Molecular aspects of superconductivity: The role of the one-particle term at the gap formation

An exact solution for the electron-vibrational problem of the nonadiabatic molecular system has been obtained. By the quasi-particle transformation technique, the fermionic Hamiltonian has been derived and solved at the ab initio level. Results clearly and unambiguously show that the gap formation due to nonadiabatic electron–phonon coupling is mediated by the one-particle electron–phonon interaction term, whereas the two-particle one represents just a correction to the correlation energy. The temperature dependence of the gap and electronic specific heat connected with the electron–phonon coupling have also been derived.     

Theoretical analyses of the host–guest interaction within chlorine hydrate

The host–guest interaction is necessary for the stabilization of hydrates. Using Density Function Theory methods, the host–guest interaction within an unconventional chlorine hydrate was investigated, in combination with typical noncovalent analyses. The host–guest interaction energy was predicted to be as high as 17.51 kcal/mol, which was stronger than the typical van der Waals (vdW) interaction, due to an involvement of up to 20 Cl…O interactions. Polarization and dispersion energies made up the main contribution to the total interaction energy. Further visualization of the host–guest interaction validated, together with the general Cl…O interaction, another vdW interaction between the guest‐Cl atom and the five‐membered H₂O cluster. Isosurfaces associated with two patterns of vdW interactions yielded a better “fit” in shape, suggesting their cooperativity in stabilizing the steric configuration. The σ‐region on the guest‐Cl atom was verified to regulate the electron redistribution over the molecular space. These results are useful for understanding specific halogen behavior, and the origin and nature of host–guest interaction in hydrates. © 2013 Wiley Periodicals, Inc.     

Generalized electronic diabatic scheme: Diagonalizing the electronic Hamiltonian for artificial molecular systems. How do molecular meccanos move?

A quantum–classic model is presented and used to describe systems ranging from normal molecules up to electronic systems sensed in real space. The quantum system is a set of n‐electrons; a positive background in real space completes the model. A generalized electronic diabatic (GED) theory is introduced. The diabatic functions diagonalize the electronic Hamiltonian for any arrangement of the positive background. Physical quantum states are represented as linear superpositions in the diabatic basis; this latter is always fixed. For systems sensed in real space, the coefficients of the linear superposition are functions of the real space configuration coordinates. Physical changes are produced by interactions with external sources/sinks of energy. An interaction couples different diabatic states; diagonalizing the electronic Hamiltonian plus the couplings leads to new coefficients describing physical states. Among other things, these couplings can be used to simulate the effects produced by scanning tunneling microscopy, atomic force, and transmission electron microscopy on substrates located in real space. The important thing is that time–evolution in electronic Hilbert space can be related to actual motion in real space. The experiment of lateral hopping of a substrate on a metallic surface induced by vibration excitation and followed with scanning tunneling microscope is discussed. A result of the present work is that motion of molecular meccanos reflects then time–evolution in electronic Hilbert space. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

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     

On the electronic structure of molecular UO2 in the presence of Ar atoms: evidence for direct U-Ar bonding

Calculations via scalar-relativistic density functional theory (DFT) and ab initio CCSD(T) methodologies are used to explore the possibility of direct interactions between molecular UO2 and Ar atoms. The 3Hg electronic state of UO2, which is an excited state of the isolated molecule, exhibits significant bonding to Ar in the model complexes UO2(Ar) and UO2(Ar)5. The calculated vibrational frequencies of ground-state 3Phiu UO2 and UO2(Ar)5 with an (fphi)1(fdelta)1 electron configuration agree well with the observed frequencies of UO2 in solid neon and solid argon, respectively. The results strongly suggest that the ground electron configuration of UO2 changes from 5f17s1 to 5f2 when the matrix host is changed from neon to argon.     

Electronic structure of linear thiophenolate-bridged heteronuclear complexes [LFeMFeL](n)(+) (M = Cr, Co, Fe; n = 1-3): a combination of kinetic exchange interaction and electron delocalization

The electronic properties of the isostructural series of heterotrinuclear thiophenolate-bridged complexes of the general formula [LFeMFeL](n)(+) with M = Cr, Co and Fe where L represents the trianionic form of the ligand 1,4,7-tris(4-tertbutyl-2-mercaptobenzyl)-1,4,7-triazacyclononane, synthesized and investigated by a number of experimental techniques in the previous work(1), are subjected now to a theoretical analysis. The low-lying electronic excitations in these compounds are described within a minimal model supported by experiment and quantum chemistry calculations. It was found indeed that various experimental data concerning the magnetism and electron delocalization in the lowest states of all seven compounds are completely reproduced within a model which includes the electron transfer between magnetic orbitals at different metal centers and the electron repulsion in these orbitals (the Hubbard model). Moreover, due to the trigonal symmetry of the complexes, only the electron transfer between nondegenerate orbital, a(1), originating from the t(2g) shell of each metal ion in a pseudo-octahedral coordination, is relevant for the lowest states. An essential feature resulting from quantum chemistry calculations, allowing to explain the unusual magnetic properties of these compounds, is the surprisingly large value and, especially, the negative sign of the electron transfer between terminal iron ions, beta'. According to their electronic properties the series of complexes can be divided as follows: (1). The complexes [LFeFeFeL](3+) and [LFeCrFeL](3+) show localized valences in the ground electronic configuration. The strong antiferromagnetic exchange interaction and the resulting spin 1/2 of the ground-state arise from large values of the transfer parameters. (2). In the complex [LFeCrFeL](+), due to a higher energy of the magnetic orbital on the central Cr ion than on the terminal Fe ones, the spin 3/2 and the single unpaired a(1) electron are almost localized at the chromium center in the ground state. (3). The complex [LFeCoFeL](3+) has one ground electronic configuration in which two unpaired electrons are localized at terminal iron ions. The ground-state spin S = 1 arises from a kinetic mechanism involving the electron transfer between terminal iron ions as one of the steps. Such a mechanism, leading to a strong ferromagnetic interaction between distant spins, apparently has not been discussed before. (4). The complex [LFeFeFeL](2+) is characterized by both spin and charge degrees of freedom in the ground manifold. The stabilization of the total spin zero or one of the itinerant electrons depends on beta', i.e., corresponds to the observed S = 1 for its negative sign. This behavior does not fit into the double exchange model. (5). In [LFeCrFeL](2+) the delocalization of two itinerant holes in a(1) orbitals takes place over the magnetic core of chromium ion. Although the origin of the ground-state spin S = 2 is the spin dependent delocalization, the spectrum of the low-lying electronic states is again not of a double exchange type. (6). Finally, the complex [LFeCoFeL](2+) has the ground configuration corresponding to the electron delocalization between terminal iron atoms. The estimated magnitude of the corresponding electron transfer is smaller than the relaxation energy of the nuclear distortions induced by the electron localization at one of the centers, leading to vibronic valence trapping observed in this compound.     

Effective polarization energy of the naphthalene molecular crystal: a study on the polarizable force field

polarization energy of the localized charge in organic solids consists of electronic polarization energy, permanent electrostatic interactions, and inter/intra molecular relaxation energies. The effective electronic polarization energies for an electron/hole carrier were successfully estimated by AMOEBA polarizable force field in naphthalene molecular crystals. Both electronic polarization energy and permanent electrostatic interaction were in agreement with the preview experimental values. In addition, the influence of the multipoles from different distributed mutipole analysis (DMA) fitting options on the electrostatic interactions are discussed in this paper. We found that the multipoles obtained from Gauss-Hermite quadrature without diffuse function or grid-based quadrature with 0.325 Å H atomic radius will give reasonable electronic polarization energies and permanent interactions for electron and hole carriers.     

Electron smearing in DFT calculations: A case study of doxorubicin interaction with single‐walled carbon nanotubes

To address the choice of an appropriate value of electron smearing to facilitate self‐consistent field (SCF) convergence, we studied the interaction of doxorubicin with short armchair and zigzag single‐walled carbon nanotube models with closed caps, at the PWC/DNP level of density functional theory. By gradually reducing the electron smearing value from a large and most commonly used one of 0.005 Ha to zero (Fermi occupation), we monitored the changes in close contacts between the interacting species, total energy of the molecular system, highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy and isosurfaces, HOMO‐LUMO gap energy, and plots of electrostatic potential. It became evident that the commonly used smearing values of ≥0.001 Ha can alter the results significantly (for example, by one order of magnitude for HOMO–LUMO gap energy). We suggest the setting of electron smearing value at 0.0001 Ha, which does not imply too high computation cost and can guarantee the results close to the ones obtained with Fermi occupation. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Photoinduced dissociation of water and transport of hydrogen between silver clusters

Theoretical electronic structure calculations are reported for the dissociation of water adsorbed on a 31-atom silver cluster, Ag31, and subsequent transfer of a H to a second Ag31 cluster leaving OH on the first cluster. Both ground and excited electronic state processes are considered for two choices of Ag cluster separation, 6.35 and 7.94 A, on the basis of preliminary calculations for a range of separation distances. The excited electronic state of interest is formed by photoemission of an electron from one Ag cluster and transient attachment of the photoemitted electron to the adsorbed water molecule. A very large energy barrier is found for the ground-state process (3.53 eV at a cluster separation of 6.35 A), while the barrier in the excited state is small (0.38 eV at a cluster separation of 6.35 A). In the excited state, partial occupancy of an OH antibonding orbital facilitates OH stretch and concomitant movement of the negatively charged OH toward the electron-hole in the metal cluster. The excited-state pathway for dissociation of water and transfer of H begins with the formation of an excited electronic state at 3.59-3.82 eV. Stretch of the OH bond occurs with little change in energy (0.38-0.54 eV up to a stretch of 1.96 A). In this region of OH stretch the molecule must return to the ground-state potential energy surface to fully dissociate and to transfer H to the other Ag cluster. Geometry optimizations are carried out using a simplex algorithm and a semigrid method. These methods allow the total energy to be calculated directly using configuration interaction theory.     

A method of incorporating quadruple correction in the scheme of multi-reference singly and doubly excited configuration interaction — a CSF based coupled pair approximation

Summary We develop an approximate size consistent method within a framework of the multi-reference configuration interaction scheme. The Rayleigh-Schrödinger perturbation theory is employed with a specific selection of the unperturbed part of the electronic Hamiltonian. The second order energy is obtained by a set of equations similar to the quasidegenerate variational perturbation theory of Cave and Davidson. The approximate fourth order energy is obtained by solving a set of equations similar to the coupled electron pair approximation (CEPA). The method has been tested for two simple systems, BeH₂ and N₂, and the results are quite encouraging.     

基于苯并噻吩平面格的张力与重组能的理论研究

有机半导体材料在有机发光二极管(OLED)、有机场效应晶体管(OFET)和有机太阳能电池(OSC)等领域应用广泛,但由于各类结构缺陷和迁移率较低,不利于载流子的传输.本文基于苯并噻吩设计并研究了一系列新型有机电荷传输纳米分子,利用密度泛函理论研究了分子轨道、电离能、电子亲和势、张力能和重组能等分子结构和电子性质;利用约化密度梯度函数和正规模式(NM)分析方法计算了分子内的弱相互作用和每个振动模式对重组能的贡献.结果表明,苯并噻吩格子化(形成四元格)之后,与其单体相比,分子的电子重组能降低了至少0.394 eV,空穴重组能降低了至少0.056 eV,证明格子化是降低重组能的一种有效策略.     

Ab initio electron propagators in molecules with strong electron-phonon interaction. I. Phonon averages

Ab initio electron propagators in molecular systems with strong electron-electron and electron-phonon interactions are considered to study molecular electronic properties. This research is important in electron transfer reactions where the electron transition is not considered any longer as a single electron transfer process or in temperature dependences of current-voltage characteristics in molecular wires or aggregates. To calculate electron Green's functions, the authors apply a small polaron canonical transformation that intrinsically contains strong electron-phonon effects. According to this transformation, the excitation energies of the noninteracting Hamiltonian are shifted down by the relaxation (solvation) energy for each state. The electron-electron interaction is also renormalized by the electron-phonon coupling. For some values of the electron-phonon coupling constants, the renormalized Coulomb integrals can be negative resulting in the attraction between two electrons. Within this transformation, they develop a diagrammatic expansion for electron Green's function in which the electron-phonon interaction is included into the multiple phonon correlation functions. The multiple phonon correlation functions are exactly found. It is pointed out that Wick's theorem for such correlation functions is invalid. Consequently, there is no Dyson equation for electron Green's functions. The proposed approach can be considered for future method developments for quantum chemical calculations that include strong nonadiabatic (non-Born-Oppenheimer) effects.     

Theoretical study of a 1 : 1 complex between quinone and hydroquinone

The Variable Electronegativity Pariser–Parr–Pople method has been successfully applied to calculate the potential energy curve for the formation of a 1: 1 complex between quinone and hydroquinone. A consistent evaluation of core and electronic repulsion integrals is important to obtain a meaningful curve. A computationally simple procedure has been suggested for separating interactions due to electron exchange between the components from other intermolecular interactions. In agreement with experimental deductions the preferred configuration for the quinone-hydroquinone complex is found to be one in which the molecules are in parallel planes with their C—O bonds parallel. The equilibrium separation between the molecular planes is found to be 2.3 Å and the stabilization energy in this position is 1.2 eV. In this equilibrium position forces due to electron exchange constitute the major contributing factor to the stability of the complex.     

Novel method of self‐interaction corrections in density functional calculations

It is demonstrated that the commonly applied self‐interaction correction (SIC) used in density functional theory does not remove all self‐interaction. We present as an alternative a novel method that, by construction, is totally free from self‐interaction. The method has the correct asymptotic 1/r dependence. We apply the new theory to localized f electrons in praseodymium and compare with the old version of SIC, the local density approximation (LDA) and with an atomic Hartree–Fock calculation. The results show a lowering of the f level, a contraction of the f electron cloud and a lowering of the total energy by 13 eV per 4 f electron compared to LDA. The equilibrium volume of the new SIC method is close to the ones given by LDA and the older SIC method and is in good agreement with experiment. The experimental cohesive energy is in better agreement using the new SIC method, both compared to LDA and another SIC method. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 247–252, 2001     

Intermolecular electrostatic energies using density fitting

A method is presented to calculate the electron-electron and nuclear-electron intermolecular Coulomb interaction energy between two molecules by separately fitting the unperturbed molecular electron density of each monomer. This method is based on the variational Coulomb fitting method which relies on the expansion of the ab initio molecular electron density in site-centered auxiliary basis sets. By expanding the electron density of each monomer in this way the integral expressions for the intermolecular electrostatic calculations are simplified, lowering the operation count as well as the memory usage. Furthermore, this method allows the calculation of intermolecular Coulomb interactions with any level of theory from which a one-electron density matrix can be obtained. Our implementation is initially tested by calculating molecular properties with the density fitting method using three different auxiliary basis sets and comparing them to results obtained from ab initio calculations. These properties include dipoles for a series of molecules, as well as the molecular electrostatic potential and electric field for water. Subsequently, the intermolecular electrostatic energy is tested by calculating ten stationary points on the water dimer potential-energy surface. Results are presented for electron densities obtained at four different levels of theory using two different basis sets, fitted with three auxiliary basis sets. Additionally, a one-dimensional electrostatic energy surface scan is performed for four different systems (H2O dimer, Mg2+-H2O, Cu+-H2O, and n-methyl-formamide dimer). Our results show a very good agreement with ab initio calculations for all properties as well as interaction energies.     

Exchange polarization effects in the interaction of closed-shell systems

Explicit formulae for the calculation of the exchange polarization energy in the interaction of closed-shell atoms or molecules have been derived by assuming neglect of the electron correlation within the noninteracting systems. The dispersion part of the exchange polarization energy has been represented as a sum of contributions arising from the interaction of two, three or four orbitals at a time. Each of these contributions is given by an integral involving the orbitals engaged in the interaction and the pair functions describing the dispersion interaction between these orbitals. The numerical calculations for the interaction of two ground-state beryllium atoms show that the exchange dispersion energy is positive and quenches about 5 to 10 per cent of the dispersion term. This results in a decrease of the interaction energy, computed as a sum of the SCF and dispersion components, by 6 to 30 per cent for interatomic distances ranging from 10 to 7 bohrs.Simplified formulae for estimating the exchange dispersion energy in the interaction of larger systems are also proposed and their accuracy is discussed.     

Formation and interaction of hydrated alkali metal ions at the graphite-water interface

Ion hydration at a solid surface ubiquitously exists in nature and plays important roles in many natural processes and technological applications. Aiming at obtaining a microscopic insight into the formation of such systems and interactions therein, we have investigated the hydration of alkali metal ions at a prototype surface-graphite (0001), using first-principles molecular dynamics simulations. At low water coverage, the alkali metal ions form two-dimensional hydration shells accommodating at most four (Li, Na) and three (K, Rb, Cs) waters in the first shell. These two-dimensional shells generally evolve into three-dimensional structures at higher water coverage, due to the competition between hydration and ion-surface interactions. Exceptionally K was found to reside at the graphite-water interface for water coverages up to bulk water limit, where it forms an "umbrellalike" surface hydration shell with an average water-ion-surface angle of 115 degrees . Interactions between the hydrated K and Na ions at the interface have also been studied. Water molecules seem to mediate an effective ion-ion interaction, which favors the aggregation of Na ions but prevents nucleation of K. These results agree with experimental observations in electron energy loss spectroscopy, desorption spectroscopy, and work function measurement. In addition, the sensitive dependence of charge transfer on dynamical structure evolution during the hydration process, implies the necessity to describe surface ion hydration from electronic structure calculations.     

Effective potential model for calculating the energy shift in the ground state of two-electron atoms

An effective operator for the electron–electron interaction derived earlier has been shown to be successful for calculating the ground-state energy shift values for 10 members of the helium isoelectronic sequence in terms of a single free parameter. Some possible applications of the modified interaction operator for semiempirical calculations are suggested.     

Al7Ag and Al7Au clusters with large highest occupied molecular orbital-lowest unoccupied molecular orbital gap

The candidate structures for the ground-state geometry of the Al(7)M (M = Li, Cu, Ag, and Au) clusters are obtained within the spin-polarized density functional theory. Absorption energy, vertical ionization potential, vertical electron affinity, and the energy gap between the highest occupied molecular orbital (HOMO) level and the lowest unoccupied molecular orbital (LUMO) level have been calculated to investigate the effects of doping. Doping with Ag or Au can lead to a large HOMO-LUMO gap, low electron affinity, and increased ionization potential of Al(7) cluster. In the lowest-energy structure of the Al(7)Au cluster, the Al atom binding to the Al(6)Au acts monovalent and the other six Al atoms are trivalent. Thus, the Al(7)Au cluster has 20 valence electrons, and its enhanced stability may be due to the electronic shell closure effect.     

Electronic structure of the ground state of the benzyl radical

Results from the -electron approximation are given for the total energy, spin-density distribution, and electron density, which have been derived by configuration interaction via self-consistent orbitals for closed and open shells and with allowance for all singly excited configurations and some doubly excited ones. Some singly excited configurations do not mix with the ground-state configuration in the first order of perturbation theory but make a contribution to the latter greater than do some of the configurations that do mix. Incorporation of all singly excited configurations results in a lower ground-state energy if orbitals for a closed shell are used instead of those for an open one. Calculations via closed-shell orbitals lead to an inhomogeneous electron-density distribution, which is gradually smoothed out as the set of configurations is expanded. The spin-density distribution is very much dependent on the number of configurations used and on the orbitals employed in them.