Corrections to energy

The thermal corrections in the table are taken from the line labeled Thermal correction to energy in the Gaussian output. 

Flambaum, V.V. and Ginges, J.S.M. (2005) Radiative potential and calculations of QED radiative corrections to energy levels and electromagnetic amplitudes in many-electron atoms. Physical Review A, 72, 052115-1-052115-13. 

Recently we developed a new approach which improves the sensitivity to a variation of a by more than an order of magnitude [1,2]. The relative value of any relativistic corrections to atomic transition frequencies is proportional to a2. These corrections can exceed the fine structure interval between the excited levels by an order of magnitude (for example, an s-wave electron does not have the spin-orbit splitting but it has the maximal relativistic correction to energy). The relativistic corrections vary very strongly from atom to atom and can have opposite signs in different transitions (for example, in s-p and d-p transitions). Thus, any variation of a could be revealed by comparing different transitions in different atoms in cosmic and laboratory spectra. 

Coulomb-Breit interaction for two-electron atom is represented by the Feynman diagrams Fig.lc, d, e, f. In this case the corrections to energy are given by... 

Goudsmit and Uhlenbeck electron spin. Thomas spin-orbit energy. Heisenberg and Jordan relativistic correction to energy. Net result recovery of Sommerfeld energy levels, different quantum numbers. 

In what follows we will consider only the Feynman graphs that describe corrections to energy levels. Then we should retain only the graphs without outer photon lines. The graphs with outer photon lines describe the processes of photon absorption, emission or photon scattering for atomic electrons. The graphs without outer photon lines arrive first in the second-order of PT (they... 

The first-order corrections to energy and the zero-order wave functions, with expansion coefficients c, are obtained as the eigenvalues and eigenfunctions. Because the matrix V generally has p different eigenvalues, the degeneracy of the refer-... 

Then, by using geometry obtained without its following optimization for each point of IRC cmve were found corrections to energy, using MRMP2 method. For estimation of rate constant calculation of frequencies of normal mode vibrations in terms of MCSCF(14,11) method. To obtain thermodynamical fimctions frequencies of vibrations of ozone with MCSCF(12, 9) and olefins (MCSCF(2,2)). Value of k were found in terms of transition state theory ... 

B. J. McKenzie, I. P. Grant, P. H. Norring-ton. A Program to Calculate Transverse Breit and QED Corrections to Energy Levels in a Multiconfiguration Dirac-Fock Environment. Comp. Phys. Commun., 21 (1980) 233-246. 

Magnetic properties are calculated as the secoud-order correction to energy. Expanding the above equation till second order in f, one obtains... 

Early implementations of dispersion corrections in computational chemistry methods were realized in HF calculations. A similar approach was applied in SCC-DFTB (self-consistent charge density functional tight-binding method) [28, 32] and dispersion correction to energies computed with conventional DFT functional was described [33]. 

Equations (5.3), (5.7), and (5.8) form the starting point for a systematic perturbation theory analysis, whose deeper details need not concern us here (see V B, p. 16ff). In this approach, the NLS model //op is regarded as the unperturbed Hamiltonian, with known eigenfunction and energy eigenvalue eP" that are assumed to be well understood. The resonance-type corrections to energy (EP ), density (pnl), or other properties can then be expressed (analyzed or evaluated) in orderly fashion from the known properties of the model Lewis system. The NBO... 

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