Keyword

Options:

ALPHA | The polarizability tensor is calculated.This is the default. | ||

BETA | The first hyperpolarizability is calculated. | ||

GAMMA | The second hyperpolarizability is calculated. |

ANALYTICAL | The polarizability is calculated analytically. This is the default. | ||

NIACPKS | The polarizability is calculated with the non-iterative coupled-perturbed Kohn-Sham method. | ||

NUMERICAL | The polarizability is calculated numerically with a finite-field method. |

DD | Dipole-dipole polarizabilities are calculated. This is the default. | ||

DQ | Dipole-quadrupole polarizabilities are calculated. Only valid in combination with the option ANALYTICAL. |

SHG | Calculate second harmonic generation. Only valid in combination with the options ANALYTICAL and W=Real. | ||

EOPE | Calculate electro-optical Pockels effect. Only valid in combination with the options ANALYTICAL and W=Real. | ||

OR | Calculate optical rectification. Only valid in combination with the options ANALYTICAL and W=Real. | ||

W=Real | Dynamical polarizability frequency (or wavelength) that can
be given in a.u., eV, cm, and nm by the unit
abbreviations AU, EV, CM, and NM, respectively. By default,
the field frequency is given in atomic units. The form
W1=Real is an equivalent input format. | ||

W2=Real | Second dynamical hyperpolarizability frequency. Input format
as for W=Real. | ||

EFISH | Activate the EFISH orientation. | ||

FFS=Real | Finite field strength for the polarizability calculation with the option NUMERICAL. | ||

TOL=Real | Threshold for numerical exchange-correlation kernel derivative pruning. Default value is 1.0. | ||

FALDA | The LDA kernel will be used in the response equation system. Note that this setting will apply to all response calculations in a run. | ||

GALDA | The LDA kernel derivative will be used for the hyperpolarizability response equation system. | ||

FDKERNEL | A finite difference kernel will be used in the response equation system. Note that this setting will apply to all response calculations in a run. |

In deMon2k polarizabilities can be calculated either analytically by auxiliary density perturbation theory (ADPT) [30,158], semi-numerically by the non-iterative coupled-perturbed Kohn-Sham (NIA-CPKS) method [37] or numerically by the finite-field method [36]. The method is selected with the options ANALYTICAL, NIACPKS or NUMERICAL. All three methods are available for RKS, UKS and ROKS. The mean polarizability and polarizability anisotropy are calculated in the principal axis system of the polarizability tensor as:

(23) | |||

(24) |

Dipole-quadrupole polarizabilities [242] can be calculated with the option ANALYTICAL or NIACPKS employing the DQ option of the POLARIZABILITY keyword. First hyperpolarizabilites, can be calculated with the options ANALYTICAL or NUMERICAL specifying BETA in the POLARIZABILITY keyword line.

DIPOLES GRID FINE SYMMETRY ON AUXIS (GEN-A2*) BASIS (TZVP-FIP1) VXCTYP AUXIS BLYP POLARIZABILITY BETA ANALYTICAL EFISH # Geometry Z-Matrix C1 O1 C1 LCO1 Constants LCO1 1.1281

In analytic first hyperpolarizability calculations the full tensor is calculated as the following output shows.

MOLECULE ORIENTATION FOR POLARIZABILITIES IN ANGSTROM NO. ATOM X Y Z Z-ATOM MASS TYPE 1 C1 0.000000 0.000000 -0.644365 6 12.011 QM 2 O1 0.000000 0.000000 0.483735 8 15.999 QM *** HYPERPOLARIZABILITY *** BETA TENSOR COMPONENTS XIJ 1 2 3 1 0.118052 0.097283 5.999359 2 0.097283 0.004124 -0.040942 3 5.999359 -0.040942 -0.133288 BETA TENSOR COMPONENTS YIJ 1 2 3 1 0.097283 0.004124 -0.040942 2 0.004124 -0.053564 5.749705 3 -0.040942 5.749705 -0.182612 BETA TENSOR COMPONENTS ZIJ 1 2 3 1 5.999359 -0.040942 -0.133288 2 -0.040942 5.749705 -0.182612 3 -0.133288 -0.182612 26.180178 HYPERPOLARIZABILITY TENSOR NORMS [A.U.] DIPOLAR BETA NORM : 29.38 QUADRUPOLAR BETA NORM : 5.44 TOTAL BETA TENSOR NORM: 29.88 AVERAGE FIRST HYPERPOLARIZABILITY: 22.76

In numerical first hyperpolarizabilty calculations only selected components
of the tensor are calculated. Therefore, the numerical calculations
are always performed in the so-called EFISH (Electric Field Induced Second Harmonic
generation) orientation. In it, the -axis of the molecule is oriented along the
permanent dipole moment of the system. The same holds for numerical second
hyperpolarizability, , calculations. In EFISH orientation, the mean first
and second hyperpolarizabilities are defined as:

(25) | |||

(26) |

Thus, the

MOLECULE ORIENTATION FOR POLARIZABILITIES IN ANGSTROM NO. ATOM X Y Z Z-ATOM MASS TYPE 1 C1 0.000000 0.000000 -0.644365 6 12.011 QM 2 O1 0.000000 0.000000 0.483735 8 15.999 QM *** FIRST HYPERPOLARIZABILITY *** INDUCED DIPOLE MOMENTS (IN A.U.) ELECTRIC FIELD X Y Z SCF CYCLES --------------------------------------------------------------------- Fz(-0.0100) 0.000000 -0.000000 -0.087547 12 Fz(-0.0100) Fz(-0.0100) 0.000000 0.000000 -0.244794 13 Fy(-0.0100) 0.000000 -0.123112 0.070726 14 Fy(-0.0100) Fy(-0.0100) -0.000000 -0.247706 0.071423 15 Fx(-0.0100) -0.123112 -0.000000 0.070726 14 Fx(-0.0100) Fx(-0.0100) -0.247706 -0.000000 0.071423 15 Fx(+0.0100) 0.123112 0.000000 0.070726 14 Fx(+0.0100) Fx(+0.0100) 0.247706 -0.000000 0.071423 15 Fy(+0.0100) -0.000000 0.123112 0.070726 14 Fy(+0.0100) Fy(+0.0100) -0.000000 0.247706 0.071423 15 Fz(+0.0100) 0.000000 0.000000 0.230419 11 Fz(+0.0100) Fz(+0.0100) 0.000000 0.000000 0.395391 12 FIRST HYPERPOLARIZABILITY [A.U.] BETA(XXX) = 0.00021 BETA(XYY) = -0.00000 BETA(XZZ) = 0.00000 BETA(YXX) = 0.00000 BETA(YYY) = -0.00000 BETA(YZZ) = 0.00000 BETA(ZXX) = 4.64573 BETA(ZYY) = 4.64570 BETA(ZZZ) = 25.74926 AVERAGE FIRST HYPERPOLARIZABILITY: 21.02

always refers to the EFISH orientation. As a consequence, analytical and numerical results can only be directly compared by using this orientation in both calculations!

Dynamical polarizabilities [243] and hyperpolarizabilities [244]
can only be calculated with the analytical ADPT approach, *i.e.* with the
option ANALYTICAL. In these calculations the option W=Real (or its alternative
form W1=Real) specifies the frequency (or wavelength) of the (first) external
field. It can be given in a.u., eV, cm, or nm by using the corresponding unit
abbreviation. By default W is set to zero. Note that for polarizabilities imaginary
frequencies are also possible [245].
They are defined in the input by real numbers with a leading
`i`, *i.e.*

POLARIZABILITY ALPHA W = i4.7257If for dynamical first hyperpolarizabilities only one frequency is specified either the second harmonic generation (SHG), the electro-optical Pockels effect (EOPE) or the optical rectification (OR) is calculated. These non-linear optical properties are characterized by the following frequency combinations for the dynamical tensor elements [246]:

SHG | = | = | = | ||||||||

EOPE | = | = | = | ||||||||

OR | = | = | = |

By default the SHG is calculated as with the following input line.

POLARIZABILITY BETA ANALYTICAL EFISH W=0.199 au

To calculate the EOPE use:

POLARIZABILITY BETA ANALYTICAL EFISH W=0.199 au EOPE

With the W2=Real option a second frequency for dynamical calculations can be explicitly specified in the input.

The default finite-field strength for the numerical polarizability calculations is 0.01 atomic units. With the option FFS, that field strength can be modified. Please note that the calculated polarizabilities are sensitive to both the finite field strength and the SCF convergence. With the FALDA and GALDA options the use of the LDA kernel and kernel derivative is requested, respectively, independent of the functional specified with the VXCTYPE keyword (see 4.2.1). With the FDKERNEL option a finite-difference kernel calculation [37] is requested. This permits static and dynamic ADPT polarizability calculations for all LDA and GGA functionals for which a potential is implemented. By default the FDKERNEL option is only activated for functionals for which no analytic ADPT kernel is available [247]. Note that the FALDA, GALDA and FDKERNEL settings apply to all response calculations in a deMon2k run.