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 bothFreqandPolarin the route section.FreqandPolarmaynotbe combined for methods lacking analytic gradients (MP4(SDTQ), QCISD(T), CCSD(T), and so on). Note thatPolaris done by default when second derivatives are computed analytically.
The polarizability and hyperpolarizability are presented in the output in the standard orientation in lower triangular and lower tetrahedral order, respectively: αxx, αxy, αyy, αxz, αyz, αzzand βxxx, βxxy, βxyy, βyyy, βxxz, βxyz, βyyz, βxzz, βyzz, βzzz.
Normally, polarizabilities and hyperpolarizabilities are computed using static frequencies. However, frequency-dependent polarizabilities and hyperpolarizabilities[Olsen85,Sekino86,Rice90,Rice91,Rice92]may be computed by includingCPHF=RdFreqin the route section and specifying the desired frequency in the input file.
Optical rotations[Rosenfeld28,Condon37,Eyring44,Buckingham67,Buckingham68,Atkins69,Barron71,Charney79,Amos82,Jorgensen88]may also be predicted via theOptRotoption[Karna91,Helgaker94,Pedersen95,Kondru98,Stephens01,Mennucci02,Ruud02,Stephens02a,Stephens03]. See[Stephens05,Wilson05,Stephens08]for example applications.
Raman and ROA intensities can be calculated separately from calculation of the force constants and normal modes, to facilitate using a larger basis for these properties as recommended in[Cheeseman11a]. The keywordPolar=Raman(orPolar=ROA) requests that the force constants be picked up from the checkpoint file (i.e., from a previousFreqcalculation) and new polarizability derivatives (and the other two tensor derivatives for ROA) be computed and combined with the force constants in predicting intensities and spectra. Test job931provides an example of a two-step ROA calculation.
OptRot
Perform optical rotation calculation. UseCPHF=RdFreqto specify the desired frequencies. Available for HF and DFT only. This option cannot be combined withNMR. IncludeIOp(10/46=7)in the route section to include the dipole-quadrupole contribution to the dipole-magnetic dipole polarizability in order to compute the full optical rotation tensor[Pedersen95,Barron04]; the latter will be labeled asOptical Rotation G’ tensorin the output. Note that doing so does not change the optical rotation.
DCSHG
Do extra frequency-dependent CPHF for dc-SHG (direct current second harmonic generation) hyperpolarizabilities. This option impliesCPHF=RdFreqas well.
Gamma
Equivalent toPolar=(DCSHG,Cubic)to do 2nd hyperpolarizabilities.
Analytic
Analytically compute the polarizability and the hyperpolarizability when analytic third derivatives are available. This option is the default for method with analytic second derivatives: RHF and UHF, CASSCF, CIS, MP2 and DFT methods. Note that the polarizability is always computed during analytic frequency calculations.
DoubleNumer
Computes hyperpolarizabilities in addition to polarizabilities for methods with analytic gradients (first derivatives). Computes polarizabilities by double numerical differentiation of the energy for methods without analytic derivatives.EnOnlyis a synonym forDoubleNumer.
Cubic
Numerically differentiate analytic polarizabilities to produce hyperpolarizabilities. Applicable only to methods having analytic frequencies but no analytic third derivatives.
Numerical
Computes the polarizability as a numerical derivative of the dipole moment (it is 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 derivative gradients are available.
Step=N
Specifies the step size in the electric field to be 0.0001Natomic units (applies to numerical differentiation).
Restart
Restarts anumericalcalculation from the checkpoint file. A failedPolarcalculation may be restarted from its checkpoint file by simply repeating the route section of the original job, adding theRestartoption to thePolarkeyword. No other input is required.
Susceptibility
Compute magnetic susceptibility as well as other properties (seeNMR). Available for HF and DFT only.
TwoPoint
When computing numerical derivatives, make two displacements in each coordinate. This is the default.FourPointwill make four displacements but only works with Link 106 (Polar=Numer). Not valid withPolar=DoubleNumer.
Dipole
Compute the dipole polarizabilities (the default).
The following table summarizes the options toPolarthat are required to compute polarizabilities and hyperpolarizabilities for the available methods.
| Methods | Polarizability | Hyperpolarizability | ||
| HF, DFT methods (including analytic 3rd derivatives) | Polar(defaults toAnalytic) | Polar(defaults toAnalytic) | ||
| Other methods with analytic frequencies (MP2, CIS, …) | Polar(defaults toAnalytic) | Polar=Cubic | ||
| Methods with analytic gradients (CCSD, BD, …) | Polar(defaults toNumeric) | Polar=DoubleNumer | ||
| Methods without analytic derivatives (CCSD(T), …) | Polar(defaults toDoubleNumer) | N/A |
Frequency-dependent polarizabilities and hyperpolarizabilities (i.e.,Polar CPHF=RdFreq) are available only for HF and DFT methods.
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=0.1Molecule specification0.1
Performing a frequency-dependentPolarcalculation produces 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 Polarizability for 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 (OptRotoption). In this case, we have performed a frequency-dependent calculation by includingCPHF=RdFreqin the route section and specified a frequency of 589.3 nm:
Dipole-magnetic dipole polarizability for W= 0.077318: 1 2 3 1 -0.428755D+01 -0.175571D+01 0.000000D+00 2 -0.552645D+01 0.987070D+01 0.000000D+00 3 0.000000D+00 0.000000D+00 -0.676292D+00 w= 0.077318 a.u., Optical Rotation Beta= -1.6356 au. Molar Mass = 172.2694 grams/mole,[Alpha] ( 5893.0 A) = -366.99 deg.
The specific rotation value is highlighted in the example output.
Last update: 10 March 2014