Normalization and Fermi–Coulomb and Coulomb hole sum rules for approximate wave functions

For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Diagrammatic formulation of the second‐order many‐body multipartitioning perturbation theory

The second‐order multireference perturbation theory employing multiple partitioning of the many‐electron Hamiltonian into a zero‐order part and a perturbation is formulated in terms of many‐body diagrams. The essential difference from the standard diagrammatic technique of Hose and Kaldor concerns the rules of evaluation of energy denominators which take into account the dependence of the Hamiltonian partitioning on the bra and ket determinantal vectors of a given matrix element, as well as the presence of several two‐particle terms in zero‐order operators. The novel formulation naturally gives rise to a “sum‐over‐orbital” procedure of correlation calculations on molecular electronic states, particularly efficient in treating the problems with large number of correlated electrons and extensive one‐electron bases. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 395–401, 1999     

Exact solution of multidimensional hyper‐radial Schrödinger equation for many‐electron quantum systems

In quantum theory, solving Schrödinger equation analytically for larger atomic and molecular systems with cluster of electrons and nuclei persists to be a tortuous challenge. Here, we consider, Schrödinger equation in arbitrary N‐dimensional space corresponding to inverse‐power law potential function originating from a multitude of interactions participating in a many‐electron quantum system for exact solution within the framework of Frobenius method via the formulation of an ansatz to the hyper‐radial wave function. Analytical expressions for energy spectra, and hyper‐radial wave functions in terms of known coefficients of inverse‐power potential function, and wave function parameters have been obtained. A generalized two‐term recurrence relation for power series expansion coefficients has been established. © 2016 Wiley Periodicals, Inc.     

Automated reaction path searches for spin‐forbidden reactions

Many catalytic and biomolecular reactions containing transition metals involve changes in the electronic spin state. These processes are referred to as “spin‐forbidden” reactions within nonrelativistic quantum mechanics framework. To understand detailed reaction mechanisms of spin‐forbidden reactions, one must characterize reaction pathways on potential energy surfaces with different spin states and then identify crossing points. Here we propose a practical computational scheme, where only the lowest mixed‐spin eigenstate obtained from the diagonalization of the spin‐coupled Hamiltonian matrix is used in reaction path search calculations. We applied this method to the ^6,4FeO⁺ + H₂ → ^6,4Fe⁺ + H₂O, ^6,4FeO⁺ + CH₄ → ^6,4Fe⁺ + CH₃OH, and ⁷Mn⁺ + OCS → ⁵MnS⁺ + CO reactions, for which crossings between the different spin states are known to play essential roles in the overall reaction kinetics. © 2018 Wiley Periodicals, Inc.     

Development of spin‐dependent relativistic open‐shell Hartree–Fock theory with time‐reversal symmetry (I): The unrestricted approach

An open‐shell Hartree–Fock (HF) theory for spin‐dependent, two‐component relativistic calculations, termed the Kramers‐unrestricted HF (KUHF) method, is developed. The present KUHF method, which is formulated as a relativistic counterpart of nonrelativistic UHF, is based on quaternion algebra and partly uses time‐reversal symmetry. The fundamental characteristics of KUHF are discussed in this study. From numerical assessments, it was revealed that KUHF gives a corresponding solution to nonrelativistic UHF; furthermore, KUHF properly describes spin‐orbit interactions. In addition, KUHF can improve the self‐consistent field convergence behavior in spin‐dependent calculations, for example, for f‐block elements.     

Unpaired electrons at the second‐order reduced density matrix level: Covalent bonding,and coulomb and fermi correlations in closed shell systems

The usual one‐electron populations in atomic orbitals of closed shell systems are split into unpaired and paired at the (spin‐dependent) second‐order reduced density matrix level. The unpaired electron in an orbital is defined as the “simultaneous occurrence of an electron and an electron hole of opposite spins in the same spatial orbital,” which for simplicity is called “electropon.” The electropon population in a given orbital reveals whether and to what degree the Coulomb correlations, and hence, the chemical bonding between this orbital and the remaining orbitals of the system are globally favorable or unfavorable. The interaction of two electropons in two target orbitals reveals the quality (favorable or unfavorable) and the strength of the covalent bonding between these orbitals; this establish a bridge between the notion of “unpaired electrons” and the traditional covalent structure of valence‐bond (VB) theory. Favorable/unfavorable bonding between two orbitals is characterized by the positive/negative (Coulomb) correlation of two electropons of opposite spins, or alternatively, by the negative/positive (Fermi) correlation of two parallel spin electropons. A spin‐free index is defined, and the relationship between the electropon viewpoint for chemical bonding and the well‐known two‐electron Coulomb and Fermi correlations is established. Benchmark calculations are achieved for ethylene, hexatriene, benzene, pyrrole, methylamine, and ammonia molecules on the basis of physically meaningful natural orbitals. The results, obtained in the framework of both orthogonal and nonorthogonal population analysis methods, provide the same conceptual pictures, which are in very good agreement with elementary chemical knowledge and VB theory. © 2013 Wiley Periodicals, Inc.     

Superconducting first‐order pairing: Finite‐temperature simulations

A recently developed first‐order mechanism for superconducting pairing has been extended from T = 0 K to finite temperatures. On the basis of quantum statistical considerations, we have suggested a direct pairing interaction that does not necessarily involve second‐order elements, such as the electron–phonon coupling or specific magnetic interactions submitted by spin fluctuations. The driving force for the (energy‐driven) first‐order pairing is an attenuation of the destabilizing influence of the Pauli antisymmetry principle (PAP). Only the moves of unpaired fermions are controlled by the PAP, while the moves of superconducting Cooper pairs are not. The quantum statistics of Cooper pairs is of a mixed type, as it combines fermionic on‐site and bosonic intersite properties. The strong correlation between the strength of PAP constraints and system topology in combination with the electron number has been discussed for some larger clusters. Detailed finite‐temperature simulations on first‐order pairing have been performed for four‐center–four‐electron clusters with different topologies. A canonical ensemble statistics has been employed to derive the electronic energy, the electronic configuration entropy, and the free energy of paired and unpaired states in thermal equilibrium. The simulations show that pairing can be caused by either the electronic energy or the electronic configuration entropy. The coexistence of two different sets of quantum particles in paired states (i.e., the Cooper pairs and the unpaired electrons) can lead to an enhanced configuration entropy. In this context, we discuss the possibility of an entropy‐driven high‐temperature superconductor emerging from a low‐temperature unpaired state. The charge and spin degrees of freedom of the four‐center–four‐electron systems have been studied with the help of the charge and spin fluctuations. The spin fluctuations are helpful in judging the validity of pairing theories based on magnetic interactions. The charge fluctuations are a measure for the carrier delocalization in unpaired and paired states. The well‐known proximity between Jahn–Teller activity and superconductivity is analyzed in the zero‐temperature limit. It is demonstrated that both processes compete in their ability to reduce PAP constraints. All theoretical results have been derived within the framework of the simple Hubbard Hamiltonian. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Spectroscopic and magnetic investigations of actinide‐based nanomagnets

Magnetic exchange is an essential feature of transition‐metal nanomagnets because it combines the relatively low spin‐only moments of several ions into a “giant spin” ground state, which can make slow magnetic relaxation very favorable in an axially anisotropic environment. In contrast, most of the early research on lanthanide‐based complexes focused on single‐ion magnets, where the required large moment is generated by the unquenched orbital contribution (which is parallel to the spin in heavy rare earths). With their unfilled 5f electronic shell being on the verge between localization and itinerancy, actinides are expected to combine the best of both 3d and 4f metals in terms of exchange and anisotropy, and are therefore under consideration as potential building blocks for the next generation of single‐molecule magnets. In this Perspective, a review of the recent development in this field is given, and some discrepancies between the spectroscopic and magnetic data are discussed. © 2014 European Commission. International Journal of Quantum Chemistry published by Wiley Periodicals, Inc.     

Statistical interpretation of the Amerithrax “morph” assay results

In the Amerithrax investigation PCR‐based “morph assays” were used to link the anthrax letters with the RMR‐1029 flask at USAMRIID. Quantitative data reported for several of these assays are not consistent with Poisson sampling statistics, but instead exhibit “Taylor's Law” behavior where the variance greatly exceeds the mean. A plausible statistical model for this behavior can explain the large number of observed negative and “inconclusive” findings, and implies a high likelihood that a repository sample could contain a “morph” mutant at concentrations well above the nominal detection limit but nonetheless give a negative or inconclusive test result. A Bayesian framework relates the assay results to the probability that a sample actually contains all four morph mutants, even though it tested negative for at least one. The analysis implies that the observed false negative rate actually does not significantly weaken the conclusion that the morph assays correctly excluded all but the stocks derived from RMR‐1029 as possible sources of the letter powders, at least when the test results were unambiguous. These findings expand upon and resolve some of the issues cited in recent reviews, and indicate the importance of developing a rigorous statistical framework for interpreting “morph” assay data.     

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     

Interaction of a two‐level cyclic XY n‐spin model with a two‐mode cavity field in off‐resonant states

The interaction of the XY n‐spin cyclic model with a two‐mode cavity field in the rotating‐wave approximation is investigated in the framework of a generalized Jaynes–Cummings two‐level system consisting of the vacuum state and a thermally averaged manifold of excited sates. Computation of the energy of this manifold allows this interaction to be examined in off‐resonant states. Time evolution of the population inversion, photon distribution, and temperature distribution for an excited initial state are computed via second‐ and third‐order perturbation expansion of the time evolution operator matrix elements for the excited and ground states, respectively and for an ideal squeezed initial coherent state of the cavity field. It was assumed that the two modes have initially the same photon distribution. The pattern of the spin population inversion appears as a manifestation of multiple and complicated inerferences, which is mathematically reflected in a double discrete summation that appears in the calculation of the dynamics. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

DNA‐backbone radio resistivity induced by spin blockade effect

Coherent control of OH‐free radicals interacting with the spin‐triplet state of a DNA molecule is investigated. A model Hamiltonian for molecular spin singlet‐triplet resonance is developed. We illustrate that the spin‐triplet state in DNA molecules can be efficiently populated, as the spin‐injection rate can be tuned to be orders of magnitudes greater than the decay rate due to small spin‐orbit coupling in organic molecules. Owing to the nano‐second life‐time of OH free radicals, a non‐equilibrium free energy barrier induced by the injected spin triplet state that lasts approximately longer than one‐micro second in room temperature can efficiently block the initial Hydrogen abstraction and DNA damage. For a direct demonstration of the spin‐blockade effect, a molecular simulation based on an ab‐initio Car‐Parrinello molecular dynamics is deployed. © 2010 Wiley Periodicals, Inc. J Comput Chem 2010     

Core‐Modified Rubyrins Containing Dithienylethene Moieties

Two stable core‐modified rubyrins bearing one and two dithienylethene (DTE) units ( 1 and 2 ) have been synthesized. With one “closed‐form” DTE unit, 1 shows aromaticity associated with its conjugated circuit of 26 π‐electrons. In contrast, rubyrin 2 containing one “open‐form” DTE unit has nonaromatic properties.     

The generator coordinate method in the unrestricted Hartree‐Fock formalism

The generator coordinate method was implemented in the unrestricted Hartree‐Fock formalism. Weight functions were built from Gaussian generator functions for 1s, 2s, and 2p orbitals of carbon and oxygen atoms. These weight functions show a similar behavior to those found in the generator coordinate restricted Hartree‐Fock method, i.e., they are smooth, continuous, and tend to zero in the limits of integration. Moreover, the weight functions obtained are different for spin‐up and spin‐down electrons what is a result from spin polarization. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Explicit and implicit multi‐center integrations

We present truncated expansions of multicenter one‐electron nuclear attraction and two‐electron repulsion integrals over localized basis functions in terms of one‐ and two‐center integrals of “Coulomb,” “exchange,” and “hybrid” type. Two variants are discussed: the “Explicit Multi‐center Integrations” and the “Implicit Multi‐Center Integrations” (abbreviated as “EMCI” and “IMCI”, respectively). While EMCI also deals with individual integrals, the IMCI option is the more appealing one: it enables us to evaluate the entire matrix elements of “Restricted Hartree–Fock”‐type in a very effective and chemically meaningful way. Due to the diatomic nature of our expansions, integrations over “Slater‐Type Orbitals” become well‐feasible, too. © 2012 Wiley Periodicals, Inc.     

GRECP/5e‐MRD‐CI calculation of the electronic structure of PbH

The correlation calculation of the electronic structure of PbH is carried out with the generalized relativistic effective core potential (GRECP) and multireference single‐ and double‐excitation configuration interaction (MRD‐CI) methods. The 22‐electron GRECP for Pb is used and the outer core 5s, 5p, and 5d pseudospinors are frozen using the level‐shift technique, so only five external electrons of PbH are correlated. A new configuration selection scheme with respect to the relativistic multireference states is employed in the framework of the MRD‐CI method. The [6, 4, 3, 2] correlation spin–orbit basis set is optimized in the coupled cluster calculations on the Pb atom using a recently proposed procedure, in which functions in the spin–orbital basis set are generated from calculations of different ionic states of the Pb atom and those functions are considered optimal that provide the stationary point for some energy functional. Spectroscopic constants for the two lowest‐lying electronic states of PbH (²Π_1/2, ²Π_3/2) are found to be in good agreement with the experimental data. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002