Sambhu Nath Datta

Electrodynamical coupled cluster (CC) methodologies have been formulated employing standard QED Hamiltonian that is written in Coulomb gauge while using the DF and the MCDF pictures of the matter field for closed-shell and open-shell cases respectively. The general methodology employs a radiative cluster, pure matter clusters and their pair modifications, and a number state distribution of photons in thermal equilibrium. The closed-shell treatment relies on the customary CC approach. For open shells, QED and electron correlation through CC are treated on the same footing. An averaging over the radiation state is done to generate Lamb, Breit and hyperfine interactions from the radiative cluster. Because of the thermal distribution, it leaves a residual transverse interaction that may modify the static correlation in open shells. Dynamical correlation effects are determined next by using the exponential matter cluster in traditional ways of single- and multi-reference CC. When the matter cluster is extended to include de-excitations to negative-energy levels, vacuum polarization effects are generated from the pair part of Coulomb interaction. The dynamical correlation energy includes relativistic corrections as well as QED contributions, namely, Lamb, Breit, hyperfine and pair energy. This work has three novelties: (i) QED interactions (Lamb, Breit and hyperfine) are obtained from a single procedure based on the radiative cluster; (ii) pair energy is determined from an extended matter cluster formalism; and (iii) additional correlation energy can be had from radiative effects and pair terms, while the option for higher order pair energy in high-Z atoms is kept open. The open-shell formalism has one more novelty in finding an additional static correlation in certain cases when the radiation is not isotropic.

The all-temperature magnon (ATM) theory [Datta and A. Panda, J. Phys. Condens. Matter 21, 336003 (2009)] has been used to analyze the temperature dependence of magnetization and internal energy components of a mono-domain ferromagnetic solid. One impact of the ATM formulation is that calculated critical exponents are in better agreement with experiments than their counterparts from mean-field and critical phenomenon theories. These exponents can vary from one ferromagnet to another of similar symmetry and dimensionality but differing in spin and can be field-dependent. The ATM finding is that exponent β depends on spin and increases as T approaches TC, whereas the exponent γ is weakly dependent on spin and the applied field but relies on crystal symmetry. The main thrust of the present work has been to derive the thermally averaged spin-center force constants in terms of the baseline related (solid) and exchange-cum-field mediated (magnetic) components and to formulate phonon frequencies and their modifications by magnon–phonon coupling. The derived expressions are suitable for correct quantum chemical evaluation. A detailed calculation on different spin configurations at varying geometries is still hardly possible and beyond the scope of the present work that emphasizes the correctness of formulas and has the significance of explaining properties. The phonon frequency shift due to lattice expansion is always negative. It is also clarified that frequency modification by the magnon–phonon interaction is negative for certain phonon branches near TC, and the ratio of frequency modification and phonon frequency is approximately proportional to the ratio of curvatures of involved energy surfaces.

The all-temperature magnon (ATM) theory [J. Phys. Condens. Matter 21, 336003/1-14, 2009] has been used to analyze the temperature dependence of magnetization as well as the internal energy components of a mono-domain ferromagnetic solid. The critical exponents have been in better agreement with experiment than their mean-field theory and critical phenomenon theory counterparts, and unlike in the latter theories, vary from one ferromagnet to another. Expressions have been derived for the thermally averaged spin-center force constants and their break-up in terms of the base-line related (solid) and exchange-cum-field mediated (magnetic) components. These components give rise to expressions for phonon frequencies and their modifications by magnon-phonon coupling. The derived expressions are suitable for a correct quantum chemical evaluation of the involved properties. A detailed numerical calculation using spin configurations at varying crystal geometries is hardly possible even today and beyond the scope of the present work. The focus here is on the correctness and explaining the trends of properties. It has been shown that the frequency modification by magnon-phonon interaction can be negative for certain phonon branches near the ferromagnetic transition temperature. Also, the ratio of frequency modification and phonon frequency is approximately proportional to the ratio of curvatures of the involved energy surfaces.

This work takes a new look at the spin alternation rule in unrestricted self-consistent-field (USCF) calculations in terms of structural characteristics such as periodicity, impurity location, and Coulomb exchange. For clarity, the systems considered are biradicals produced from linear conjugated hydrocarbons. Both site-parametrized Hamiltonian models for theoretical analysis and spin unrestricted density functional theory (DFT) calculations are used. Theoretical analysis leads to the following conclusions: (1) The diradical state is an excited state of a linear chain of N conjugated carbon atoms (when N is about ≤ 10). Spin alternation is a consequence of the (truncated) periodic symmetry combined with filling each closed-shell pi orbital with two electrons and each singly occupied molecular orbital (SOMO) with one electron. Spin polarization is evident in triplet (T) and broken symmetry (BS) solutions for an odd N and only in the T solution for an even N. Spin alternation is visible in the BS for an odd N and always remains muted in the calculated T. (2) For a doped chain with two radical centers, spin alternation is generally visible in the BS for an odd N. The sign of spin population on the radical centers in the BS indicates the stable spin. For radical centers separated by an odd (even) number of p_z electrons, spin alternation favors T (S) state with FM (AFM) interaction. Spin oscillation remains less transparent for an even N without exchange. (3) In an unrestricted treatment with exchange, spin alternation becomes observable. Without SCF iterations, the more stable state can be identified from a clear spin oscillation in the BS. An irregular oscillation indicates a possible singlet ground state. These observations are supported by density functional calculations using the B3LYP functional and the 6-311+g(d,p) basis set on linear decapentaene diradicals with nitronyl nitroxide moieties substituted on two sets of conjugated atoms, (3,9) and (3,10). Because of the SCF procedure, one finds spin alternation in the T (BS) solution and erratic oscillation in the BS (T) solution of the 3,9 (3,10) diradical in respective equilibrium geometries. The ground state is T (S). DFT adiabatic coupling constants, SOMO energies, spin population plots, and SOMO lobe diagrams compare well with molecular electronic characteristics from theoretical analysis using Hamiltonian parameters.

An electrodynamical coupled cluster (CC) methodology starting from a covariant formalism and an equal time approximation, and finally based on the Dirac-Fock picture of the electron and positron fields and Coulomb gauge, is given here. The formalism first leads to different physical interactions from the use of an exponential cluster operator for radiative effects. Lamb, Breit and hyperfine interactions are obtained. Next, relativistic many-body effects are determined using the matter cluster in a way familiar from the nonrelativistic CC. This step can be nontrivial. By allowing the matter cluster to deviate from its traditional excitation-only form, vacuum polarization effects are generated using the pair part of Coulomb interaction. The resulting ground state correlation energy includes both relativistic and QED corrections, the latter including contributions from Lamb, Breit, hyperfine and vacuum polarization effects. The many-electron part of the theory is explicitly formulated for closed shell species. The conservatism of the second step indicates that extensions to multireference and state-specific cases are possible. To illustrate the CC approach, expressions are derived for relativistic and QED corrections to the orbital energies, configuration energies and the ground state correlation energy in a minimal basis calculation on noninteracting H2 molecules. Size-consistency is maintained at every step. Because spinors of nonzero orbital angular momentum are absent, the spin-orbit interaction and Lamb shift corrections vanish in this example. However, one finds the kinetic energy correction, Darwin terms and corrections to the two-electron interaction in relativistic energy values through order mc2a4Z4, and Breit interaction energy and hyperfine splitting of levels as QED effects through the same order. Pair energies are explicitly shown through the lowest possible orders.