Population inversion,temperature, and photon distributions of the generalized fermionic Ising ferromagnetic model: Path‐integral representation of the spin system

The quantum partition function and the emerging energy of a fermionic Ising ferromagnetic model involving all possible interactions (generalized Ising model) are obtained from an appropriate tracing of the analytic propagator path integral over Grassmann variable coherent nonorthogonal states in the imaginary time domain. The dynamics derived from the interaction of this system with a single‐mode cavity field in the rotating wave approximation is investigated for nonresonant states within the framework of the Jaynes–Cummings two‐level model consisting of the vacuum state and a thermally averaged manifold of excited states. Time evolution of the population inversion is computed in the nanosecond time scale, assuming that the initial coherent state of the field is given by a Poisson distribution. The limit of high temperatures characterizing the manifold of excited states becomes chaotic with rapid oscillations, whereas the ground state is described correctly in the thermodynamic limit by the vacuum state. A breakup is seen in the photon distribution into a series of peaks because of the detuning between the spin system and the field. However, this structure is smeared out, and the general shape is preserved in the computation emerging from the Laplace transform of the photon distribution. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Feynman path integral representation for many-fermion interacting systems

A many-fermion interacting system is investigated within the scenario of the Feynman path integral representation of quantum mechanics. Short-time propagator algorithms and a basis set, closely related to the coherent states, are used to obtain the many-body analytic propagator. A second-quantized Hamiltonian involving a restricted set of two-body interactions and the whole set of Coulomb interactions are separately and shown to lead to an exact and an approximate propagator, respectively. In the latter case, use of a grand canonical ensemble allows the grand partition function and the density operator matrix to be readily obtained. No further approximations are required in the calculation of the trace of the evolution operator involved in the evaluation of statistical expectation values. © 1994 John Wiley & Sons, Inc.     

Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach

A generalized quantum master equation theory that governs the exact, nonperturbative quantum dissipation and quantum transport is formulated in terms of hierarchically coupled equations of motion for an arbitrary electronic system in contact with electrodes under either a stationary or a nonstationary electrochemical potential bias. The theoretical construction starts with the influence functional in path integral, in which the electron creation and annihilation operators are Grassmann variables. Time derivatives on the influence functionals are then performed in a hierarchical manner. Both the multiple-frequency dispersion and the non-Markovian reservoir parametrization schemes are considered for the desired hierarchy construction. The resulting hierarchical equations of motion formalism is in principle exact and applicable to arbitrary electronic systems, including Coulomb interactions, under the influence of arbitrary time-dependent applied bias voltage and external fields. Both the conventional quantum master equation and the real-time diagrammatic formalism of Schon and co-workers can be readily obtained at well defined limits of the present theory. We also show that for a noninteracting electron system, the present hierarchical equations of motion formalism terminates at the second tier exactly, and the Landuer-Buttiker transport current expression is recovered. The present theory renders an exact and numerically tractable tool to evaluate various transient and stationary quantum transport properties of many-electron systems, together with the involving nonperturbative dissipative dynamics.     

Low‐frequency ESR studies on permeable and impermeable deuterated nitroxyl radicals in corn oil solution

Low‐frequency electron spin resonance studies were performed for 2 mM concentration of deuterated permeable and impermeable nitroxyl spin probes, 3‐methoxycarbonyl‐2,2,5,5‐tetramethyl‐pyrrolidine‐1‐oxyl and 3‐carboxy‐2,2,5,5,‐tetramethyl‐1‐pyrrolidinyloxy in pure water and various concentrations of corn oil solution. The electron spin resonance parameters such as the line width, hyperfine coupling constant, g factor, rotational correlation time, permeability, and partition parameter were estimated. The broadening of line width was observed for nitroxyl radicals in corn oil mixture. The rotational correlation time increases with increasing concentration of corn oil, which indicates the less mobile nature of spin probe in corn oil mixture. The membrane permeability and partition parameter values were estimated as a function of corn oil concentration, which reveals that the nitroxyl radicals permeate equally into the aqueous phase and oil phase at the corn oil concentration of 50%. The electron spin resonance spectra demonstrate the permeable and impermeable nature of nitroxyl spin probes. From these results, the corn oil concentration was optimized as 50% for phantom studies. In this work, the corn oil and pure water mixture phantom models with various viscosities correspond to plasma membrane, and whole blood membrane with different hematocrit levels was studied for monitoring the biological characteristics and their interactions with permeable nitroxyl spin probe. These results will be useful for the development of electron spin resonance and Overhauser‐enhanced magnetic resonance imaging modalities in biomedical applications.     

Symmetry in the design of NMR multiple-pulse sequences

The symmetry principles of NMR pulse-sequence design are summarized. The discussion is guided by an analogy with tiling schemes in the decorative arts. The symmetry operations for NMR pulse sequences are discussed in terms of excitation field modifiers and temporal modifiers. The quantum operators which describe the effect of these modifiers on the excitation field spin Hamiltonian are provided. The symmetry transformations of spin propagators, and the different types of pulse-sequence elements are discussed. The common types of symmetry expansion are treated using the propagator transformations and the Euler angles for the excitation field propagators. The selection rules associated with symmetrical pulse sequences are discussed using average Hamiltonian theory.     

Matrix‐covariant representation of high‐order configuration interaction and coupled cluster theories

We present the closed form of the reduced density matrices (RDMs) of arbitrary order for configuration interaction (CI) wave functions at any excitation level, up to the full CI. A special operator technique due to Bogoliubov is applied and extended. It focuses on constructions of matrix‐covariant expressions independent of the basis set used. The corresponding variational CI equations are given in an explicit form containing the matrices related to conventional excitation operators. A subsequent transformation of the latter to an irreducible form makes it possible to generate the matrix‐covariant representation for coupled cluster (CC) models. Here this transformation is performed for a simplified high‐order CC scheme somewhat reminiscent of the quadratic CI model. A generalized spin‐flip approximation closely related to high‐order CI and CC models is presented, stressing on a possible inclusion of nondynamical and dynamical correlation effects for multiple bond breaking. A derivation of the full CI and simple CC models for systems involving effective three‐electron interactions is also given, thereby demonstrating the capability of the proposed method to deal with complicated many‐body problem. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Spin—orbit and vibronic perturbations on the chiroptical spectra of dissymmetric pseudo-tetragonal metal complexes

The influence of spin—orbit and vibronic interactions upon the chiroptical properties of nearly degenerate dd transitions in metal complexes of pseudo-tetragonal symmetry is investigated. A model system is considered in which three nearly degenerate dd excited states are coupled via both spinorbit and vibronic interactions. Vibronic interactions among the three nearly degenerate dd electronic states are assumed to arise from a pseudo-Jahn—Teller (PJT) mechanism involving three different vibrational modes (each nontotally symmetric in the point group of the undistorted model system).A vibronic hamiltonian is constructed (for the excited states of the model system) which includes linear coupling terms in each of the three PJT-active vibrational modes as well as a linear coupling term in one totally symmetric mode of the system and a spin—orbit interaction term. Wavefunctions and eigenvalues for the spin—orbit/vibronic perturbed excited states. of the model system are obtained by diagonalizing this hamiltonian in a basis constructed of uncoupled vibrational and electronic (orbital and spin) wavefunctions.Rotatory strengths associated with transitions to vibronic levels of the perturbed system are calculated and “rotatory strength spectra” are computed assuming gaussian shaped vibronic spectral components. Calculations are carried out for a number of vibronic and spin—orbit coupling parameters and for various splitting energies between the interacting electronic states. The calculated results suggest that chiroptical spectra associated with transitions to a set of nearly degenerate dd excited states of a chiral transition metal complex cannot be interpreted directly without some consideration of the effects introduced by spin—orbit and vibronic perturbations. These perturbations can lead to substantial alterations in the sign patterns and intensity distributions of rotatory strength among vibronic levels derived from the interacting electronic states and it is generally not valid to assign specific features in the observed circular dichroism spectra to transitions between states with well-defined electronic (orbital and spin) identities.Our theoretical model is conservative with respect to the total (or net) rotatory strength associated with transitions to levels derived from the three interacting electronic states; the vibronic and spin—orbit coupling operators are operative only within this set of states. That is, the total (or net) rotatory strength associated with these transitions remains invariant to the vibronic and spin—orbit coupling parameters of the model.     

Nuclear magnetic resonance J coupling constant polarizabilities of hydrogen peroxide: A basis set and correlation study

In this article, we present the so far most extended investigation of the calculation of the coupling constant polarizability of a molecule. The components of the coupling constant polarizability are derivatives of the nuclear magnetic resonance (NMR) indirect nuclear spin–spin coupling constant with respect to an external electric field and play an important role for both chiral discrimination and solvation effects on NMR coupling constants. In this study, we illustrate the effects of one‐electron basis sets and electron correlation both at the level of density functional theory as well as second‐order polarization propagator approximation for the small molecule hydrogen peroxide, which allowed us to perform calculations with the largest available basis sets optimized for the calculation of NMR coupling constants. We find a systematic but rather slow convergence with the one‐electron basis set and that augmentation functions are required. We observe also large and nonsystematic correlation effects with significant differences between the density functional and wave function theory methods. © 2012 Wiley Periodicals, Inc.     

Relativistic theory for indirect nuclear spin–spin couplings within the polarization propagator approach

We present a relativistic theory for the nuclear spin–spin coupling tensor within the polarization propagator approach using the particle-hole Dirac–Coulomb–Breit Hamiltonian and the full four-component wave function. We give explicit expressions for the coupling tensor in the random-phase approximation, neglecting the Breit interaction. A purely relativistic perturbative electron–nuclear Hamiltonian is used and it is shown how the single relativistic contribution to the coupling tensor reduces to Ramsey's three second-order terms (Fermi contact, spin–dipole, and paramagnetic spin–orbit) in the nonrelativistic limit. The principal propagator becomes complex and the leading property integrals mix atomic orbitals of different parity. The well-known propagator expressions for the coupling tensor in the nonrelativistic limit is obtained neglecting terms of the order c^?n (n ? 1). © 1993 John Wiley & Sons, Inc.     

Derivatives of the polarization propagator including orbital relaxation effects

In this article, we relate derivatives of the polarization propagator used in many-body theory to the nonlinear (quadratic) polarization propagator, and we relate derivatives of the quadratic polarization propagator to the nonlinear propagator of the next higher order, the cubic polarization propagator. We restrict the analysis to differentiation with respect to parameters eta for which the derivative of the Hamiltonian can be written as a sum of one-electron operators. Geometrical derivatives are obtained by specializing to the parameter eta to the alpha coordinate of nucleus I. We treat orbital relaxation explicitly by allowing for the eta dependence of creation and annihilation operators in the propagators. This treatment entails an extension of the geometrical derivative relations among response functions proven by Olsen and Jorgensen [J. Chem. Phys. 82, 3235 (1985)], because the propagator derivatives may involve changes in the one-electron orbitals that do not appear in the susceptibility derivatives. These results underlie the relations between Raman intensities and electric-field shielding tensors, which have been explained in terms of nonlocal polarizability and hyperpolarizability densities. The results suggest an alternative computational route to geometrical or other derivatives of both linear- and nonlinear-response functions: these derivatives can be evaluated without numerical differentiation, directly from the propagator of the next higher order.     

Ab initio quasirelativistic calculations on electronic transitions in ICl by the multireference many‐body perturbation theory

A quasirelativistic perturbative method of ab initio calculations on ground and excited molecular electronic states and transition properties within the relativistic effective core potential approximation is presented and discussed. The method is based on the construction of a state‐selective many‐electron effective Hamiltonian in the model space spanned by an appropriate set of Slater determinants by means of the second‐order many‐body multireference perturbation theory. The neglect of effective spin–orbit interactions outside of the model space allows the exploitation of relatively high nonrelativistic symmetry during the evaluation of perturbative corrections and therefore dramatic reduction of the cost of computations without any contraction of the model‐space functions. One‐electron transition properties are evaluated via the perturbative construction of spin‐free transition density matrices. Illustrative calculations on the X0⁺ ? A1, B0⁺, and (ii)1 transitions in the ICl molecule are reported. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Spin‐free quantum chemistry: What one can gain from fock's cyclic symmetry

The spin‐free wave function due to Fock (Zh Eksp Teor Fiz, 1940, 10, 961) is re‐examined with a stress on the reduced density matrix (RDM) theory. The key notion of the Fock approach is the cyclic symmetry of wave functions. It is a specific algebraic identity involving transpositions of numbers taken from two different columns of the corresponding Young tableau. We show first how to construct symmetry adapted states by accounting for high‐order cyclic symmetry conditions. For Young's projectors, it gives a new expression including nothing but antisymmetrizers. Next, transforming the Fock spin‐free state by a duality operator (the star operator in exterior algebra), we arrive at the representation closely related to spin‐flip models. In such spin‐flip models, a coupling operator is the basic object for which we show that the cyclic symmetry is transformed into a tracelessness of the coupling operator. The main results are related to the spin‐free theory of spin properties. In particular, the theorem previously stated (Luzanov and Whyman, Int J Quantum Chem, 1981, 20, 1179) is refined by an explicit general representation of spin density operators through spin‐free (charge) RDMs. Some applications implicating high‐order RDMs (collectivity numbers, the unpaired electron problem, cumulant spin RDMs, spin correlators, etc.) are also considered. For spin‐free RDM components, a new projection procedure without constructing any symmetry adapted state is proposed. An unsolved problem of constructing orthogonal representation matrices within the Fock theory is raised. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Acidity predictions in an electron propagator approach

An alternative way to calculate vertical ionization potentials (VIP) and vertical electron affinity (VEA) is the application of Koopman's theorem, using the electron propagator theory. In the present work, the results of the application of this theorem using the electron propagator formalism have been compared with the experiment in order to validate different basis set. Using the basis set with the best performance, the acidity tendencies in some substituted acetic acid molecules have been analyzed by correlating the proton affinity (PA) with molecular electronegativity (χ) and hardness (η); these last indexes were obtained from the calculated VIP and VEA considering the finite difference approximation. The above correlations were compared with equivalent correlations using the energy of the frontier Hartree–Fock orbitals and the corresponding Kohn–Sham orbitals, which were calculated with the B3LYP‐DFT procedure. The results indicate that the electron propagator theory could be an interesting alternative to evaluate reactivity indexes, since this theory gives reliable values of VIP and VEA. It was also found that (i) the VIP values are very close to experiment, with only a 0.38% of error; (ii) acceptable results are inferred for VEA; (iii) a triple zeta quality function works quite well in these calculations, and particularly the 6‐311G(d,p) basis set is the best, as it had been reported; and (iv) using the depronation energy (DPE), good results were obtained in the correlations δDPE‐VEA and δDPE‐χ. The results tested that P3 approximation in the electron propagator approach can be a new and interesting alternative in predicting VIP, VEA, and some reactivity indexes, such as χ and η, at least for the compounds studied. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Modification of optimal complete active space choices for the multiconfigurational spin‐tensor electron propagator method for ionization potentials

The multiconfigurational spin tensor electron propagator (MCSTEP) method was developed as an implementation of electron propagator/single particle Green's function methods. MCSTEP was specifically designed for open‐shell and highly correlated (nondynamically correlated) initial states. Ionization or electron attachment is always from a state of pure spin symmetry to a state of pure spin symmetry even if the initial state is open shell. MCSTEP can be used as well for molecules with initial states that can be accurately described by a single determinant‐based theory. The initial state that is used in MCSTEP is typically a small complete active space (CAS) multiconfigurational self‐consistent field (MCSCF) state. We previously examined different small CAS choices for MCSTEP initial states and have developed a generally workable scheme. This article further examines some different ways to choose the CAS for MCSTEP. With several logical CAS choices, we have calculated the low‐lying vertical MCSTEP ionization potentials (IPs) of C₂, N₂, linear H₂O, O₂, CH₂, and NH₂, comparing them with large multireference configuration interaction (MRCI) calculations. We conclude that generally a small modification and extension of our previous schemes for choosing the MCSTEP CAS gives IPs that most effectively mimics the results of large scale MRCI IPs in general. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Approximate MCSCF optimization for multiconfigurational spin‐tensor electron propagator method (MCSTEP): The vertical ionization potentials of CO,HCN, HNC,H2CO,and O3

The multiconfigurational spin tensor electron propagator method (MCSTEP) was developed as an implementation of electron propagator/single particle Green's function methods. MCSTEP was specifically designed for open shell and highly correlated (nondynamically correlated) initial states. The initial state used in MCSTEP is typically a small complete active space (CAS) with multiconfigurational self‐consistent field (MCSCF) state. In some cases, because of our use of a small CAS in MCSTEP, the Lagrangian eigenvalues of the MCSCF reference state are in an undesired order (u). The desired order (d) can usually be obtained by excluding one or more orbital rotations in MCSCF optimization between the doubly occupied and partially occupied orbitals. We systematically examine several cases where the undesired order occurs for the low‐lying vertical MCSTEP ionization potentials (IPs) of the molecules CO, HCN, HNC, H₂CO, and O₃ with our recently established CAS choices for MCSCF/MCSTEP. By excluding one or more orbital rotations between the partially and doubly occupied orbitals, an approximate MCSCF reference state with the same CAS choice is obtained for use in standard MCSTEP calculations that, in general, gives more reliable vertical MCSTEP IPs. © 2007 Wiley Periodicals, Inc. J Quantum Chem, 2008     

Synergistic Spin Transition between Spin Crossover and Spin‐Peierls‐like Singlet Formation in the Halogen‐Bonded Molecular Hybrid System: [Fe(Iqsal)2][Ni(dmit)2]⋅CH3CN⋅H2O

To introduce halogen‐bond interactions between a cation and an anion, a novel Fe^III complex from iodine‐substituted ligands involving a paramagnetic nickel dithiolene anion was prepared and characterized. The compound exhibited the synergy between a spin‐crossover transition and a spin‐Peierls‐like singlet formation. The halogen‐bond interactions between the iodine and the sulfur atoms stabilized the paramagnetic state of π‐spins and played a crucial role in the synergistic magnetic transition between d‐ and π‐spins. In addition, the compound showed the light‐induced excited spin state trapping effect.     

A quantum propagator for path-integral simulations of rigid molecules

The expression for the quantum propagator for rigid tops, proposed by Mu?ser and Berne [Phys. Rev. Lett. 77, 2638 (1996)], has been extended to asymmetric tops. Path-integral Monte Carlo simulations are provided that show that the quantum propagator proposed in this work exactly reproduces the rotational energy of free asymmetric tops as evaluated from the partition function. This propagator can subsequently be used in path-integral simulations of condensed phases if a rigid molecular model is used.