Kohn-Sham perturbed

Table 1 Electric dipole polarizabilities of benzene and naphthalene in the coupled and uncoupled Kohn-Sham perturbation theory...

According to the variational principle, the ground state of the system is described by those electronic wavefunctions which minimize the Kohn-Sham functional. The presence of an external perturbation is represented by a perturbation functional, Ep, that is added to the unperturbed Kohn-Sham functional ... 

Because of the separation into a time-independent unperturbed wavefunction and a time-dependent perturbation correction, the time derivative on the right-hand side of the time-dependent Kohn-Sham equation will act only on the response orbitals. From this perturbed wavefunction the first-order response density follows as ... 

The combination of TDDFT with a QM/MM approach is, in principle, straightforward. The surrounding system of point charges modifies the electrostatic potential of the system, which enters the perturbation equations through the Kohn-Sham Hamiltonian Hks. This causes a change in the excitation wavelenghts which reflects the influence of the environment. 

We call the Fukui function / (r) the HOMO response. Equation 24.39 is demonstrated as follows. The PhomoW is the so-called Kohn-Sham Fukui function denoted as f (r) [32]. According to the first-order perturbation theory, one has... 

It is worth noting that screened response x/C r ) can be computed from the Kohn-Sham orbital wave functions and energies using standard first-order perturbation theory [3]... 

Few years later, Fuentealba and Cedillo [23] has shown that the variation of the Kohn-Sham FF with respect to the external perturbation depends on the knowledge on the highest occupied molecular orbital (HOMO) density and a mean energy difference of all of the occupied and unoccupied orbital. The quantity, mean energy difference, has been approximately interpreted as hardness. Under this approximation, it has been stated that the greater the hardness, the smaller the variation of the FF, under the external perturbation. This statement then signifies that the system will become less reactive as the hardness of the system increases due to the external perturbation. 

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... 

NBO analysis can be used to quantify this phenomenon. Since tire NBOs do not diagonalize the Fock operator (or tire Kohn-Sham operator, if the analysis is carried out for DFT instead of HF), when the Fock matrix is formed in the NBO basis, off-diagonal elements will in general be non-zero. Second-order perturbation tlieory indicates that these off-diagonal elements between filled and empty NBOs can be interpreted as the stabilization energies... 

A DFT-based third order perturbation theory approach includes the FC term by FPT. Based on the perturbed nonrelativistic Kohn-Sham orbitals spin polarized by the FC operator, a sum over states treatment (SOS-DFPT) calculates the spin orbit corrections (35-37). This approach, in contrast to that of Nakatsuji et al., includes both electron correlation and local origins in the calculations of spin orbit effects on chemical shifts. In contrast to these approaches that employed the finite perturbation method the SO corrections to NMR properties can be calculated analytically from... 

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