Freq Keyword
Last Update: 6/26/2001

DESCRIPTION

This calculation type keyword computes force constants and the resulting vibrational frequencies. Intensities are also computed. By default, the force constants are determined analytically if possible (for RHF, UHF, MP2, CIS, all DFT methods, and CASSCF), by single numerical differentiation for methods for which only first derivatives are available (MP3, MP4(SDQ), CID, CISD, CCD, QCISD, and all semi-empirical methods), and by double numerical differentiation for those methods for which only energies are available. When frequencies are done analytically, polarizabilities are also computed automatically; when numerical differentiation is required, polarizabilities must be explicitly requested using the Polar keyword (e.g., QCISD Freq Polar).

The VCD option may be used to compute the vibrational circular dichroism (VCD) intensities in addition to the normal frequency analysis [313].

Vibrational frequencies are computed by determining the second derivatives of the energy with respect to the Cartesian nuclear coordinates and then transforming to mass-weighted coordinates. This transformation is only valid at a stationary point! Thus, it is meaningless to compute frequencies at any geometry other than a stationary point for the method used for frequency determination. For example, to compute 3-21G frequencies at a STO-3G optimized geometry produces meaningless results. It is also incorrect to compute frequencies for a correlated method using frozen-core at a structure optimized with all electrons correlated, or vice-versa. The recommended practice is to compute frequencies following a previous geometry optimization using the same method. This may be accomplished automatically by specifying both Opt and Freq within the route section for a job.

Note also that the coupled perturbed Hartree-Fock (CPHF) method used in determining analytic frequencies is not physically meaningful if a lower energy wavefunction of the same spin multiplicity exists. Use the Stable keyword to test the stability of Hartree-Fock and DFT wavefunctions.

The keyword Opt=CalcAll requests that analytic second derivatives be done at every point in a geometry optimization. Once the requested optimization has completed all the information necessary for a frequency analysis is available. Therefore, the frequency analysis is performed and the results of the calculation are archived as a frequency job.

OPTIONS

VCD
Compute the vibrational circular dichroism (VCD) intensities in addition to the normal frequency analysis [313]. This option is valid for SCF and DFT methods.

Raman
Compute Raman intensities in addition to IR intensities. This is the default for SCF frequency calculations. It may be specified for DFT and MP2 calculations in order to produce Raman intensities by numerical integration.

NoRaman
Skips the extra steps required to compute the Raman intensities during analytic frequency calculations, saving 10-30% in CPU time. This option is operative only for the HF method.

ReadIsotopes
Specify alternate temperature, pressure, and/or isotopes (the defaults are 298.15 K, 1 atmosphere, and the most abundant isotopes). This information appears in a separate input section having the format:

temp pressure [scale] -- Must be real numbers.
isotope mass for atom 1
isotope mass for atom 2
...
isotope mass for atom n

where temp, pressure, and scale are the desired temperature, pressure, and an optional scale factor for frequency data when used for thermochemical analysis (the default value of 1/1.12 (approx. 0.8929) if scale is omitted or set to 0.0). The remaining lines hold the isotope masses for the various atoms in the molecule, arranged in the same order as they appeared in the molecule specification section. If integers are used to specify the atomic masses, the program will automatically use the corresponding actual exact isotopic mass (e.g., 18 specifies O¹⁸, and Gaussian 98 uses the value 17.99916).

ReadFC
Requests that the force constants from a previous frequency calculation be read from the checkpoint file, and the normal mode and thermochemical analysis be repeated, presumably using a different temperature, pressure, or isotopes, at minimal computational cost. Note that since the basis set is read from the checkpoint file, no general basis should be input.

HPModes
Include the high precision format (to five figures) vibrational frequency eigenvectors in the frequency output in addition to the normal three-figure output.

Analytic
This specifies that the second derivatives of the energy are to be computed analytically. This option is available only for RHF, UHF, CIS, CASSCF, MP2, and all DFT methods, and it is the default for those cases.

Numerical
This requests that the second derivatives of the energy are to be computed numerically using analytically calculated first derivatives. It can be used with any method for which gradients are available and is the default for those for which gradients but not second derivatives are available. Freq=Numer can be combined with Polar=Numer in one job step.

EnOnly
This requests double numerical differentiation of energies to produce force constants. It is the default and only choice for those methods for which no analytic derivatives are available. This option is not available for the restricted open shell (RO) methods, for the semi-empirical methods, or for the CI methods. EnergyOnly is a synonym for EnOnly.

Cubic
Requests numerical differentiation of analytic second derivatives to produce third derivatives.

Step=N
Specifies the step-size for numerical differentiation to be 0.0001*N (in Angstroms unless Units=Bohr has been specified). If Freq=Numer and Polar=Numer are combined, N also specifies the step-size in the electric field. The default is 0.001 Å for Hartree-Fock and correlated Freq=Numer, 0.005 for GVB and CASSCF Freq=Numer, and 0.01 Å for Freq=EnOnly.

Restart
This option restarts a numerical frequency calculation after the last completed geometry (analytic frequency calculations are not restartable). A failed numerical frequency job may be restarted from its checkpoint file by simply repeating the route section of the original job, adding the Restart option to the Freq keyword. No other input is required.

Projected
For a point on a mass-weighted reaction path (IRC), compute the projected frequencies for vibrations perpendicular to the path. For the projection, the gradient is used to compute the tangent to the path. Note that this computation is very sensitive to the accuracy of the structure and the path [303]. Accordingly, the geometry should be specified to at least 5 significant digits. This computation is not meaningful at a minimum.

Hindered
Requests the identification of internal rotation modes during the harmonic vibrational analysis {Ayala, 1998 #448}. If any normal modes are identified as internal rotation, hindered or free, the thermodynamic functions are corrected. The identification of the rotating groups is made possible by the use of redundant internal coordinates. Thus, redundant internal coordinates must be used for the Hindered option to function properly. Because some structures, such as transition states, may have a specific bonding pattern not automatically recognized, the set of redundant internal coordinates may need to be altered via the Geom=Modify keyword.

If the force constants are available on a previously generated checkpoint file, additional vibrational/internal rotation analyses may be performed by specifying Freq=(ReadFC,Hindered). Since Opt=CalcAll automatically performs a vibrational analysis on the optimized structure, Opt=(CalcAll,Hindered) may also be used.

Read Info
Specify parameter values for a Freq=Hindered calculation (default values are automatically assigned by the program) via the additional input lines below:

VMax
J K N1 N2 N3                            Repeated as needed.
...                                     Blank line terminates input.

AVAILABILITY

Analytic frequencies are available for the HF, DFT, MP2, CIS and CASSCF methods. Numerical frequencies are available for MP3, MP4(SDQ), CID, CISD, CCD and QCISD.

RELATED KEYWORDS

Polar, Opt, Stable

The following two-step job contains an initial frequency calculation followed by a second thermochemistry analysis using a different temperature, pressure, and selection of isotopes:

%Chk=freq
# HF/6-31G(d,p) Freq Test

Frequencies for test 34

molecule specification

--Link1--
%Chk=freq
%NoSave
# HF/6-31G(d,p) Freq(ReadIso,ReadFC) Geom=Check Test

Repeat at 300 K

0,1

300.0 1.0
16
 2
 3
 ...

Note also that the freqchk utility (described in chapter 5) may be used to rerun the thermochemical analysis for the frequency data stored in a Gaussian 98 checkpoint file.

The basic components of the output from a frequency calculation are discussed in detail in chapter 4 of Exploring Chemistry with Electronic Structure Methods304

You may be surprised to see output that looks like it belongs to a geometry optimization at the beginning of a frequency job:

 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
 Berny optimization.
 Initialization pass.

Link 103, which performs geometry optimizations, is executed at the beginning and end of all frequency calculations. This is so that the quadratic optimization step can be computed using the correct second derivatives. Occasionally an optimization will complete according to the normal criterion using the approximate Hessian matrix, but the step size is actually larger than the convergence criterion when the correct second derivatives are used. The next step is printed at the end of a frequency calculation so that such problems can be identified. If you think this concern is applicable, use Opt=CalcAll instead of Freq in the route section of the job, which will complete the optimization if the geometry is determined not to have fully converged (usually, given the full second derivative matrix near a stationary point, only one additional optimization step is needed), and will automatically perform a frequency analysis at the final structure.

Specifying #P in the route section produces some additional output for frequency calculations. Of most importance are the polarizability and hyperpolarizability tensors (they still may be found in the archive entry in normal print-level jobs). They are presented in lower triangular and lower tetrahedral order, respectively (i.e., a_XX, a_XY, a_YY, a_XZ,a_YZ,a_ZZ and b_XXX, b_XXY, b_XYY, b_YYY, b_XXZ, b_XYZ,b_YYZ,b_XZZ,b_YZZ, b_ZZZ), in the standard orientation:

Dipole        = 2.37312183D-16 -6.66133815D-16 -9.39281319D-01
Polarizability= 7.83427191D-01  1.60008472D-15  6.80285860D+00
               -3.11369582D-17  2.72397709D-16  3.62729494D+00
HyperPolar    = 3.08796953D-16 -6.27350412D-14  4.17080415D-16
                5.55019858D-14 -7.26773439D-01 -1.09052038D-14
               -2.07727337D+01  4.49920497D-16 -1.40402516D-13
               -1.10991697D+01

#P also produces a bar-graph of the simulated spectra for small cases.

Thermochemistry analysis follows the frequency and normal mode data. The zero-point energy output in Gaussian 98 has been expanded over that produced by previous versions:

 Zero-point correction=                   .023261 (Hartree/Particle)
 Thermal correction to Energy=            .026094
 Thermal correction to Enthalpy=          .027038
 Thermal correction to Gibbs Free Energy= .052698
 Sum of electronic and zero-point Energies=   -527.492585

 Sum of electronic and thermal Energies=      -527.489751
 Sum of electronic and thermal Enthalpies=    -527.488807
 Sum of electronic and thermal Free Energies= -527.463147

The raw zero-point energy correction and the thermal corrections to the total energy, enthalpy, and Gibbs free energy (all of which include the zero-point energy) are listed, followed by the corresponding corrected energy. The analysis uses the standard expressions for an ideal gas in the canonical ensemble. Details can be found in McQuarrie [238] and other standard statistical mechanics texts. In the output, the various quantities are labeled as follows: E=(Thermal) contributions to the thermal energy correction, CV=constant volume molar heat capacity, S=entropy, and Q=partition function.

The thermochemistry analysis treats all modes other than the free rotations and translations as harmonic vibrations. For molecules having hindered internal rotations, this can produce slight errors in the energy and heat capacity at room temperatures and can have a significant effect on the entropy. The contributions of any very low frequency vibrational modes are listed separately so that if they are group rotations and high accuracy is needed, their harmonic contributions can be subtracted from the totals, and their correctly computed contributions included. Expressions for hindered rotational contributions to these terms can be found in Benson [239]. The partition functions are also computed, with both the bottom of the vibrational well and the lowest (zero-point) vibrational state as reference.