Comparison of 6-31G*-based MST/SCRF and FEP evaluations of the free energies of hydration for small neutral molecules

A comparison between Miertus–Scrocco–Tomasi (MST) SCRF and free energy perturbation (FEP) estimates of the free energy of hydration of eight small neutral molecules is presented. In both cases, the 6-31G* molecular electrostatic potential is used to describe the electrostatic properties of the molecules. The results demonstrate the ability of both methodologies to provide useful theoretical estimates of the total free energy of hydration; the average errors are only 1.5 kcal/mol (FEP) and 0.8 kcal/mol (MST/SCRF). The largest errors in the FEP and MST/SCRF results are less than 1.5 kcal/mol for all molecules except acetic acid, where the FEP method overestimates the free energy of hydration by 3.3 kcal/mol. © John Wiley & Sons, Inc.     

A simple model for the Slater exchange potential and its performance for solids

A simple local model for the Slater exchange potential is determined by least square fit procedure from Hartree–Fock (HF) atomic data. Since the Slater potential is the exact exchange potential yielding HF electron density from Levy‐Perdew‐Sahni density functional formalism (Levy et al., Phys. Rev. A 1984, 30, 2745), the derived local potential is significantly more negative than the conventional local density approximation. On the set of 22 ionic, covalent and van der Waals solids including strongly correlated transition metal oxides, it has been demonstrated, that this simple model potential is capable of reproducing the band gaps nearly as good as popular meta GGA potentials in close agreement with experimental values.     

Phase‐equilibrium behavior of vinyl chloride/n‐butane and its application in determination of vinyl chloride heterogeneous polymerization kinetics

Studies of the phase‐equilibrium behavior of vinyl chloride (VCM)/n‐butane mixtures and the kinetics of VCM heterogeneous polymerization, using n‐butane as a reaction medium, were carried out using a 1‐L glass autoclave. The vapor composition was measured by gas chromatography, showing that the vapor pressure of the VCM/n‐butane mixture was located above the line connecting the points for pure VCM and n‐butane. The concentration of VCM in the vapor phase was greater than that in the corresponding liquid phase. It was confirmed that the presence of poly(vinyl chloride) (PVC) resin had no significant influences on the phase equilibrium of VCM/n‐butane mixtures. Thus, the phase‐equilibrium equations were applied to determine the conversion of VCM during heterogeneous polymerization. The conversions calculated from the variations of vapor pressure or composition agreed with those determined by the weighing method. The conversion–time and polymerization rate–time curves obtained for VCM heterogeneous polymerization showed that the polymerization accelerated at low initiator concentration, but the polymerization rate decreased with an increase of conversion at relatively high initiator concentrations. The chain‐transfer reaction to n‐butane was confirmed by a decrease of the molecular weight and broadening of the molecular weight distribution of PVC. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2179–2188, 2001     

A fast SHAKE algorithm to solve distance constraint equations for small molecules in molecular dynamics simulations

A common method for the application of distance constraints in molecular simulations employing Cartesian coordinates is the SHAKE procedure for determining the Lagrange multipliers regarding the constraints. This method relies on the linearization and decoupling of the equations governing the atomic coordinate resetting corresponding to each constraint in a molecule, and is thus iterative. In the present study, we consider an alternative method, M‐SHAKE, which solves the coupled equations simultaneously by matrix inversion. The performances of the two methods are compared in simulations of the pure solvents water, dimethyl sulfoxide, and chloroform. It is concluded that M‐SHAKE is significantly faster than SHAKE when either (1) the molecules contain few distance constraints (solvent), or (2) when a high level of accuracy is required in the application of the constraints. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 501–508, 2001     

Use of the normal coordinates in variational and perturbative ab initio handling of the vibronic and spin–orbit couplings in Π electronic states of linear tetra‐atomic molecules

Avariational and a perturbative approach are developed to handle the combined effect of the vibronic and spin–orbit couplings in Π electronic states of tetra‐atomic molecules with linear equilibrium geometry. Both of them are based on the use of the normal vibrational bending coordinates. The perturbative treatment is carried out via two schemes for partition of the model Hamiltonian: In the first, the spin–orbit coupling term is treated as a perturbation; in the second, it is included in the zeroth‐order Hamiltonian. It is demonstrated that both perturbative approaches lead to the same second‐order formulae when the spin–orbit coupling constant is small compared to the bending frequency, but much larger than the splitting of potential surfaces upon bending. These approaches are used to calculate the vibronic and spin–orbit structure in the X²Π electronic state of HCCS by employing the ab initio‐computed potential energy surfaces. Complete numerical equivalence of the results obtained with the present variational approach and those generated by the algorithms employing internal vibrational coordinates is demonstrated. The restrictions concerning the applicability of the perturbative approaches are discussed in terms of the agreement between the results obtained by means of them with those generated in the corresponding variational computations. The general reliability of the model employed is checked by comparing the theoretical results with the available experimental data. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Tensorial green‐function theory of atomic‐wire T‐junction transmission

A tensorial Green‐function treatment of the electronic transmission properties of an atomic wire T‐junction is presented within the framework of the tight‐binding approximation. The adoption of the tensorial formalism enables overlap effects to be included in a straightforward manner, without the need to resort to a change in the Hilbert space. The T‐junction structure and the presence of overlap effects both give rise to antiresonances. Although those due to the former are located inside the energy band, the latter appear at the band edges. The transmission is seen to depend in different ways on the bond energy and the overlap between the attached atom and the wire. © 2012 Wiley Periodicals, Inc.     

A numerical solution of the pair equation of a model two‐electron diatomic system

It has been well‐documented that about 90% of the total correlation energy of atomic systems can be obtained by solving so‐called pair equations. For atoms, this approach requires solving partial differential equations (PDE) in two variables. In case of a diatomic molecule, we face devising a method for treating PDEs in five variables. This article shows how a well‐established finite difference method used to solve Hartree–Fock equations for diatomic molecules can be extended to solve numerically a model two‐electron Schrödinger equation for such systems. We show that using less than 100 grid points in each variable, it is possible to obtain the total energy of the helium atom and hydrogen molecule with a chemical accuracy and the S energy of the helium atom and hydride ion as accurately as the best results available. © 2015 Wiley Periodicals, Inc.     

The UBI-QEP method: Basic formalism and applications to chemisorption phenomena on transition metal surfaces. Chemisorption energetics

The paper reviews the state of the art in the unity bond index-quadratic exponential potential (UBI-QEP) method. Assumptions made in the framework of the method, as well as their validity and generality, are discussed. The method is based only on well-defined observable energetic and structural parameters. UBI-QEP formulas for calculating reaction energetics (the binding energies of atomic and molecular adsorbates, the reaction enthalpies, and the intrinsic activation barriers) at different surface coverages are discussed. The UBI-QEP formalism is best suited for calculations of the adsorption of atoms and diatomic molecules but also allows one to consider polyatomic molecules in the quasi-diatomic approximation. A new formalism is discussed for determining the binding energies of various polyatomic molecules without resorting to hypothetical (and largely ambiguous) bond energy partitioning schemes. Instead, this new formalism considers the total bond energy of gas-phase species, which is an observable value. This formalism is the recent advance in the method. Various examples of calculating the energetics of atomic and molecular adsorption are presented. In most cases, the agreement of calculated and experimental values is good. The UBI-QEP method makes it possible to consider uniformly various processes on metal surfaces: adsorption, dissociation, diffusion, recombination, disproportionation, and desorption. Examples of complicated UBI-QEP calculations of molecular adsorption are presented.     

Partial atomic multipoles for internally consistent microelectrostatic calculations

An extension of the extant microelectrostatic methodologies, based on the concept of distributed generalized polarizability matrix derived from the Coupled Perturbed Hartree–Fock (CPHF) equations, is proposed for self‐consistent calculation of charge carrier and charge‐transfer (CT) state electrostatic energies in molecular solids, including the doped, defected and disordered ones. The CPHF equations are solved only once and the generalized molecular polarizability they yield enables low cost iterations that mutually adjust the molecular electronic distributions and the local electric field in which the molecules are immersed. The approach offers a precise picture of molecular charge densities, accounting for atomic partial multipoles up to order 2, which allows one to reproduce the recently reported large charge‐quadrupole contributions to CT state energies in low‐symmetry local environments. It is particularly well suited for repetitive calculations for large clusters (up to 300,000 atoms), and may potentially be useful for describing electrostatic solvent effects. © 2017 Wiley Periodicals, Inc.     

Toward the multi-component quantum theory of atoms in molecules: a variational derivation

The general formalism of an extended quantum theory of atoms in molecules (QTAIM) dealing with the multi-component quantum systems, composed of various types of quantum particles, is disclosed in this contribution. This novel methodology, termed as the multi-component QTAIM (MC-QTAIM), is able to deal with non-adiabatic ab initio wavefunctions extracting atoms in molecules quantifying their properties. It can also be applied to elucidate the AIM structure of exotic species and bound quantum systems consisting of fundamental elementary particles like positrons and muons. The formalism is based on the previously disclosed density combination idea that is extended to derive the multi-component subsystem hypervirial theorem as well as the extended subsystem energy functional. Through the extended subsystem variational procedure, inspired from Schrödinger’s original variational principle, the surface terms containing the flux of the current property densities are derived. Accordingly, the extended Gamma field is introduced during this variational procedure that is used as the basic scalar field in the topological analysis yielding atoms in molecules and their real space boundaries. The Gamma field is central to the MC-QTAIM, replacing the usual one-electron density employed in the orthodox QTAIM and corresponding topological analysis. Through the multi-component hypervirial theorem, various regional theorems are derived which are then used to quantify the mechanical properties of atoms in molecules; these include the force, virial, torque, power, continuity and current theorems. In order to demonstrate the capability of the formalism, isotopically asymmetric hydrogen molecules, HD, HT and DT as well as YX systems (Y = ⁶Li, ⁷Li; X = H, D, T) composed of electrons and two different nuclei, all treated equally as quantum waves instead of clamped particles, are analyzed within context of the MC-QTAIM. The resulting computational analysis demonstrates that the MC-QTAIM is able to yield reasonable topological structures similar to those observed previously for diatomic species within context of the orthodox QTAIM. The asymmetrical nature of these species, inherent in their non-Born–Oppenhiemer wavefunctions, manifests itself clearly in the MC-QTAIM analysis yielding two distinguishable atomic basins with different properties. These differences are rationalized generally by the observed electron transfer from one basin to the other. Finally, some possible future theoretical extensions are considered briefly.     

A quantum theory atoms in molecules investigation of Lewis base protonation

This investigation uses atomic properties derived from the quantum theory of atoms in molecules formalism to rationalize the infrared intensity of the stretching vibration that arises as a Lewis base (B) is protonated (B‐H mode). Moreover, the interacting quantum atom (IQA) partition is employed to evaluate the energetics of protonation. All calculations are performed at the CCSD/cc‐pVQZ level except by the IQA analysis, which is carried out by means of the B3LYP/cc‐pVQZ//CCSD/cc‐pVQZ treatment. First, an efficiency scale is established for Lewis bases in terms of the electronic charge transfer potential. Next, this study shows that the intensity of the B‐H stretching depends mostly on the electronic charge amount transferred to the proton. Thus, intensity data provide empirical assessment of Lewis base charge transfer efficiency. Finally, the group separation observed during correlation of proton affinities and electronic charge transfer potential is explained by the interaction energy between fragments of the protonated system.     

Bonding in C2 and Be2: Broken symmetry and correlation in DFT solutions

Summary The solution of both Hartree-Fock (HF) and Kohn-Sham (KS) equations is based on the variational principle. Exact wavefunctions would obey the same symmetry restrictions contained in the total hamiltonian. However, the variational principle does not guarantee these symmetry restrictions and the HF and KS solutions are not necessarily symmetric in spin and space. Spatial and spin symmetry broken solutions with lower energies than their restricted analogues are examined for C₂ and Be₂, in the context of the KS formalism. Comparison with UHF solutions shows that KS instabilities are far less pronounced. The main differences between HF and KS solutions are related to effects of electron correlation.     

The quantum theory of atoms in positronic molecules: The subsystem variational procedure

This contribution deals with the subsystem variational procedure within the context of the quantum theory of atoms in positronic molecules (QTAIPM). Before introducing the subsystem energy functional termed as joint subsystem energy functional, a novel notation and the combination strategy are disclosed in detail by restating the positronic subsystem hypervirial theorem. They are employed in proposing the proper subsystem energy functional, the validity of which is checked by various criteria. The zero flux surfaces of the joint density distribution are used to define the topological atoms in the positronic molecules, and they are incorporated into the subsystem variational procedure as proper real space boundary conditions. The variational procedure finally yields the flux of the joint current property density that also appears in the positronic subsystem hypervirial theorem. At every stage, the corresponding equations for the purely electronic systems within the context of the quantum theory of atoms in molecules (QTAIM) are presented to clearly reveal the analogy between these two formalisms and to emphasize the importance of combining the property density distributions in the QTAIPM. The presented material demonstrates the internal consistency of the whole framework and discloses the fact that the QTAIM must be regarded as a variant of the QTAIPM. Furthermore, this formalism promises an extended QTAIM, which is hoped to resolve the issue of molecular structure beyond the clamp nuclei approximation. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

On the influence of nuclear fluctuations on calculated NMR shieldings of benzene and ethylene: a Feynman path integral–ab initio investigation*

The absolute magnetic shieldings of benzene and ethylene have been theoretically studied under the conditions of thermal equilibrium, i.e., under explicit consideration of the nuclear degrees of freedom. For this purpose we have combined the Feynman path integral quantum Monte Carlo (PIMC) formalism with the gauge‐including atomic orbital (GIAO) approach in the Hartree–Fock (HF) approximation. The HF operator has been employed to derive the NMR parameters of the two hydrocarbons via an ensemble averaging over large sets of molecular configurations that are populated in thermal equilibrium. The nuclear fluctuations are responsible for a deshielding of the nuclei relative to the shieldings at the vibrationless minimum of the potential energy surface (PES). The influence of the nuclear degrees of freedom is largest for the isotropic part of the ¹³C shielding tensor. The theoretical results can be explained on the basis of simple geometrical considerations. The bond lengths in thermal equilibrium are larger than the bond lengths at the minimum of the PES. This length enhancement is the prerequisite for a deshielding of the nuclei in thermal equilibrium. The vibrational corrections of the nuclear magnetic resonance (NMR) parameters of benzene and ethylene are quantum driven; classical thermal degrees of freedom of the nuclei are of minor importance. Conceptual problems of theoretical studies of NMR parameters on the basis of a single molecular geometry are emphasized. The influence of the spatial uncertainty of the nuclei becomes decisive in molecules with light atoms. It is pointed out that the combination of the PIMC formalism with electronic Hamiltonians of state‐of‐the‐art quality renders possible accurate determinations of NMR parameters. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem 86: 280–296, 2002     

Density functional study of structural and electronic properties of AlnN (1 ≤ n ≤ 12) clusters

Low‐lying equilibrium geometric structures of Al_nN (n = 1–12) clusters obtained by an all‐electron linear combination of atomic orbital approach, within spin‐polarized density functional theory, are reported. The binding energy, dissociation energy, and stability of these clusters are studied within the local spin density approximation (LSDA) and the three‐parameter hybrid generalized gradient approximation (GGA) due to Becke–Lee–Yang–Parr (B3LYP). Ionization potentials, electron affinities, hardness, and static dipole polarizabilities are calculated for the ground‐state structures within the GGA. It is observed that symmetric structures with the nitrogen atom occupying the internal position are lowest‐energy geometries. Generalized gradient approximation extends bond lengths as compared with the LSDA lengths. The odd–even oscillations in the dissociation energy, the second differences in energy, the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps, the ionization potential, the electron affinity, and the hardness are more pronounced within the GGA. The stability analysis based on the energies clearly shows the Al₇N cluster to be endowed with special stability. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

WKB and MAF quantization rules for spatially confined quantum mechanical systems

A formalism is developed to obtain the energy eigenvalues of spatially confined quantum mechanical systems in the framework of the usual Wentzel–Kramers–Brillouin (WKB) and modified airy function (MAF) methods. To illustrate the working rule, the techniques are applied to three different cases, viz. the confined one‐dimensional harmonic and quartic oscillators and a boxed‐in charged particle subject to an external electric field. The energies thus obtained are compared with those from shifted 1/N expansion, variational, and other methods, as well as the available exact numerical results. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 497–504, 1999     

Orbital functional theory of linear response and excitation

Orbital functional theory (OFT) is based on a rule that determines a single‐determinant reference state Φ for any exact N‐electron eigenstate Ψ. An OFT model postulates an explicit correlation energy functional E_c of occupied orbital functions {?_i} and occupation numbers {n_i}. The orbital Euler–Lagrange equations are analogous to Kohn–Sham equations, but do not in general contain local potential functions. Time‐dependent Hartree–Fock theory is generalized in OFT to a formally exact linear response theory that includes electronic correlation. In the exchange‐only limit, the theory reduces to the random‐phase approximation of many‐body theory. The formalism determines excitation energies. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

A simple approximation for the Pauli potential yielding self‐consistent electron densities exhibiting proper atomic shell structure

A simple approximation for the Pauli potential for the groundstate of atomic systems is given, which in connection with Hohenberg–Kohn variational procedure yields self‐consistent electron densities exhibiting proper atomic shell structure. © 2015 Wiley Periodicals, Inc.     

A comparison of variational and non-variational internally contracted multiconfiguration-reference configuration interaction calculations

Summary The internally contracted multiconfiguration-reference configuration interaction (CMRCI) method and several non-variational variants of this method (averaged coupled pair approximation (ACPF), quasidegenerate variational perturbation theory (QD-VPT), linearized coupled pair many electron theory (LCPMET)) have been employed to compute potential energy functions and other properties for a number of diatomic molecules (F₂, O₂, N₂, CN, CO) using large basis sets and full valence CASSCF reference wavefunctions. In most cases the variational CMRCI wavefunctions yield more accurate spectroscopic constants than any of the employed non-variational methods. Several basis sets are compared for the N₂ molecule. It is found that atomic natural orbital (ANO) contractions led to significant errors in the computedr _e , _e , andD _e values.     

Force related atomic multipoles in planar molecules. Derivation of atomic quadrupole and octupole moments

Atomic multipoles as defined by current methods generally do not account for forces in molecules that arise from external electrostatic fields. It is pointed out that such forces and the electrostatic potential that the molecule itself generates are both determined by the molecular multipolar tensors. The latter constitute therefore the fundamental molecular constants that determine the molecular electrostatics apart from polarization. In general the multipolar tensors include contributions from the atomic multipoles and their fluxes. In planar molecules, however, the perpendicular charge flux is zero by symmetry. This gives rise to a (previously introduced) formalism that extracts analytical, force-related, atomic multipoles from the molecular multipolar tensors. This formalism is extended in this work to include force-related (FR) atomic quadrupoles and octupoles in planar molecules. The properties of the FR atomic multipoles, including their perpendicular fluxes, are discussed and some formal theoretical and computational advantages that characterize them are indicated. As an example, the electrostatics of OCS, including the molecular electrostatic potential and the forces on the nuclei due to an external point charge, is discussed.