Search results for "Kohn–Sham equations"
showing 10 items of 10 documents
Anharmonic vibrational frequency calculations for solvated molecules in the B3LYP Kohn–Sham basis set limit
2012
Abstract The solvent dependence of harmonic and anharmonic vibrational wavenumbers of water, formaldehyde and formamide was studied using the B3LYP method. The results obtained with the hierarchy of Jensen's polarization-consistent basis sets were fitted with two-parameter formula toward the B3LYP Kohn–Sham complete basis set (CBS) limit. Anharmonic corrections have been obtained by a second order perturbation treatment (VPT2) and vibrational configuration interaction (VCI) method. The solvent environment was treated according to the self-consistent reaction field polarizable continuum model (SCRF PCM) approach.
H2 O, H2 , HF, F2 and F2 O nuclear magnetic shielding constants and indirect nuclear spin-spin coupling constants (SSCCs) in the BHandH/pcJ-n and BHa…
2009
Good performance of segmented contracted basis sets XZP, where X = D, T, Q and 5, for obtaining H(2)O, H(2), HF, F(2) and F(2)O nuclear isotropic shielding constants in the BHandH Kohn-Sham basis set limit was shown. The results of two- and three-parameter complete basis set limit extrapolation schemes were compared with experimental results, earlier literature data and benchmark ab initio results. Similar convergence patterns of shieldings obtained from calculations using general purpose XZP basis sets and from polarization-consistent basis sets pcS-n and pcJ-n, where n = 0, 1, 2, 3 and 4, designed to accurately predict magnetic properties were observed. On the contrary, the SSCCs were mor…
Basis Set Convergence of Indirect Spin-Spin Coupling Constants in the Kohn-Sham Limit for Several Small Molecules
2012
The performance of more than 40 density functionals in predicting indirect spin-spin coupling constants (SSCCs) in the Kohn-Sham basis set limit was tested. For comparison, similar calculations were performed using the RHF, SOPPA, SOPPA(CC2), and SOPPA(CCSD) methods, and the results were estimated toward the complete basis set (CBS) limit. The SSCCs of nine small molecules (N(2), CO, CO(2), NH(3), CH(4), C(2)H(2), C(2)H(4), C(2)H(6), and C(6)H(6)) were calculated using the dedicated Jensen pcJ-n polarization-consistent basis sets and used for the CBS limit estimations within the Kohn-Sham limit. These CBS results were compared with calculations using the aug-cc-pVTZ-J basis set. Among the 4…
Prediction of water's isotropic nuclear shieldings and indirect nuclear spin–spin coupling constants (SSCCs) using correlation‐consistent and polariz…
2009
Density functional theory (DFT) was used to estimate water's isotropic nuclear shieldings and indirect nuclear spin-spin coupling constants (SSCCs) in the Kohn-Sham (KS) complete basis set (CBS) limit. Correlation-consistent cc-pVxZ and cc-pCVxZ (x = D, T, Q, 5, and 6), and their modified versions (ccJ-pVxZ, unc-ccJ-pVxZ, and aug-cc-pVTZ-J) and polarization-consistent pc-n and pcJ-n (n = 0, 1, 2, 3, and 4) basis sets were used, and the results fitted with a simple mathematical formula. The performance of over 20 studied density functionals was assessed from comparison with the experiment. The agreement between the CBS DFT-predicted isotropic shieldings, spin-spin values, and the experimenta…
Time-dependent Kohn-Sham approach to quantum electrodynamics
2010
We prove a generalization of the van Leeuwen theorem towards quantum electrodynamics, providing the formal foundations of a time-dependent Kohn-Sham construction for coupled quantized matter and electromagnetic fields. Thereby we circumvent the symmetry-causality problems associated with the action-functional approach to Kohn-Sham systems. We show that the effective external four-potential and four-current of the Kohn-Sham system are uniquely defined and that the effective four-current takes a very simple form. Further we rederive the Runge-Gross theorem for quantum electrodynamics.
Predicting the structure and vibrational frequencies of ethylene using harmonic and anharmonic approaches at the Kohn–Sham complete basis set limit
2016
In this work, regular convergence patterns of the structural, harmonic, and VPT2-calculated anharmonic vibrational parameters of ethylene towards the Kohn–Sham complete basis set (KS CBS) limit are demonstrated for the first time. The performance of the VPT2 scheme implemented using density functional theory (DFT-BLYP and DFT-B3LYP) in combination with two Pople basis sets (6-311++G** and 6-311++G(3df,2pd)), the polarization-consistent basis sets pc-n, aug-pc-n, and pcseg-n (n = 0, 1, 2, 3, 4), and the correlation-consistent basis sets cc-pVXZ and aug-cc-pVXZ (X = D, T, Q, 5, 6) was tested. The BLYP-calculated harmonic frequencies were found to be markedly closer than the B3LYP-calculated h…
Convergence of Nuclear Magnetic Shieldings in the Kohn-Sham Limit for Several Small Molecules.
2015
Convergence patterns and limiting values of isotropic nuclear magnetic shieldings were studied for several small molecules (N2, CO, CO2, NH3, CH4, C2H2, C2H4, C2H6, and C6H6) in the Kohn-Sham limit. Individual results of calculations using dedicated families of Jensen's basis sets (pcS-n and pcJ-n) were fitted toward the complete basis set limit (CBS) using a simple two-parameter formula. Several density functionals were used; calculated vibrational corrections (ZPV) applied; and, for comparison purposes, similar calculations performed using RHF, MP2, SOPPA, SOPPA(CCSD), and CCSD(T) methods and additionally, the aug-cc-pVTZ-J basis set. Finally, the CBS estimated results were critically com…
From correlation-consistent to polarization-consistent basis sets estimation of NMR spin–spin coupling constant in the B3LYP Kohn–Sham basis set limit
2008
Abstract Based on B3LYP spin–spin coupling constants (SSCC) of several molecules calculated with cc-pV x Z, cc-pCV x Z, cc-pCV x Z-sd and cc-pCV x Z-sd+ t basis sets, a reasonably fit, using the two-parameter formula, to the Kohn–Sham complete basis set limit (CBS) is shown. Improvement in the CBS values going from cc-pV x Z to the most elaborated cc-pCV x Z-sd+ t basis set family is observed: standard deviation for all data drops from 33.7 to 23.1, and from 6.0 to 4.8 Hz after excluding problematic 1 J (F,H) and 1 J (F,C). Calculation of water’s 1 J (OH) using B3LYP/cc-pCV x Z and B3LYP/pcJ- n significantly improved the FC term convergence.
Kohn–Sham energy decomposition for molecules in a magnetic field
2018
We study the total molecular electronic energy and its Kohn–Sham components within the framework of magnetic-field density-functional theory (BDFT), an alternative to current-dependent density-functional theory (CDFT) for molecules in the presence of magnetic fields. For a selection of closed-shell dia- and paramagnetic molecules, we investigate the dependence of the total electronic energy and its Kohn–Sham components on the magnetic field. Results obtained from commonly used density-functional approximations are compared with those obtained from Lieb optimizations based on magnetic-field dependent relaxed coupled-cluster singles-and-doubles (CCSD) and second-order Moller–Plesset (MP2) den…
Kohn-Sham Decomposition in Real-Time Time-Dependent Density-Functional Theory An Efficient Tool for Analyzing Plasmonic Excitations
2017
The real-time-propagation formulation of time-dependent density-functional theory (RT-TDDFT) is an efficient method for modeling the optical response of molecules and nanoparticles. Compared to the widely adopted linear-response TDDFT approaches based on, e.g., the Casida equations, RT-TDDFT appears, however, lacking efficient analysis methods. This applies in particular to a decomposition of the response in the basis of the underlying single-electron states. In this work, we overcome this limitation by developing an analysis method for obtaining the Kohn-Sham electron-hole decomposition in RT-TDDFT. We demonstrate the equivalence between the developed method and the Casida approach by a be…