Gaussian 03 Online Manual
Last update: 2 October 2006


This method keyword requests that the dipole electric field polarizabilities (and hyperpolarizabilities, if possible) be computed. No geometry change or derivatives are implied, but this keyword may be combined in the same job with numerical differentiation of forces by specifying both Freq and Polar in the route section. Freq and Polar may not be combined for methods lacking analytic gradients (MP4(SDTQ), QCISD(T), CCSD(T), BD, and so on). Note that Polar is done by default when second derivatives are computed analytically.

Normally, polarizabilities and hyperpolarizabilities are computed using static frequencies. However, frequency-dependent polarizabilities and hyperpolarizabilities [220,221,222,224,225] may be computed by including CPHF=RdFreq in the route section and specifying the desired frequency in the input file.

Optical rotations [261,262,263,264,265,266,550,551,552,553] may also be predicted via the OptRot option [223,267,268,269,270,271,305,554].

Perform optical rotation calculation.

Do extra frequency-dependent CPHF for dc-SHG (direct current second harmonic generation) hyperpolarizabilities. This option implies CPHF=RdFreq as well.

Specifies the step size in the electric field to be 0.0001N atomic units.

Analytically compute the polarizability and, if possible, the hyperpolarizability. This is possible for RHF and UHF and MP2 for which it is the default. The polarizability is always computed during analytic frequency calculations.

Numerically differentiate analytic polarizabilities to produce hyperpolarizabilities.

Computes the polarizability as a numerical derivative of the dipole moment (itself the analytic derivative of the energy, of course, not the expectation value in the case of MP2 or CI energies). The default for methods for which only analytic first derivatives are available.

Requests double numerical differentiation of energies to produce polarizabilities. EnergyOnly, a synonym for EnOnly, is a misnomer, since analytic first derivatives will also be differentiated twice, to produce hyperpolarizabilities, when they are available.

Restarts a numerical polarizability calculation from the checkpoint file. A failed Polar calculation may be restarted from its checkpoint file by simply repeating the route section of the original job, adding the Restart option to the Polar keyword. No other input is required.

Compute the dipole polarizabilities (this is the default).

Polarizabilities and hyperpolarizabilities will be automatically computed for HF and MP2. Polar will compute polarizabilities only, and Polar=EnOnly will produce both polarizabilities and hyperpolarizabilities for CIS, MP2, MP3, MP4(SDQ), CID, CISD, CCD, CCSD, QCISD, CASSCF and DFT methods. Polar will produce only polarizabilities for all other methods (for which no analytic derivatives are available, making EnOnly the default). Note that Polar is not available for any semi-empirical method.

Freq CPHF=RdFreq

Frequency-Dependent Properties. The following job will compute frequency-dependent polarizabilities and hyperpolarizabilities using ω=0.1 Hartrees:

# Polar CPHF=RdFreq HF/6-31G(d)

Frequency-dependent calculation: w=0.1

Molecule specification


Performing a frequency-dependent Polar calculation results in the results for the specified frequency following those for the static case within the output. For example, here are the polarizability values for a frequency-dependent job (ω=0.1 Hartree):

SCF Polarizabilityfor W=     0.000000:
                1                2                 3
     1  0.482729D+01   
     2  0.000000D+00    0.112001D+02 
     3  0.000000D+00    0.000000D+00       0.165696D+02
Isotropic polarizability for W=    0.000000             10.87 Bohr**3
SCF Polarizability for W=    0.100000: 
                1               2                 3
     1  0.491893D+01
     2  0.000000D+00    0.115663D+02
     3  0.000000D+00    0.000000D+00       0.171826D+02 
Isotropic polarizability for W=     0.100000            11.22 Bohr**3.

A static polarizability calculation would include only the first section. Similar output follows for hyperpolarizabilities and additional properties.

Optical Rotations. Here is the key part of the output for optical rotations jobs (OptRot option). In this case, we have performed a frequency-dependant calculation by including CPHF=RdFreq in the route section and specified a frequency of 500 nm:

w=    0.000000 a.u., Optical Rotation Beta=      1.2384 au. 
Molar Mass = 74.4103 grams/mole,[Alpha]D =  643.30 deg. 
G' tensor for W=    0.091127: 
-27.88112715  8.27183975  58.48555729 
-7.74920313   9.64293589  28.50024234 
-14.62301919  4.52918305  10.26760578 
w=     0.091127 a.u., Optical Rotation Beta=     2.6569 au. 
Molar Mass = 74.4103 grams/mole, [Alpha] ( 5000.0 A) = 1917.10 deg. 

The static results are listed first in the output (ω=0.0), followed by those for the specified frequency. The specific rotation value is highlighted in the output.