Relativistic quantum chemistry and rigorous variational analysis

Abstract

A brief review of relativistic quantum chemistry is given here. Relativistic effects and their importance in chemistry are discussed. An outline of different theoretical aspects is presented. Aspects of variation techniques relevant to relativistic calculations are discussed in detail. These involve the derivation of min-max theorems for Dirac, Dirac-Hartree-Foek and Dirac-Coulomb calculations. The consequence of relativistic Hamiltonians being unbounded are also discussed for other lines of investigation. The upper bounds derived are physically interpreted. Sample Dirac-Hartree-Fock results for the Be atom, calculated using both STO and GTO bases for the nonrelativistic orbitals and the upper components of the relativistic orbitals, are given. The inadequacy of the so-called kinetically balanced basis set is discussed and illustrated with these results. The importance of the variational or dynamical balance and hence the merit of the LCAS-MS scheme is pointed out. The possibility of calculating quantum etectrodynamical pair energy from relativistic configuration interaction calculations on a two-electron atom is discussed and exemplified.The present status of relativistic molecular calculations is briefly reviewed. Conclusions on the aspects of variational analysis and molecular calculations are enclosed.

Solution of the Dirac equation using the Rayleigh-Ritz method: Flexible basis coupling large and small components. Results for one-electron systems

“…Variationally optimum values for ζ are obtained by the Rayleigh−Ritz variational method. The same basis set approximation as in [49] is employed. The values for principal quantum numbers are determined by,…”

Antioxidant novel activities of curcumin complexes with Mg(II), Ca(II), Cu(II), Cr(III) and Se(IV) metal ions: synthesis and spectral studies

“…For the curcumin-free ligand, the FTIR spectrum shown in Figure 1A curcumin and Table 1 showed a band at 3500 cm -1 due to O-H phenolic group and vibrational motion of (C=C) aromatic appeared at 1427 cm -1 and for ν(C=C) aliphatic appeared at 1504 cm -1 . Other bands appeared at (720 and 807 cm -1 ) assigned to the aromatic stretching vibrations of (-C=CH) [30,31]. At 1271 cm -1 , an intense band appeared due to the OH phenolic group's δ (C-O) bending vibration.…”

A multireference coupled cluster theory based on quantum electrodynamics: Physical aspects of open-shell treatment

“…A trial square-integrable spinor can be written as a linear combination of the eigenvectors of both positive energy (usually representing bound state components only) and negative energy (spurious solutions). This leads to the possibility of variation collapse [37] and a min-max principle for solving the involved wave equation [23], [25], [38][39][40][41][42].…”

“…The 1-pair (and 2-pair) term(s) appear(s) when the all-energy eigenvectors are considered (AERCI), that is, (spurious) negative energy solutions from the DF are included to obtain de-excitations from the ground state configuration in the RCI. The AERCI corresponds to a many-electron min-max procedure, and the (AERCI -PERCI) energy difference was shown [38][39] to be in excellent agreement with an analytical estimate made by Sucher of the 1-pair energy for helium-like species when Z ≤ 0.2 [43]. The vacuum polarization effect on energy is fundamentally a correlation effect, and it can be realized from the cluster operator technique if one considers the more complete Coulomb interaction while exploring the influence of a more detailed matter cluster.…”