Coupled perturbed Kohn-Sham,

Using Neese s coupled-perturbed Kohn-Sham hybrid density functional (UPBEO, UBILYP) techniques, the gyromagnetic (g) and hyperfine tensor components of the thiophene-1,3,2-dithiazoly radical (TDTA) were computed and found to be in very good agreement with values from experimental determination <2006CPL(418)30>. 

The If1 coefficients corresponding to occupied-virtual orbital pairs can be obtained from the magnetic form of the coupled-perturbed Kohn-Sham (CPKS) equations... 

Hesselmann A, Jansen G (2002) Intermolecular induction and exchangeinduction energies from coupled-perturbed Kohn—Sham density functional theory. Chem Phys Lett 362 319—325... 

Kohn-Sham formalism, which suffers from the spin contamination problem, and on the sum-over-states or coupled perturbed Kohn-Sham approaches. In recent articles devoted to computations of elechonic g-tensors we advocated the use of an alternative approach, namely linear response theory based on the spin-restricted open-shell Kohn-Sham formalism, which is free from spin contamination problem (see Theory section). In the following we briefly review the applicability of this approach for some paramagnetic compounds. 

Unrestricted coupled perturbed Kohn-Sham calculations in gauge invariant atomic orbitals. [151]. Unrestricted coupled perturbed Kohn-Sham calculations. 

Complete Active Space (CAS) 141 configuration interaction singles (CIS) 89, 93-95 coupled cluster (CC) theory 140, 142 coupled perturbed Hartree-Fock (CPHF) 19 coupled perturbed Kohn-Sham (CPKS) 19 CPCM 9... 

However, it seems impossible to obtain the derivative exactly, because Eq. (4.48) contains the sum for all excitations created from a Kohn-Sham electron configuration. What makes it possible is the coupled perturbed Kohn-Sham method. 

In the coupled perturbed Kohn-Sham method, the first wavefunction derivatives are given by calculating the first derivatives of the orbitals in terms of perturbations. The Kohn-Sham method is based on the Slater determinant. Therefore, since the Kohn-Sham wavefunction is represented with orbitals, the corresponding first wavefunction derivatives are also described by the first derivatives of the orbitals. For simplicity, let us consider the Kohn-Sham-Roothaan equation in Eq. (4.13), which is a matrix equation using basis functions based on the Roothaan method. 

Using Eqs. (4.61) and (4.63), matrix U is calculated to give the response properties in terms of the uniform electric field dipole moments, polarizabilities, hyperpolarizabilities, and so forth. Equation (4.61) is called the coupled perturbed Kohn-Sham equation. Other response properties are calculated by solving Eq. (4.61) after setting the first derivative of the Fock operator, F, in terms of each perturbation. Note, however, that this method has problems in actual calculations similarly to the time-dependent response Kohn-Sham method. For example, using most functionals, this method tends to overestimate the electric field response properties of long-chain polyenes. 

The vector potential is also incorporated in the coupled-perturbed Kohn-Sham method. In this method, the following term is supplemented to matrix (F ) in Eq.(4.61) ... 

F. Neese. Metal and ligand hyperfine couplings in transition metal complexes The effect of spin-orbit coupling as studied by coupled perturbed Kohn-Sham theory. /. Chem. Phys., 118(9) (2003) 3939-3948. 

The polarizability and first hyperpolarizability of p-nitroaniline and its methyl-substituted derivatives have been calculated using a non-iterative approximation to the coupled-perturbed Kohn-Sham equation where the first-order derivatives of the field-dependent Kohn-Sham matrix are estimated using the finite field method" . This approximation turns out to be reliable with differences with respect to the fully coupled-perturbed Kohn-Sham values smaller than 1% and 5% for a and p, respectively. The agreement with the MP2 results is also good, which enables to employ this simplified method to deduce structure-property relationships. 

Kamiya M, Sekino H, Tsuneda T, Hirao K (2005) Nonlinear optical property calculations by the long-range-corrected coupled-perturbed Kohn-Sham method. J Chem Phys 122(23) 234111... 

Hesselmann, A., 8c Jansen, G. (2002b). Intermolecular induction and exchange-induction energies from coupled-perturbed Kohn-Sham density functional theory. Chemical Physics Letters, 362, 319-325. 

Shedge, S. V., Carmona-Espindola, J., Pal, S., Koster, A. M. (2010). Comparison of the auxiliary density perturbation theory and the noniterative approximation to the coupled perturbed Kohn-Sham method Case study of the polarizabilities of disubstituted azoarene molecules. Journal of Physical Chemistry A, 114, 2357. 

In principle, density functional theory calculations should be able to give answers that are more reliable than Hartree-Fock but at similar cost. Static a and can be calculated by finite field methods or by coupled perturbed Kohn-Sham theory (CPKS) and give answers that are broadly comparable with MP2. In 1986 Sennatore and Subbaswamy did some calculations of the dynamic polarizability and second hyperpolarizability of rare gas atoms, but there have been no calculations of frequency dependent polarizabilities or hyperpolarizabilities of molecules until very recently. 

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