans below.

Performing Partial Optimizations. The following job illustrates the method for freezing variables during an optimization:

The central cluster (the first four atoms) will be optimized while the phenylthiolates are frozen.

Restarting an Optimization. A failed optimization may be restarted from its checkpoint file by simply repeating the route section of the original job, adding the Restart option to the Opt keyword. For example, this route section restarts a B3LYP/6-31G(d) Berny optimization to a second-order saddle point:

%Chk=saddle2
# Opt=(TS,Restart,MaxCyc=50) Test

The model chemistry and starting geometry are retrieved from the checkpoint file. Options specifying the optimization type and procedure are required in the route section for the restart job (e.g., TS in the preceding example). Some parameter-setting options can be omitted to use the same values are for the original job, or they can be modified for the restarted job, such as MaxCycle in the example. Note that you must include CalcFC to compute the Hessian at the first point of the restarted job. Second derivatives are computed only when this option is present in the route section of the restarted job, regardless of whether it was specified for the original job.

Reading a Structure from the Checkpoint File. Redundant internal coordinate structures may be retrieved from the checkpoint file with Geom=Checkpoint as usual. The read-in structure may be altered by specifying Geom=ModRedundant as well; modifications have a form identical to the input for Opt=ModRedundant:

[Type] N1 [N2 [N3 [N4]]] [Action [Params]] [[Min] Max]]

Locating a Transition Structure with the STQN Method. The QST2 option initiates a search for a transition structure connecting specific reactants and products. The input for this option has this general structure (blank lines are omitted):

Note that each molecule specification is preceded by its own title section (and separating blank line). If the ModRedundant option is specified, then each molecule specification is followed by any desired modifications to the redundant internal coordinates.

Gaussian will automatically generate a starting structure for the transition structure midway between the reactant and product structures, and then perform an optimization to a first-order saddle point.

The QST3 option allows you to specify a better initial structure for the transition state. It requires the two title and molecule specification sections for the reactants and products as for QST2 and also additional, third title and molecule specification sections for the initial transition state geometry (along with the usual blank line separators), as well as three corresponding modifications to the redundant internal coordinates if the ModRedundant option is specified. The program will then locate the transition structure connecting the reactants and products closest to the specified initial geometry.

                    ----------------------------
                    !   Optimized Parameters   !
                    ! (Angstroms and Degrees)  !
---------------------                          ----------------------
! Name  Definition    Value    Reactant  Product  Derivative Info.  !
-------------------------------------------------------------------
! R1    R(2,1)        1.0836    1.083     1.084    -DE/DX =    0.  !
! R2    R(3,1)        1.4233    1.4047    1.4426   -DE/DX =   -0.   !
! R3    R(4,1)        1.4154    1.4347    1.3952   -DE/DX =   -0.   !
! R4    R(5,3)        1.3989    1.3989    1.3984   -DE/DX =    0.   !
! R5    R(6,3)        1.1009    1.0985    1.0995   -DE/DX =    0.   !
! …                                                              !
-------------------------------------------------------------------

In addition to listing the optimized values, the table includes those for the reactants and products.

Performing a Relaxed Potential Energy Surface Scan. The Opt=ModRedundant option may also be used to perform a relaxed potential energy surface (PES) scan. Like the facility provided by Scan, a relaxed PES scan steps over a rectangular grid on the PES involving selected internal coordinates. It differs from Scan in that a constrained geometry optimization is performed at each point.

Relaxed PES scans are available only for the Berny algorithm. If any scanning variable breaks symmetry during the calculation, then you must include NoSymm in the route section of the job, since it may fail with an error.

Redundant internal coordinates specified with the Opt=ModRedundant option may be scanned using the S code letter: N1 N2 [N3 [N4]] S steps step-size. For example, this input adds a bond between atoms 2 and 3, specifying three scan steps of 0.05 Å each:

2 3 S 3 0.05

Wildcards in the ModRedundant input may also be useful in setting up relaxed PES scans. For example, the following input is appropriate for a potential energy surface scan involving the N1-N2-N3-N4 dihedral angle:

Examples of Using GICs

Basic GIC input. Here is an example of using the generalized internal coordinates defined by the user from scratch for the geometry optimization of the water molecule.

# HF opt=readallgic

Title

 0 1
O    0.0000    0.0000    0.0000
H    0.0000    0.0000    1.3112
H    1.0354    0.0000   -0.6225

R(1,2)
R(1,3)
HOH=A(2,1,3)

The atomic indexes 1, 2, and 3 refer to the oxygen atom, the first and the second hydrogen atom, respectively. The first and the second expression define the O-H bonds, and the third one defines the H-O-H valence angle (with the user-provided label “HOH”). An excerpt of the output with a table containing the initial values of the GICs is shown below.

                           ----------------------------
                           !    Initial Parameters    !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.3112         estimate D2E/DX2                !
 ! R2    R(1,3)                  1.2081         estimate D2E/DX2                !
 ! HOH   A(2,1,3)              121.015          estimate D2E/DX2                !
 --------------------------------------------------------------------------------

Note that the labels “R1” and “R2” above were assigned by default. The coordinates R1=R(1,2) and R2=R(1,3) are parsed as pure distances and given here in Angstroms, and the HOH=A(2,1,3) is a pure valence angle in degrees.

# HF opt=readallgic

Title 

 0 1
O    0.0000    0.0000    0.0000
H    0.0000    0.0000    1.3112
H    1.0354    0.0000   -0.6225

OHSym1=(R(1,2)+R(1,3))/sqrt(2)
OHSym2=(R(1,2)-R(1,3))/sqrt(2)
HOH=A(2,1,3)

The first and the second expression in the example above define the symmetrized O-H bonds, and the third one is the H-O-H valence angle.

                           ----------------------------
                           !    Initial Parameters    !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name   Definition             Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! OHSym1 GIC-1                  3.3664         estimate D2E/DX2                !
 ! OHSym2 GIC-2                  0.1377         estimate D2E/DX2                !
 ! HOH    A(2,1,3)             121.015          estimate D2E/DX2                !
 --------------------------------------------------------------------------------
 NOTE: GIC-type coordinates are in arbitrary units.

The coordinates OHSym1 and OHSym2 are parsed as generic GICs and therefore given here in arbitrary units. The units are actually Bohrs in this case because the 2^-1/2 factor is taken as dimensionless and the values of R(1,2) and R(1,3) are taken in Bohrs.

# HF opt=readallgic

Title

 0 1
O
H  1  1.3
H  1  1.2  2  120.

R12=SQRT[{X(2)-X(1)}^2+{Y(2)-Y(1)}^2+{Z(2)-Z(1)}^2]
R13=SQRT[{X(3)-X(1)}^2+{Y(3)-Y(1)}^2+{Z(3)-Z(1)}^2]
A0(Inactive)=DotDiff(2,1,3,1)/{R12*R13}
A213=ArcCos(A0)

The GIC input section above defines two bond distances and one valence angle expressed via Cartesian coordinates. The coordinate A0 is defined as the dot-product (DotDiff) of the vectors R→₁₂ and R→₁₃ divided by the product of their lengths, and it is selected as “inactive” (i.e., excluded from the geometry optimization). An excerpt of the output with a table containing the initial values of the GICs is shown below.

                           ----------------------------
                           !    Initial Parameters    !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R12   GIC-1                   2.4566         estimate D2E/DX2                !
 ! R13   GIC-2                   2.2677         estimate D2E/DX2                !
 ! A213  GIC-3                   2.0944         estimate D2E/DX2                !
 --------------------------------------------------------------------------------
 NOTE: GIC-type coordinates are in arbitrary units.

The values of R12, R13, and the dot-product are calculated using the Cartesian coordinates given in Bohrs. The GIC arbitrary units are Bohrs (for R12 and R13) and radians (for A213).