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Density-functional-theory-based chemical reactivity indicators are formulated for degenerate and near-degenerate ground states. For degenerate states, the functional derivatives of the energy with respect to the external potential do not exist, and must be replaced by the weaker concept of functional variation. The resultant reactivity indicators depend on the specific perturbation. Because it is sometimes impractical to compute reactivity indicators for a specific perturbation, we consider two special cases: point-charge perturbations and Dirac delta function perturbations. The Dirac delta function perturbations provide upper bounds on the chemical reactivity. Reactivity indicators using the common used 'average of degenerate states approximation' for degenerate states provide a lower bound on the chemical reactivity. Unfortunately, this lower bound is often extremely weak. Approximate formulas for the reactivity indicators within the frontier-molecular-orbital approximation and special cases (two or three degenerate spatial orbitals) are presented in the supplementary material. One remarkable feature that arises in the frontier molecular orbital approximation, and presumably also in the exact theory, is that removing electrons sometimes causes the electron density to increase at the location of a negative (attractive) Dirac delta function perturbation. That is, the energetic response to a reduction in the external potential can increase even when the number of electrons decreases. [ABSTRACT FROM AUTHOR]

This article is a response to a comment made by Professor Liu regarding a previously published paper. The response addresses questions raised by Professor Liu and focuses on three key aspects of the validity of the paper. It explains the use of different contractions in the construction of the QED Hamiltonians and clarifies the commutation relations used in the calculations. The article also highlights that the formulation of the molecular orbital method described in the paper is independent of the ordering of the operators and can derive expressions for various perturbation theories. The response concludes by stating that alternative criteria for the QED Hamiltonians are not ruled out and could be explored in future research. [Extracted from the article]

Second-order N-electron valence state perturbation theory (NEVPT2) is an exactly size-consistent and intruder-state-free multi-reference theory. To accelerate the NEVPT2 computation, Guo and Neese combined it with the local pair-natural orbital (PNO) method using the projected atomic orbitals (PAOs) as the underlying local basis [Guo et al., J. Chem. Phys. 144, 094111 (2016)]. In this paper, we report the further development of the PNO-NEVPT2 method using the orthonormal and non-redundant localized virtual molecular orbitals (LVMOs) instead of PAOs. The LVMOs were previously considered to perform relatively poor compared to PAOs because the resulting orbital domains were unacceptably large. Our prior work, however, showed that this drawback can be remedied by re-forming the domain construction scheme using differential overlap integrals [Saitow et al., J. Chem. Phys. 157, 084101 (2022)]. In this work, we develop further refinements to enhance the feasibility of using LVMOs. We first developed a two-level semi-local approach for screening out so-called weak-pairs to select or truncate the pairs for PNO constructions more flexibly. As a refinement specific to the Pipek–Mezey localization for LVMOs, we introduced an iterative scheme to truncate the Givens rotations using varying thresholds. We assessed the LVMO-based PNO-NEVPT2 method through benchmark calculations for linear phenyl alkanes, which demonstrate that it performs comparably well relative to the PAO-based approach. In addition, we evaluated the Co–C bond dissociation energies for the cobalamin derivatives composed of 200 or more atoms, which confirms that the LVMO-based method can recover more than 99.85% of the canonical NEVPT2 correlation energy. [ABSTRACT FROM AUTHOR]

We report further investigations to aid the development of a Laplace MP2 (second-order Møller Plesset) method with a range separated Coulomb potential partitioned into short- and long-range parts. The implementation of the method extensively uses sparse matrix algebra, density fitting techniques for the short-range part, and a Fourier transformation in spherical coordinates for the long-range part of the potential. Localized molecular orbitals are employed for the occupied space, whereas virtual space is described by orbital specific virtual orbitals (OSVs) associated with localized molecular orbitals. The Fourier transform is deficient for very large distances between localized occupied orbitals, and a multipole expansion for widely separated pairs is introduced for the direct MP2 contribution, which is applicable also to non-Coulombic potentials that do not satisfy the Laplace equation. For the exchange contribution, an efficient screening of contributing localized occupied pairs is employed, which is discussed more completely here. To mitigate errors due to the truncation of OSVs, a simple and efficient extrapolation procedure is used to obtain results close to MP2 for the full basis set of atomic orbitals Using a suitable set of default parameters, the accuracy of the approach is demonstrated. The current implementation of the approach is not very efficient, and the aim of this paper is to introduce and critically discuss ideas that can have more general applicability beyond MP2 calculations for large molecules. [ABSTRACT FROM AUTHOR]

In this paper, we propose to compute the electronic circular dichroism (ECD) spectra of chiral molecules using a real-time propagation of the time-dependent Schrödinger equation (TDSE) in the space of electronic field-free eigenstates, by coupling TDSE with a given treatment of the electronic structure of the target. The time-dependent induced magnetic moment is used to compute the ECD spectrum from an explicit electric perturbation. The full matrix representing the transition magnetic moment in the space of electronic states is generated from that among pairs of molecular orbitals. In the present work, we show the ECD spectra of methyloxirane, of several conformers of L-alanine, and of the Λ-Co(acac)3 complex, computed from a singly excited ansatz of time-dependent density functional theory eigenstates. The time-domain ECD spectra properly reproduce the frequency-domain ones obtained in the linear-response regime and quantitatively agree with the available experimental data. Moreover, the time-domain approach to ECD allows us to naturally go beyond the ground-state rotationally averaged ECD spectrum, which is the standard outcome of the linear-response theory, e.g., by computing the ECD spectra from electronic excited states. [ABSTRACT FROM AUTHOR]

This paper presents a state-averaged complete active space self-consistent field (SA-CASSCF) in the atomic multipole optimized energetics for biomolecular application (AMOEBA) polarizable water model, which enables rigorous simulation of non-adiabatic molecular dynamics with nonequilibrium solvation effects. The molecular orbital and configuration interaction coefficients of the solute wavefunction, and the induced dipoles on solvent atoms, are solved by minimizing the state averaged energy variationally. In particular, by formulating AMOEBA water models and the polarizable continuum model (PCM) in a unified way, the algorithms developed for computing SA-CASSCF/PCM energies, analytical gradients, and non-adiabatic couplings in our previous work can be generalized to SA-CASSCF/AMOEBA by properly substituting a specific list of variables. Implementation of this method will be discussed with the emphasis on how the calculations of different terms are partitioned between the quantum chemistry and molecular mechanics codes. We will present and discuss results that demonstrate the accuracy and performance of the implementation. Next, we will discuss results that compare three solvent models that work with SA-CASSCF, i.e., PCM, fixed-charge force fields, and the newly implemented AMOEBA. Finally, the new SA-CASSCF/AMOEBA method has been interfaced with the ab initio multiple spawning method to carry out non-adiabatic molecular dynamics simulations. This method is demonstrated by simulating the photodynamics of the model retinal protonated Schiff base molecule in water. [ABSTRACT FROM AUTHOR]

In order to prepare highly heat-resistant packaging insulation materials, in this paper, bismaleimide/epoxy resin (BMI/EP55) composites with different contents of BMI were prepared by melt blending BMI into amino tetrafunctional and phenolic epoxy resin (at a ratio of 5:5). The microstructures and thermal and electrical properties of the composites were tested. The electrostatic potential distribution, energy level distribution, and molecular orbitals of BMI were calculated using Gaussian. The results showed that the carbonyl group in BMI is highly electronegative, implying that the carbonyl group has a strong electron trapping ability. The thermal decomposition temperature of the composites gradually increased with the increase of BMI content, and the 20% BMI/EP55 composites had the highest heat-resistance index, along with a glass transition temperature (Tg) of >250 °C. At different test temperatures, with increase in the BMI content, the conductivity of epoxy resin composites showed a tendency to first decrease and then increase, the breakdown field strength showed a tendency to first increase and then decrease, and the dielectric constant was gradually decreased. Two trap centers were present simultaneously in the composites, where the shallow trap energy level is the deepest in 20% BMI/EP composites and the deep trap energy level is the deepest in 10% BMI/EP55 composites. Correspondingly, the 10% BMI/EP55 composite had a slower charge decay rate, while the 20% BMI/EP55 had a faster charge decay rate. In summary, the BMI/EP55 composites with high heat resistance and insulating properties were prepared in this study, which provided ideas for preparing high-temperature packaging insulating materials. [ABSTRACT FROM AUTHOR]

The multireference second-order perturbation theory (CASPT2) is known to deliver a quantitative description of various complex electronic states. Despite its near-size-consistent nature, the applicability of the CASPT2 method to large, real-life systems is mostly hindered by large computational and storage costs for the two-external tensors, such as two-electron integrals, amplitudes, and residuum. To this end, Menezes and co-workers developed a reduced-scaling CASPT2 scheme by incorporating the local pair-natural orbital (PNO) representation of the many-body wave functions using non-orthonormal projected atomic orbitals (PAOs) into the CASPT theory [F. Menezes et al., J. Chem. Phys. 145, 124115 (2016)]. Alternatively, in this paper, we develop a new PNO-based CASPT2 scheme using the orthonormal localized virtual molecular orbitals (LVMOs) and assess its performance and accuracy in comparison with the conventional PAO-based counterpart. Albeit the compactness, the LVMOs were considered to perform somewhat poorly compared to PAOs in the local correlation framework because they caused enormously large orbital domains. In this work, we show that the size of LVMO domains can be rendered comparable to or even smaller than that of PAOs by the use of the differential overlap integrals for domain construction. Optimality of the MOs from the CASSCF treatment is a key to reducing the LVMO domain size for the multireference case. Due to the augmented Hessian-based localization algorithm, an additional computational cost for obtaining the LVMOs is relatively minor. We demonstrate that the LVMO-based PNO-CASPT2 method is routinely applicable to large, real-life molecules such as Menshutkin SN2 reaction in a single-walled carbon nanotube reaction field. [ABSTRACT FROM AUTHOR]

C4n cyclacenes exhibit strong bond-alternation in their equilibrium geometry. In the two equivalent geometries, the system keeps an essentially closed-shell character. The two energy minima are separated by a transition state suppressing the bond-alternation, where the wave function is strongly diradical. This paper discusses the physical factors involved in this energy difference and possible evaluations of the barrier height. The barrier given as the energy difference between the restricted density functional theory (DFT)/B3LYP for the equilibrium and the broken symmetry DFT/B3LYP of the transition state is either negative or small, in contradiction with the most reliable Wave Function Theory calculations. The minimal (two electrons in two molecular orbitals) Complete Active Space self-consistent field (CASSCF) overestimates the barrier, and the subsequent second-order perturbation cancels it. Due to the collective character of the spin-polarization effect, it is necessary to perform a full π CASSCF + second-order perturbation to reach a reasonable value of the barrier, but this type of treatment cannot be applied to large molecules. DFT procedures treating on an equal foot the closed-shell and open-shell geometries have been explored, such as Mixed-Reference Spin-Flip Time-dependent-DFT and a new spin-decontamination proposal, namely, DFT-dressed configuration interaction, but the results still depend on the density functional. M06-2X without or with spin-decontamination gives the best agreement with the accurate wave function results. [ABSTRACT FROM AUTHOR]

The common basis sets constructed for use in electronic structure calculations have been found inadequate for the representation of electrons participating in nonadiabatic time-dependent dynamics calculations. In this paper we outline an approach to construct electronic bases better suited for dynamical processes such as energy deposition and charge transfer in binary collisions of ions, atoms, and molecules. Since electrons of many-atom systems commonly are represented by orbitals formed as linear combinations of atomic orbitals, the focus is on atomic basis sets. The main idea is to construct basis sets that adequately reproduce the first few excitation energies of neutral atoms. In this paper we outline a method for such basis set construction of various levels of accuracy for first-row atoms and give a few illustrative examples. [ABSTRACT FROM AUTHOR]

We report the development of a new Laplace MP2 (second-order Møller–Plesset) implementation using a range separated Coulomb potential, partitioned into short- and long-range parts. The implementation heavily relies on the use of sparse matrix algebra, density fitting techniques for the short-range Coulomb interactions, while a Fourier transformation in spherical coordinates is used for the long-range part of the potential. Localized molecular orbitals are employed for the occupied space, whereas orbital specific virtual orbitals associated with localized molecular orbitals are obtained from the exchange matrix associated with specific localized occupied orbitals. The range separated potential is crucial to achieve efficient treatment of the direct term in the MP2, while extensive screening is employed to reduce the expense of the exchange contribution in MP2. The focus of this paper is on controllable accuracy and linear scaling of the data entering the algorithm. [ABSTRACT FROM AUTHOR]

In a preceding paper (referred to as part I) we presented a theoretical study of the initial stages of the oxidation of the Si(111). Specifically, we discussed the structure of the molecular precursors and the stable products, using approximate molecular orbital calculations of the extended Hückel type. In this contribution (part II) we propose pathways which lead from one oxygen chemisorption configuration to another. A scheme is constructed to account for the reaction sequence from the clean Si(111) surface to molecular precursors, through dissociated states and finally to SiO4 units which are precursors for bulklike SiO2. [ABSTRACT FROM AUTHOR]

A full configuration interaction calculation (FCI) ultimately defines the innate molecular orbital description of a molecule. Its density matrix and the natural orbitals obtained from it quantify the difference between having N-dominantly occupied orbitals in a reference determinant for a wavefunction to describe N-correlated electrons and how many of those N-electrons are left to the remaining virtual orbitals. The latter provides a measure of the multi-determinantal character (MDC) required to be in a wavefunction. MDC is further split into a weak correlation part and a part that indicates stronger correlation often called multi-reference character (MRC). If several virtual orbitals have high occupation numbers, then one might argue that these additional orbitals should be allowed to have a larger role in the calculation, as in MR methods, such as MCSCF, MR-CI, or MR-coupled-cluster (MR-CC), to provide adequate approximations toward the FCI. However, there are problems with any of these MR methods that complicate the calculations compared to the uniformity and ease of application of single-reference CC calculations (SR-CC) and their operationally single-reference equation-of-motion (EOM-CC) extensions. As SR-CC theory is used in most of today's "predictive" calculations, an assessment of the accuracy of SR-CC at some truncation of the cluster operator would help to quantify how large an issue MRC actually is in a calculation, and how it might be alleviated while retaining the convenient SR computational character of CC/EOM-CC. This paper defines indices that identify MRC situations and help assess how reliable a given calculation is. [ABSTRACT FROM AUTHOR]

This paper is a logical continuation of the 22 parameter, localized orbital correction (LOC) methodology that we developed in previous papers [R. A. Friesner et al., J. Chem. Phys. 125, 124107 (2006); E. H. Knoll and R. A. Friesner, J. Phys. Chem. B 110, 18787 (2006).] This methodology allows one to redress systematic density functional theory (DFT) errors, rooted in DFT’s inherent inability to accurately describe nondynamical correlation. Variants of the LOC scheme, in conjunction with B3LYP (denoted as B3LYP-LOC), were previously applied to enthalpies of formation, ionization potentials, and electron affinities and showed impressive reduction in the errors. In this paper, we demonstrate for the first time that the B3LYP-LOC scheme is robust across different basis sets [6-31G*, 6-311++G(3df,3pd), cc-pVTZ, and aug-cc-pVTZ] and reaction types (atomization reactions and molecular reactions). For example, for a test set of 70 molecular reactions, the LOC scheme reduces their mean unsigned error from 4.7 kcal/mol [obtained with B3LYP/6-311++G(3df,3pd)] to 0.8 kcal/mol. We also verified whether the LOC methodology would be equally successful if applied to the promising M05-2X functional. We conclude that although M05-2X produces better reaction enthalpies than B3LYP, the LOC scheme does not combine nearly as successfully with M05-2X than with B3LYP. A brief analysis of another functional, M06-2X, reveals that it is more accurate than M05-2X but its combination with LOC still cannot compete in accuracy with B3LYP-LOC. Indeed, B3LYP-LOC remains the best method of computing reaction enthalpies. [ABSTRACT FROM AUTHOR]

By using perturbations in the molecular external potential, the authors deduce the Fukui function from the change in Kohn-Sham orbital energies, avoiding the troublesome differentiation of the density with respect to electron number. Though this paper focuses on the Fukui function, the same general technique can be used to compute the functional derivative of any observable with respect to the external potential. In this paper, the method is used to compute the Fukui function for the beryllium atom and the formaldehyde molecule. The follow-up paper (part II) addresses the problem of computing condensed reactivity indicators. [ABSTRACT FROM AUTHOR]

Obtaining ultracold samples of dipolar molecules is a current challenge which requires an accurate knowledge of their electronic properties to guide the ongoing experiments. In this paper, we systematically investigate the ground state and the lowest triplet state of mixed alkali dimers (involving Li, Na, K, Rb, Cs) using a standard quantum chemistry approach based on pseudopotentials for atomic core representation, Gaussian basis sets, and effective terms for core polarization effects. We emphasize on the convergence of the results for permanent dipole moments regarding the size of the Gaussian basis set, and we discuss their predicted accuracy by comparing to other theoretical calculations or available experimental values. We also revisit the difficulty to compare computed potential curves among published papers, due to the differences in the modelization of core-core interaction. [ABSTRACT FROM AUTHOR]

In a previous paper [J. Chem. Phys. 116, 7544 (2002) (Paper I)] a model, based on the energy corrected sudden approximation, was proposed for the construction of the line-mixing relaxation matrix. It was successfully tested by comparisons with measured infrared spectra of ammonia–helium mixtures. The present paper extends this preliminary study by considering mixtures of NH[sub 3] with H[sub 2] and Ar. Measurements have been made at room temperature in the regions of the ν[sub 2] and ν[sub 1] bands for pressures up to several hundred atmospheres. As in Paper I, the relaxation operator is constructed, within the impact approximation, using the ECS approximation. The data required are dynamical factors (which can be predicted from the NH[sub 3]–X potential energy surface) and a scaling length (adjusted using line broadening data). Comparisons between measured and calculated absorptions demonstrate the quality of the model which satisfactory corrects for the large deviations with respect to the purely Lorentzian behavior. Line-mixing effects for NH[sub 3]–Ar and NH[sub 3]–H[sub 2] are qualitatively similar to those observed for NH[sub 3]–He but quantitative differences exist, particularly when intra- and interbranch couplings are considered. Finally, the proposed model leads to very satisfactory results in the wings of both the purely rotational and ν[sub 2] bands of NH[sub 3] diluted in H[sub 2], opening promising perspectives for the remote sensing study of planetary atmospheres. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The vibrational properties of octahedrane (C12H12) are calculated using density-functional theory employing two different computational methods: an all-electron Gaussian orbital approach and a Naval Research Laboratory-tight-binding scheme (NRL-TB) coupled with molecular dynamics (NRL-TBMD). Both approaches yield vibrational densities of states for octahedrane that are in good general agreement with each other. NRL Molecular Orbital Library can also provide accurate infrared and Raman spectra which can be analyzed and compared with experimental results, while NRL-TBMD can be conveniently scaled up for larger finite-temperature simulations. This latter approach is used in our paper to produce a theoretical prediction for a stable room temperature structure of octahedrane. [ABSTRACT FROM AUTHOR]

The distinguishable cluster approximation proposed in Paper I [D. Kats and F. R. Manby, J. Chem. Phys. 139, 021102 (2013)] has shown intriguing abilities to accurately describe potential energy surfaces in various notoriously difficult cases. The question that still remained open is to what extend the accuracy and the stability of the method is due to the special choice of orbital-relaxation treatment. In this paper we introduce orbital relaxation in terms of Brueckner orbitals, orbital optimization, and projective singles into the distinguishable cluster approximation and investigate its importance in single- and multireference cases. All three resulting methods are able to cope with many multiple-bond breaking problems, but in some difficult cases where the Hartree-Fock orbitals seem to be entirely inadequate the orbital-optimized version turns out to be superior. [ABSTRACT FROM AUTHOR]

Exploiting locality in the electron correlation reduces the computational cost for solving the Coupled-Cluster (CC) equations. This is important for making CC theory applicable to routine computational chemistry applications where it promises to deliver results of “gold-standard” quality. Recently, we have proposed a series of CC formulations in the domain-based local pair-natural orbital framework [DLPNO-coupled-cluster with singles and doubles (CCSD) and DLPNO-coupled-cluster singles and doubles with perturbative triples] which are designed to reproduce approximately 99.9% of the canonical correlation energy. In our previous work, the DLPNO-CCSD method has been extended to the high-spin open-shell reference and shown to possess comparable accuracy to the closed-shell counterpart [M. Saitow et al., J. Chem. Phys. 146, 164105 (2017)]. The so-called Λ-equations have been formulated in the DLPNO framework for the closed-shell species as an exact derivative of the DLPNO-CCSD Lagrangian with respect to the PNO-based cluster amplitudes [D. Datta et al., J. Chem. Phys. 145, 114101 (2016)]. In this paper, we extend the DLPNO-based Lagrangian scheme to the high-spin open-shell reference cases, thus enabling the accurate computation of the electron- and spin-densities for large open-shell species. We apply this newly developed approach to various first-order electronic and magnetic properties such as isotropic and anisotropic components in the hyperfine coupling interactions and the electric field gradient. We demonstrate that the DLPNO-CCSD results converge toward the respective canonical CC density and also that the DLPNO-CCSD-based properties are more accurate than the conventional density functional theory (DFT) results in real-life applications. The additional computational cost is not more than one energy evaluation in the DLPNO-CCSD framework. [ABSTRACT FROM AUTHOR]

A simple molecular orbital treatment of local current distributions inside single molecular junctions is developed in this paper. Using the first-order perturbation theory and nonequilibrium Green's function techniques in the framework of Hückel theory, we show that the leading contributions to local current distributions are directly proportional to the off-diagonal elements of transition density matrices. Under the orbital approximation, the major contributions to local currents come from a few dominant molecular orbital pairs which are mixed by the interactions between the molecule and electrodes. A few simple molecular junctions consisting of single- and multi-ring conjugated systems are used to demonstrate that local current distributions inside molecular junctions can be decomposed by partial sums of a few leading contributing transition density matrices. [ABSTRACT FROM AUTHOR]

In the Fermi-Löwdin orbital method for implementing self-interaction corrections (FLO-SIC) in density functional theory (DFT), the local orbitals used to make the corrections are generated in a unitary-invariant scheme via the choice of the Fermi orbital descriptors (FODs). These areMpositions in 3-d space (for an M-electron system) that can be loosely thought of as classical electron positions. The orbitals that minimize the DFT energy including the SIC are obtained by finding optimal positions for the FODs. In this paper, we present optimized FODs for the atoms from Li-Kr obtained using an unbiased search method and self-consistent FLO-SIC calculations. The FOD arrangements display a clear shell structure that reflects the principal quantum numbers of the orbitals. We describe trends in the FOD arrangements as a function of atomic number. FLO-SIC total energies for the atoms are presented and are shown to be in close agreement with the results of previous SIC calculations that imposed explicit constraints to determine the optimal local orbitals, suggesting that FLO-SIC yields the same solutions for atoms as these computationally demanding earlier methods, without invoking the constraints. [ABSTRACT FROM AUTHOR]

A preliminary discussion of the general problem of localization of wave functions, and the way it is approached in theoretical condensed matter physics (Wannier functions) and theoretical chemistry (localized or fragment orbitals) is followed by an application of the ideas of Paper II in this series to the structures of hydrogen as they evolve under increasing pressure. The idea that emerges is that of simultaneously operative physical (reduction of available space by an increasingly stiff wall of neighboring molecules) and chemical (depopulation of the σg bonding molecular orbital of H2, and population of the antibonding σu* MO) factors. The two effects work in the same direction of reducing the intermolecular separation as the pressure increases, but compete, working in opposite directions, in their effect on the intramolecular (nearest neighbor, intra-pair) distance. We examine the population of σg and σu* MOs in our numerical laboratory, as well as the total electron transfer (small), and polarization (moderate, where allowed by symmetry) of the component H2 molecules. From a molecular model of two interacting H2 molecules we find a linear relationship between the electron transfer from σg to σu* of a hydrogen molecular fragment and the intramolecular H-H separation, and that, in turn, allows us to estimate the expected bond lengths in H2 under pressure if the first effect (that of simple confinement) was absent. In essence, the intramolecular H-H separations under pressure are much shorter than they would be, were there no physical/confinement effect. We then use this knowledge to understand how the separate E and PV terms contribute to hydrogen phase changes with increasing pressure. [ABSTRACT FROM AUTHOR]

The 'open' and 'closed' isomers of the diarylethene molecule that can be converted between each other upon photo-excitation are found to have drastically different current-voltage characteristics when sandwiched between two graphene nanoribbons (GNRs). More importantly, when one GNR is metallic and another one is semiconducting, strong rectification behavior of the 'closed' diarylethene isomer with the rectification ratio >103 is observed. The surprisingly high rectification ratio originates from the band gap of GNR and the bias-dependent variation of the lowest unoccupied molecular orbital of the diarylethene molecule, the combination of which completely shuts off the current at positive biases. Results presented in this paper may form the basis for a new class of molecular electronic devices. [ABSTRACT FROM AUTHOR]

In this paper, we develop a rigorously spin-adapted version of Mukherjee's state-specific multireference coupled cluster theory (SS-MRCC, also known as Mk-MRCC) [U. S. Mahapatra, B. Datta, and D. Mukherjee, J. Chem. Phys. 110, 6171 (1999)] for reference spaces comprising open-shell configurations. The principal features of our approach are as follows: (1) The wave operator Ω is written as Ω = ∑μΩμ|[lowercase_phi_synonym]μ>cμ, where {[lowercase_phi_synonym]μ} is the set of configuration state functions spanning a complete active space. (2) In contrast to the Jeziorski-Monkhorst Ansatz in spin-orbital basis, we write Ωμ as a power series expansion of cluster operators Rμ defined in terms of spin-free unitary generators. (3) The operators Rμ are either closed-shell-like n hole-n particle excitations (denoted as Tμ) or they involve valence (active) destruction operators (denoted as Sμ); these latter type of operators can have active-active scatterings, which can also carry the same active orbital labels (such Sμ's are called to have spectator excitations). (4) To simulate multiple excitations involving powers of cluster operators, we allow the Sμ's carrying the same active orbital labels to contract among themselves. (5) We exclude Sμ's with direct spectator scatterings. (6) Most crucially, the factors associated with contracted composites are chosen as the inverse of the number of ways the Sμ's can be joined among one another leading to the same excitation. The factors introduced in (6) have been called the automorphic factors by us. One principal thrust of this paper is to show that the use of the automorphic factors imparts a remarkable simplicity to the final amplitude equations: the equations consist of terms that are at most quartic in cluster amplitudes, barring only a few. In close analogy to the Mk-MRCC theory, the inherent linear dependence of the cluster amplitudes leading to redundancy is resolved by invoking sufficiency conditions, which are exact spin-free analogues of the spin-orbital based Mk-MRCC theory. This leads to manifest size-extensivity and an intruder-free formulation. Our formalism provides a relaxed description of the nondynamical correlation in presence of dynamical correlation. Pilot numerical applications to doublet systems, e.g., potential energy surfaces for the first two excited 2A' states of asymmetric H2S+ ion and the ground 2Σ+state of BeH radical are presented to assess the viability of our formalism over an wide range of nuclear geometries and the manifest avoidance of intruder state problem. [ABSTRACT FROM AUTHOR]

This paper discusses the nuclear volume dependence of uranium isotope fractionations in the U3+–U4+ and U4+–UO22+ systems by reference to a series of ab initio molecular orbital calculations. Nuclear volume-dependent terms (≡ln Knv) in isotope fractionation coefficients (≡[variant_greek_epsilon]) are calculated from the energetic balance of the isotopomers involved in the systems. We used the Dirac–Coulomb Hartree–Fock (DCHF) method with the Gaussian-type finite-nucleus model. We employed three types of generally contracted Gaussian basis sets to check the basis set dependences. In the U3+–U4+ system, the present values of ln Knv for uranium, other than those with the smallest double-zeta basis set, are in good agreement with previous values of ln Knv obtained from a numerical atomic multiconfigurational DCHF method with the Fermi-type finite-nucleus model. The present calculations reasonably reproduce the experimental value of [variant_greek_epsilon] in the U3+–U4+ system, and the value of ln Knv in the U4+–UO22+ system, obtained empirically by temperature-dependent fitting of the experimental [variant_greek_epsilon] values. For instance, in the U4+–UO22+ system, the present ab initio ln Knv value for a 235U–238U isotope pair is 0.002 09 using the largest basis set, while the experimental value is 0.002 24. This paper also shows that nuclear volume effects are negligibly small on the U–O bond length and two force constants of UO22+. Hence, the molecular vibrational terms of the isotope fractionation coefficients mainly depend on the nuclear mass rather than the nuclear volume. [ABSTRACT FROM AUTHOR]

Problems appear in discrete variable representations (DVRs) based on general basis sets when the coordinate matrix has degenerate eigenvalues. Then the DVR is not uniquely defined. This paper shows that this problem can be caused by symmetry. Taking the symmetry into account when constructing the DVR solves the problem. The symmetry effect can be particularly important for the time-dependent DVR used in multiconfigurational time-dependent Hartree calculations employing the correlation DVR (CDVR) approach. Problems reported previously for the initial-state selected treatment of the H+H2 reaction can be attributed to this symmetry effect. They can be solved by using a symmetry-adapted approach to construct the time-dependent DVR. Thus, the present paper shows that the CDVR scheme can be employed also in initial-state selected scattering calculations if the symmetry of the system is properly taken into account in the construction of the time-dependent DVR. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Full configuration interaction (FCI) restricted to a pairing space yields size-extensive correlation energies but its cost scales exponentially with molecular size. Restricting the variational two-electron reduced-density-matrix (2-RDM) method to represent the same pairing space yields an accurate lower bound to the pair FCI energy at a mean-field-like computational scaling of O(r3) where r is the number of orbitals. In this paper, we show that localized molecular orbitals can be employed to generate an efficient, approximately size-extensive pair 2-RDM method. The use of localized orbitals eliminates the substantial cost of optimizing iteratively the orbitals defining the pairing space without compromising accuracy. In contrast to the localized orbitals, the use of canonical Hartree-Fock molecular orbitals is shown to be both inaccurate and non-size-extensive. The pair 2-RDM has the flexibility to describe the spectra of one-electron RDM occupation numbers from all quantum states that are invariant to time-reversal symmetry. Applications are made to hydrogen chains and their dissociation, n-acene from naphthalene through octacene, and cadmium telluride 2-, 3-, and 4-unit polymers. For the hydrogen chains, the pair 2-RDM method recovers the majority of the energy obtained from similar calculations that iteratively optimize the orbitals. The localized-orbital pair 2-RDM method with its mean-field-like computational scaling and its ability to describe multireference correlation has important applications to a range of strongly correlated phenomena in chemistry and physics. [ABSTRACT FROM AUTHOR]

This paper shows how to include Pauli (exclusion principle) effects within a treatment of ballistic molecular conduction that uses the tight-binding Hückel Hamiltonian and the source-sink-potential (SSP) method. We take into account the many-electron ground-state of the molecule and show that we can discuss ballistic conduction for a specific molecular device in terms of four structural polynomials. In the standard one-electron picture, these are characteristic polynomials of vertex-deleted graphs, with spectral representations in terms of molecular-orbital eigenvectors and eigenvalues. In a more realistic many-electron picture, the spectral representation of each polynomial is retained but projected into the manifold of unoccupied spin-orbitals. Crucially, this projection preserves interlacing properties. With this simple reformulation, selection rules for device transmission, expressions for overall transmission, and partition of transmission into bond currents can all be mapped onto the formalism previously developed. Inclusion of Pauli spin blockade, in the absence of external perturbations, has a generic effect (suppression of transmission at energies below the Fermi level) and specific effects at antibonding energies, which can be understood using our previous classification of inert and active shells. The theory predicts the intriguing phenomenon of Pauli perfect reflection whereby, once a critical electron count is reached, some electronic states of devices can give total reflection of electrons at all energies. [ABSTRACT FROM AUTHOR]

A simple four configuration model that quantitatively reproduces all of the 11Bu and 21Ag state 0-0 energies that have been measured in high resolution spectroscopic experiments has been described previously. This model has been useful for explaining trends in the electronic properties of series of unsubstituted and substituted linear polyenes. While this model led to analytical expressions for the excitation energies, there were no closed form expressions for other quantities, such as the transition dipoles, that depend explicitly on the coefficients of the one-electron molecular orbitals. This paper derives exact expressions for the one-electron molecular orbital coefficients for an alternating chain as well as exact expressions for the transition dipole moments. This facilitates a detailed examination of the dependence of the transition dipole moments on the polyene length and alternation parameter which leads to an expression that accurately describes the dependence of the transition dipole moments on these chain parameters. The application of these expressions to an analytical analysis of nonlinear response in linear polyenes will be the subject of a subsequent paper. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A detailed theory for electronic aspects of electronic excitation (energy) transfer (EET) for sandwich dimers was derived in paper II of this series [J. Chem. Phys. 101, 10 521 (1994)]. In II, the electronic transfer matrix element for EET was evaluated, then simplified to various levels of approximation. The results of ab initio molecular orbital calculations on an ethene sandwich dimer are reported here in order to test and quantify the theory of II. The calculations were undertaken using a STO-6G basis set and localized molecular orbitals, with separations of 4, 5, and 6 Å between the molecules. It is demonstrated that the important electronic factors contributing to EET are the Coulombic interaction (for direct singlet–singlet transfer) and, for both singlet–singlet and triplet–triplet EET, orbital overlap-dependent interactions. The dominant orbital overlap-dependent terms arise from through-configuration interaction, which involves successive one-electron transfers mediated via bridging ionic configurations, first presented in II. The results confirm that the Dexter-type exchange interaction is small in comparison. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

An improved complete basis set-quadratic configuration interaction/atomic pair natural orbital (CBS-QCI/APNO) model is described in this paper. It provides chemical energy differences (i.e., D0 I.P., and E.A.) with a mean absolute error of 0.53 kcal/mol for the 64 first-row examples from the G2 test set, and is computationally feasible for species with up to three first-row atoms. A set of 20 CBS-QCI/APNO bond dissociation energies of hydrocarbons also agree with known experimental values to within less than 1 kcal/mol. Calculations on the cyclopropenyl radical and cyclopropenylidene provide new dissociation energies which are in accord with an interpretation of the thermochemistry emphasizing ring strain and aromaticity. [ABSTRACT FROM AUTHOR]

We present a very general form of electronic friction as present when a molecule with multiple orbitals hybridizes with a metal electrode. To develop this picture of friction, we embed the quantum-classical Liouville equation (QCLE) within a classical master equation (CME). Thus, this article extends our previous work analyzing the case of one electronic level, as we may now treat the case of multiple levels and many electronic molecular states. We show that, in the adiabatic limit, where electron transitions are much faster than nuclear motion, the QCLE-CME reduces to a Fokker-Planck equation, such that nuclei feel an average force as well as friction and a random force-as caused by their interaction with the metallic electrons. Finally, we show numerically and analytically that our frictional results agree with other published results calculated using non-equilibrium Green's functions. Numerical recipes for solving this QCLE-CME will be provided in a subsequent paper. [ABSTRACT FROM AUTHOR]

The density-matrix renormalization group (DMRG) method, which can deal with a large active space composed of tens of orbitals, is nowadays widely used as an efficient addition to traditional complete active space (CAS)-based approaches. In this paper, we present the DMRG algorithm with a multi-level (ML) control of the active space based on chemical intuition-based hierarchical orbital ordering, which is called as ML-DMRG with its self-consistent field (SCF) variant MLDMRG- SCF. Ground and excited state calculations of H2O, N2, indole, and Cr2 with comparisons to DMRG references using fixed number of kept states (M) illustrate that ML-type DMRG calculations can obtain noticeable efficiency gains. It is also shown that the orbital re-ordering based on hierarchical multiple active subspaces may be beneficial for reducing computational time for not only ML-DMRG calculations but also DMRG ones with fixed M values. [ABSTRACT FROM AUTHOR]

In this contribution, we report two different methodologies for characterizing the electronic structure reorganization occurring when a chromophore undergoes an electronic transition. For the first method, we start by setting the theoretical background necessary to the reinterpretation through simple tensor analysis of (i) the transition density matrix and (ii) the natural transition orbitals in the scope of reduced density matrix theory. This novel interpretation is made more clear thanks to a short compendium of the one-particle reduced density matrix theory in a Fock space. The formalism is further applied to two different classes of excited states calculation methods, both requiring a single-determinant reference, that express an excited state as a hole-particle mono-excited configurations expansion, to which particle-hole correlation is coupled (time-dependent Hartree-Fock/timedependent density functional theory) or not (configuration interaction single/Tamm-Dancoff approximation). For the second methodology presented in this paper, we introduce a novel and complementary concept related to electronic transitions with the canonical transition density matrix and the canonical transition orbitals. Their expression actually reflects the electronic cloud polarisation in the orbital space with a decomposition based on the actual contribution of one-particle excitations from occupied canonical orbitals to virtual ones. This approach validates our novel interpretation of the transition density matrix elements in terms of the Euclidean norm of elementary transition vectors in a linear tensor space. A proper use of these new concepts leads to the conclusion that despite the different principles underlying their construction, they provide two equivalent excited states topological analyses. This connexion is evidenced through simple illustrations of (in)organic dyes electronic transitions analysis. [ABSTRACT FROM AUTHOR]

Organic crystals have unique charge transport properties that lie somewhere between delocalised band-type transport and localised hopping transport. In this paper, we use a stochastic tight-binding model to explore how dynamical disorder in organic crystals affects charge transport. By analysing the model in terms of Feynman diagrams (virtual processes), we expose the crucial role of correlated dynamical disorder to the charge transport dynamics in the model at short times in the order of a few hundred femtoseconds. Under correlated dynamical disorder, the random motions of molecules in the crystal allow for low-energy "bonding"-type interactions between neighboring molecular orbitals can persist over long periods of time. On the other hand, the dependence of charge transport on correlated dynamical disorder also tends to localize the charge, as correlated disorder cannot persist far in space. This concept of correlation may be the "missing link" for describing the intermediate regime between band transport and hopping transport that occurs in organic crystals. [ABSTRACT FROM AUTHOR]

The number of singly occupied orbitals in the ground-state atomic configuration of an element defines its nominal valence. For carbon and sulfur, with two singly occupied orbitals in their ³P ground states, the nominal valence is two. However, in both cases, it is possible to form more bonds than indicated by the nominal valenceâ€"up to four bonds for carbon and six bonds for sulfur. In carbon, the electrons in the 2s lone pair can participate in bonding, and in sulfur the electrons in both the 3p and 3s lone pairs can participate. Carbon 2s and sulfur 3p recoupled pair bonds are the basis for the tetravalence of carbon and sulfur, and 3s recoupled pair bonds enable sulfur to be hexavalent. In this paper, we report generalized valence bond as well as more accurate calculations on the a4Σ- states of CF and SF, which are archetypal examples of molecules that possess recoupled pair bonds. These calculations provide insights into the fundamental nature of recoupled pair bonds and illustrate the key differences between recoupled pair bonds formed with the 2s lone pair of carbon, as a representative of the early p-block elements, and recoupled pair bonds formed with the 3p lone pair of sulfur, as a representative of the late p-block elements. [ABSTRACT FROM AUTHOR]

The formalism developed in the companion Paper I is used here for the interpretation of spectra obtained recently on the nitrogen molecule. Double core-hole ionization K-2 and core ionization-core excitation K-2V processes have been observed by coincidence electron spectroscopy after ionization by synchrotron radiation at different photon energies. Theoretical and experimental cross sections reported on an absolute scale are in satisfactory agreement. The evolution with photon energy of the relative contribution of shake-up and conjugate shake-up processes is discussed. The first main resonance in the K-2V spectrum is assigned to a K-2Π* state mainly populated by the 1s→ lowest unoccupied molecular orbital dipolar excitation, as it is in the K-1V NEXAFS (Near-Edge X-ray Absorption Fine Structure) signals. Closer to the K-2 threshold Rydberg resonances have been also identified, and among them a K-2σ* resonance characterized by a large amount of 2s/2p hybridization, and double K-2(2σ*/1Π/3σ)-11Π*2 shake-up states. These resonances correspond in NEXAFS spectra to, respectively, the well-known σ* shape resonance and double excitation K-1(2σ*/1Π/3σ)-11Π*² resonances, all being positioned above the threshold. [ABSTRACT FROM AUTHOR]

This article presents comments of the authors on the paper "In situ X-Ray Photoelectron Spectroscopic and Density-Functional Studies of Si Atoms Adsorbed on a C60 Film," that was published in a 2004 issue of the periodical "The Journal of Chemical Physics." In this paper, the researchers report that x-ray photoelectron spectroscopy (XPS) results on a C60+Si film, together with some theoretical calculations on C60- Si clusters. The XPS measurements were performed in situ, in ultrahigh vacuum, on a C60 film obtained by sublimation and subsequently exposed to a Si-atom beam. The analysis of the Si 2p core peak leads the authors to conclude that the silicon atoms in the film are in three distinct environments, with peaks corresponding to bulk silicon crystal, silicon suboxides, and Si atoms adsorbed on C60. From the experimental Si 2p core-level shill, the charge transfer from Si to C60 is evaluated to be 0.59 e.

Our purpose is to identify a computational level sufficiently dependable and affordable to assess trends in the interaction of a variety of radical or closed shell unsaturated hydro-carbons A adsorbed on soot platelet models B. These systems, of environmental interest, would unavoidably have rather large sizes, thus prompting to explore in this paper the performances of relatively low-level computational methods and compare them with higher-level reference results. To this end, the interaction of three complexes between non-polar species, vinyl radical, ethyne, or ethene (A) with benzene (B) is studied, since these species, involved themselves in growth processes of polycyclic aromatic hydrocarbons (PAHs) and soot particles, are small enough to allow high-level reference calculations of the interaction energy ΔEAB. Counterpoise-corrected interaction energies ΔEAB are used at all stages. (1) Density Functional Theory (DFT) unconstrained optimizations of the A-B complexes are carried out, using the B3LYP-D, ωB97X-D, and M06-2X functionals, with six basis sets: 6-31G(d), 6-311 (2d,p), and 6-311++G(3df,3pd); aug-cc-pVDZ and aug-cc-pVTZ; N07T. (2) Then, unconstrained optimizations by Mo\ller-Plesset second order Perturbation Theory (MP2), with each basis set, allow subsequent single point Coupled Cluster Singles Doubles and perturbative estimate of the Triples energy computations with the same basis sets [CCSD(T)//MP2]. (3) Based on an additivity assumption of (i) the estimated MP2 energy at the complete basis set limit [EMP2/CBS] and (ii) the higher-order correlation energy effects in passing from MP2 to CCSD(T) at the aug-cc-pVTZ basis set, ΔECC-MP, a CCSD(T)/CBS estimate is obtained and taken as a computational energy reference. At DFT, variations in ΔEAB with basis set are not large for the title molecules, and the three functionals perform rather satisfactorily even with rather small basis sets [6-31G(d) and N07T], exhibiting deviation from the computational reference of less than 1 kcal mol-1. The zero-point vibrational energy corrected estimates Δ(EAB+ZPE), obtained with the three functionals and the 6-31G(d) and N07T basis sets, are compared with experimental D0 measures, when available. In particular, this comparison is finally extended to the naphthalene and coronene dimers and to three π-π associations of different PAHs (R, made by 10, 16, or 24 C atoms) and P (80 C atoms). [ABSTRACT FROM AUTHOR]

In this paper, by applying the reduced density matrix (RDM) approach for nonorthogonal orbitals developed in the first paper of this series, efficient algorithms for matrix elements between VB structures and energy gradients in valence bond self-consistent field (VBSCF) method were presented. Both algorithms scale only as nm4 for integral transformation and d2nβ2 for VB matrix elements and 3-RDM evaluation, while the computational costs of other procedures are negligible, where n, m, d, and nβ are the numbers of variable occupied active orbitals, basis functions, determinants, and active β electrons, respectively. Using tensor properties of the energy gradients with respect to the orbital coefficients presented in the first paper of this series, a partial orthogonal auxiliary orbital set was introduced to reduce the computational cost of VBSCF calculation in which orbitals are flexibly defined. Test calculations on the Diels-Alder reaction of butadiene and ethylene have shown that the novel algorithm is very efficient for VBSCF calculations. [ABSTRACT FROM AUTHOR]

In this series, the n-body reduced density matrix (n-RDM) approach for nonorthogonal orbitals and their applications to ab initio valence bond (VB) methods are presented. As the first paper of this series, Hamiltonian matrix elements between internally contracted VB wave functions are explicitly provided by means of nonorthogonal orbital based RDM approach. To this end, a more generalized Wick's theorem, called enhanced Wick's theorem, is presented both in arithmetical and in graphical forms, by which the deduction of expressions for the matrix elements between internally contracted VB wave functions is dramatically simplified, and the matrix elements are finally expressed in terms of tensor contractions of electronic integrals and n-RDMs of the reference VB self-consistent field wave function. A string-based algorithm is developed for the purpose of evaluating n-RDMs in an efficient way. Using the techniques presented in this paper, one is able to develop new methods and efficient algorithms for nonorthogonal orbital based many-electron theory much easier than by use of the first quantized formulism. [ABSTRACT FROM AUTHOR]

Different sets of molecular orbitals and the rotations connecting them are of great significance in molecular electronic structure. Most electron correlation methods depend on a reference wave function that separates the orbitals into occupied and unoccupied spaces. Energies and properties from these methods depend upon rotations between the spaces. Some electronic structure methods, such as modified coupled electron pair approximations and the recently developed parametric two-electron reduced density matrix (2-RDM) methods [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], also depend upon rotations between occupied orbitals and rotations between unoccupied orbitals. In this paper, we explore the sensitivity of the ground-state energies from the parametric 2-RDM method to rotations within the occupied space and within the unoccupied space. We discuss the theoretical origin of the rotational dependence and provide computational examples at both equilibrium and non-equilibrium geometries. We also study the effect of these rotations on the size extensivity of the parametric 2-RDM method. Computations show that the orbital rotations have a small effect upon the parametric 2-RDM energies in comparison to the energy differences observed between methodologies such as coupled cluster and parametric 2-RDM. Furthermore, while the 2-RDM method is rigorously size extensive in a local molecular orbital basis set, calculations reveal negligible deviations in nonlocal molecular orbital basis sets such as those from canonical Hartree-Fock calculations. [ABSTRACT FROM AUTHOR]

Mixed quantum/classical (MQC) simulations treat the majority of a system classically and reserve quantum mechanics only for a few degrees of freedom that actively participate in the chemical process(es) of interest. In MQC calculations, the quantum and classical degrees of freedom are coupled together using pseudopotentials. Although most pseudopotentials are developed empirically, there are methods for deriving pseudopotentials using the results of quantum chemistry calculations, which guarantee that the explicitly-treated valence electron wave functions remain orthogonal to the implicitly-treated core electron orbitals. Whether empirical or analytically derived in nature, to date all such pseudopotentials have been subject to the frozen core approximation (FCA) that ignores how changes in the nuclear coordinates alter the core orbitals, which in turn affects the wave function of the valence electrons. In this paper, we present a way to go beyond the FCA by developing pseudopotentials that respond to these changes. In other words, we show how to derive an analytic expression for a pseudopotential that is an explicit function of nuclear coordinates, thus accounting for the polarization effects experienced by atomic cores in different chemical environments. We then use this formalism to develop a coordinate-dependent pseudopotential for the bonding electron of the sodium dimer cation molecule and we show how the analytic representation of this potential can be used in one-electron MQC simulations that provide the accuracy of a fully quantum mechanical Hartree-Fock (HF) calculation at all internuclear separations. We also show that one-electron MQC simulations of Na2+ using our coordinate-dependent pseudopotential provide a significant advantage in accuracy compared to frozen core potentials with no additional computational expense. This is because use of a frozen core potential produces a charge density for the bonding electron of Na2+ that is too localized on the molecule, leading to significant overbinding of the valence electron. This means that FCA calculations are subject to inaccuracies of order ∼10% in the calculated bond length and vibrational frequency of the molecule relative to a full HF calculation; these errors are fully corrected by using our coordinate-dependent pseudopotential. Overall, our findings indicate that even for molecules like Na2+, which have a simple electronic structure that might be expected to be well-treated within the FCA, the importance of including the effects of the changing core molecular orbitals on the bonding electrons cannot be overlooked. [ABSTRACT FROM AUTHOR]

Core vacancies created on opposite sides of a molecule operate against each other in polarizing the environment between them. Consequently, the relaxation energy associated with the simultaneous creation of these two core holes turns out to be smaller than the sum of the relaxation energies associated with each individual single core vacancy created independently. The corresponding residual, termed interatomic relaxation energy, is sensitive to the environment. In the present paper we explore how the interatomic relaxation energy depends on the length and type of carbon chains bridging two core ionized nitrile groups (-C≡N). We have uncovered several trends and discuss them with the help of simple electrostatic and quantum mechanical models. Namely, the absolute value of the interatomic relaxation energy depends strongly on the orbital hybridization in carbons being noticeably larger in conjugated chains (sp and sp2 hybridizations) possessing highly mobile electrons in delocalized π-type orbitals than in saturated chains (sp3 hybridization) where only σ bonds are available. The interatomic relaxation energy decreases monotonically with increasing chain length. The corresponding descent is determined by the energetics of the molecular bridge, in particular, by the HOMO-LUMO gap. The smallest HOMO-LUMO gap is found in molecules with the sp2-hybridized backbone. Here, the interatomic relaxation energy decreases slowest with the chain length. [ABSTRACT FROM AUTHOR]

We have recently introduced a parameterized coupled-cluster singles and doubles model (pCCSD(α, β)) that consists of a bivariate parameterization of the CCSD equations and is inspired by the coupled electron pair approximations. In our previous work, it was demonstrated that the pCCSD(-1, 1) method is an improvement over CCSD for the calculation of geometries, harmonic frequencies, and potential energy surfaces for single bond-breaking. In this paper, we find suitable pCCSD parameters for applications in reaction thermochemistry and thermochemical kinetics. The motivation is to develop an accurate and economical methodology that, when coupled with a robust local correlation framework based on localized pair natural orbitals, is suitable for large-scale thermochemical applications for sizeable molecular systems. It is demonstrated that the original pCCSD(-1, 1) method and several other pCCSD methods are a significant improvement upon the standard CCSD approach and that these methods often approach the accuracy of CCSD(T) for the calculation of reaction energies and barrier heights. We also show that a local version of the pCCSD methodology, implemented within the local pair natural orbital (LPNO) based CCSD code in ORCA, is sufficiently accurate for wide-scale chemical applications. The LPNO based methodology allows us for routine applications to intermediate sized (20-100 atoms) molecular systems and is a significantly more accurate alternative to MP2 and density functional theory for the prediction of reaction energies and barrier heights. [ABSTRACT FROM AUTHOR]

In this series of studies, we systematically apply the analytical energy gradients of the direct symmetry-adapted cluster-configuration interaction singles and doubles nonvariational method to calculate the equilibrium geometries and vibrational frequencies of excited and ionized states of molecules. The harmonic vibrational frequencies were calculated using the second derivatives numerically computed from the analytical first derivatives and the anharmonicity was evaluated from the three-dimensional potential energy surfaces around the local minima. In this paper, the method is applied to the low-lying valence singlet and triplet excited states of HAX-type molecules, HCF, HCCl, HSiF, HSiCl, HNO, HPO, and their deuterium isotopomers. The vibrational level emission spectra of HSiF and DSiF and absorption spectra of HSiCl and DSiCl were also simulated within the Franck-Condon approximation and agree well with the experimental spectra. The results show that the present method is useful and reliable for calculating these quantities and spectra. The change in geometry in the excited states was qualitatively interpreted in the light of the electrostatic force theory. The effect of perturbation selection with the localized molecular orbitals on the geometrical parameters and harmonic vibrational frequencies is also discussed. [ABSTRACT FROM AUTHOR]

A formalism is derived for the computation of partial differential cross sections for electron photodetachment and photoionization processes that leave the residual or target molecule in electronic states that are strongly coupled by conical intersections. Because the electronic states of the target are nonadiabatically coupled, the standard adiabatic states approach of solving the electronic Schrödinger equation for the detached electron at fixed nuclear geometries and then vibrationally averaging must be fundamentally modified. We use a Lippmann-Schwinger equation based approach, which leads naturally to a partitioning of the transition amplitude into a Dyson orbital like part plus a scattering correction. The requisite Green's function is that developed in our previous paper for the direct determination of total integral cross sections. The method takes proper account of electron exchange, possible nonorthogonality of the orbital describing the detached electron, and nonadiabatic effects in the product molecule. The Green's function is constructed in an L2 basis using complex scaling techniques. The accurate treatment of nonadiabatic effects in the residual molecule is accomplished using the multimode vibronic coupling model. For photodetachment, an approximate approach, which is less computationally demanding, is suggested. [ABSTRACT FROM AUTHOR]

Scanning tunneling microscopy (STM) has been a fundamental tool to characterize many-body effects in condensed matter systems, from extended solids to quantum dots. STM of molecules decoupled from the supporting conductive substrate has the potential to extend STM characterization of many-body effects to the molecular world as well. In this paper, we describe a many-body tunneling theory for molecules decoupled from the STM substrate, and we report on the use of standard quantum chemical methods to calculate the quantities necessary to provide the 'correlated' STM molecular image. The developed approach has been applied to 18 different molecules to explore the effects of their chemical nature and of their substituents, as well as to verify the possible contribution by transition metal centers. Whereas the bulk of calculations has been performed with the configuration interaction method with single and double excitations (CISD), because of the computational cost some tests have been also performed with the more accurate coupled cluster with single and double excitations (CCSD) method to quantify the importance of the computational level on many-body STM images. We have found that correlation induces a remarkable squeezing of the images, and that correlated images are not derived from Hartree-Fock HOMO or LUMO alone, but include contributions from other orbitals as well. Although correlation effects are too small to be resolved by present STM experiments for the studied molecules, our results provide hints for seeking out other species with larger, and possibly experimentally detectable, correlation effects. [ABSTRACT FROM AUTHOR]

A general strategy to calculate potential curves at multiconfigurational self-consistent field (MCSCF) level for inner-shell states is reported in this paper. Convergence is commonly very tough for inner-shell states, especially at this level of calculation, due to the problem of variational collapse of the inner-shell wave function to the ground or to a low-lying excited state. The present method allows to avoid this drawback by a sequence of constrained optimization in the orbital mixing step. The specific states studied are that resulting from transitions X 1Σ+ → (C 1s-1 π*) 1,3Π of CO. Accurate values are achieved for transition energies and vibrational splittings. A comparison is made with other approach, i.e., inner-shell CI based on a MCSCF wave function optimized for ground or low-lying excited states. This last approach is shown to fail in describing the whole potential curve. [ABSTRACT FROM AUTHOR]