Coulomb-Hole–Hartree–Fock functional

We have extended to molecules a density functional previously parametrized for atomic computations. The Coulomb-hole–Hartree–Fock functional, introduced by Clementi in 1963, estimates the dynamical correlation energy by the computations of a Hartree–Fock-type single-determinant wave function, where the Hartree–Fock potential was augmented with an effective potential term, related to a hard Coulomb hole enclosing each electron. The method was later revisited by S. Chakravorty and E. Clementi [Phys. Rev. A 39 , 2290 (1989)], where a Yukawa-type soft Coulomb hole replaced the previous hard hole; atomic correlation energies, computed for atoms with Z = 2 to Z = 54 as well as for a number of excited states, validated the method. In this article, we parametrized a function, which controls the width of the soft Coulomb hole, by fitting the first and second atomic ionization potentials of the atoms with 1 ? Z ? 18. The parametrization has been preliminarily validated by computing the dissociation energy for a number of molecules. A few-determinant version of the Coulomb-hole–Hartree–Fock method, necessary to account for the nondynamic correlation corrections, is briefly discussed. © 1994 John Wiley & Sons, Inc.     

Coulomb-hole-Hartree-Fock functional for molecular systems

We have extended to molecules a density functional previously parametrized for atomic computations. The Coulombhole-Hartree-Fock functional, introduced by Clementi in 1963, estimated the dynamic correlation energy by the computation of a Hartree-Fock type single-determinant wavefunction, where the Hartree-Fock potential was augmented with an effective potential term, related to a hard Coulomb hole enclosing each electron. The method was later revised by S. Chakravorty and E. Clementi, Phys. Rev. A, 38 (1989) 2290, so that a Yukawa-type soft Coulomb hole replaced the previous hard hole. Atomic correlation energies, computed for atoms with Z = 2 to 54, as well as for a number of excited states, validated the method. In this work we have parametrized for molecules a function which controls the width of the soft Coulomb hole by fitting the first and second atomic ionization potentials of atoms with 1 Z 18 and the binding energies of a few diatomic molecules. The parametrization was successfully validated by computing the dissociation energy for a number of molecules. A few-determinant version of the Coulomb-Hartree-Fock method (CHF-N) necessary to account for the non-dynamic correlation correction and to ensure proper dissociation products, is briefly discussed with reference to a previous proposal by G.C. Lie and E. Clementi, J. Chem. Phys., 60 (1974) 1275 and 60 (1974) 1288.     

A Dirac–Fock self-consistent field method for closed-shell molecules including Breit interaction

We present a method for including the Breit interaction in relativistic self-consistent field calculations for closed-shell molecular systems using atomic basis spinors of kinetically balanced Gaussian-type functions. The method extends the formalism described in a previous paper [A. Mohanty and E. Clementi, Int. J. Quantum Chem. 39 , 487–517 (1991)] that dealt with the two-electron effect due to Coulomb interaction only. It is shown that both frequency-dependent and frequency-independent Breit interactions can be treated on equal footing, and the corresponding matrix elements are evaluated following the well-known Fourier transform technique applied to electron repulsion integral evaluation in nonrelativistic molecular calculations.     

On the hydrogen atom beyond the Born–Oppenheimer approximation

Recently a new formulation of quantum mechanics has been suggested which is based on the concept of signed particles, that is, classical objects provided with a position, a momentum and a sign simultaneously. In this article, we comment on the plausibility of simulating atomic systems beyond the Born–Oppenheimer approximation by means of the signed particle formulation of quantum mechanics. First, to show the new perspective offered by this new formalism, we provide an example studying quantum tunnelling through a simple Gaussian barrier in terms of the signed particle formulation. Then, we perform a direct simulation of the hydrogen atom as a full quantum two‐body system, showing that the formalism can be a very promising tool for first‐principle‐only quantum chemistry.     

Application of an optimization technique to the discretized version of the Griffin–Hill–Wheeler–Hartree–Fock equations

Application of the SIMPLEX optimization method to define the mesh of the discretized version of the Griffin–Hill–Wheeler–Hartree–Fock (GHWHF ) equations was studied. Improved discretization parameters with respect to the original method were obtained for atomic systems with two or four electrons and for the H₂ molecule. For the atomic systems, the following correlations between the discretization parameters and the total energy were found: N = a · In(ΔE) + b; Ω₀ = a′ · In(ΔΩ) + a″; and In(ΔΩ) = b′ · ln(N) + b″. These equations provide a systematic procedure to reach a desired degree of accuracy in the energy for the atomic systems studied as well as to fix the basis set to be employed. These equations are similar to those found earlier for eventempered basis sets and permit the establishment of a relationship between the two methods. The even-tempered method is also an approximate solution of the GHWHF equations. The optimized integral discretized basis is more efficient in representing small basis sets for atoms and the basis for the hydrogen molecule in comparison to the even-tempered one. The optimization procedure was successfully applied to generate the universal basis for the atomic systems studied.     

Analytical density-dependent representation of Hartree—Fock atomic potentials

A procedure to represent atomic electron charge densities [L. Fernandez Pacios, J. Phys. Chem., 95 , 10653 (1991); J. Phys. Chem., 96 , 7294 (1992)] is here generalized to obtain simple analytical functions for potential energy contributions. Based upon suitable functions to describe atomic electron densities in a physically meaningful form, the procedure is developed to define density-dependent analytical expressions for the electrostatic (classical) and exchange (quantum) potentials by means of proper approximate functionals. Calculations of correlation energies by using various density-functional approaches are also performed. The whole scheme is used to represent Hartree–Fock limit atomic wave functions by Clementi–Roetti. This way, a set of analytically simple, nonbasis set-dependent functions are defined with the aim to be further implemented in energy decomposition schemes for molecular interactions studies using atomic instead of electronic building blocks. © 1993 John Wiley & Sons, Inc.     

Improved Pöschl–Teller potential energy model for diatomic molecules

By employing the dissociation energy and the equilibrium internuclear distance for a diatomic molecule as explicit parameters, we construct an improved Pöschl–Teller potential energy model. We analyze the average absolute deviations of the improved Pöschl–Teller and Morse potentials from the experimental Rydberg–Klein–Rees (RKR) potentials for six diatomic molecules. It is found that the improved Pöschl–Teller potential is more accurate than the Morse potential in fitting experimental RKR potential curves over a large range of internuclear distances for six molecules examined.     

Coarse‐grained molecular dynamics simulations of protein–ligand binding

Coarse‐grained molecular dynamics (CGMD) simulations with the MARTINI force field were performed to reproduce the protein–ligand binding processes. We chose two protein–ligand systems, the levansucrase–sugar (glucose or sucrose), and LinB–1,2‐dichloroethane systems, as target systems that differ in terms of the size and shape of the ligand‐binding pocket and the physicochemical properties of the pocket and the ligand. Spatial distributions of the Coarse‐grained (CG) ligand molecules revealed potential ligand‐binding sites on the protein surfaces other than the real ligand‐binding sites. The ligands bound most strongly to the real ligand‐binding sites. The binding and unbinding rate constants obtained from the CGMD simulation of the levansucrase–sucrose system were approximately 10 times greater than the experimental values; this is mainly due to faster diffusion of the CG ligand in the CG water model. We could obtain dissociation constants close to the experimental values for both systems. Analysis of the ligand fluxes demonstrated that the CG ligand molecules entered the ligand‐binding pockets through specific pathways. The ligands tended to move through grooves on the protein surface. Thus, the CGMD simulations produced reasonable results for the two different systems overall and are useful for studying the protein–ligand binding processes. © 2014 Wiley Periodicals, Inc.     

Efficient Intramolecular Charge Transfer in Oligoyne‐Linked Donor–π–Acceptor Molecules

Studies are reported on a series of triphenylamine–(C?C)_n–2,5‐diphenyl‐1,3,4‐oxadiazole dyad molecules (n=1–4, 1 , 2 , 3 and 4 , respectively) and the related triphenylamine‐C₆H₄–(C?C)₃–oxadiazole dyad 5 . The oligoyne‐linked D–π–A (D=electron donor, A=electron acceptor) dyad systems have been synthesised by palladium‐catalysed cross‐coupling of terminal alkynyl and butadiynyl synthons with the corresponding bromoalkynyl moieties. Cyclic voltammetric studies reveal a reduction in the HOMO–LUMO gap in the series of compounds 1 – 4 as the oligoyne chain length increases, which is consistent with extended conjugation through the elongated bridges. Photophysical studies provide new insights into conjugative effects in oligoyne molecular wires. In non‐polar solvents the emission from these dyad systems has two different origins: a locally excited (LE) state, which is responsible for a π*→π fluorescence, and an intramolecular charge transfer (ICT) state, which produces charge‐transfer emission. In polar solvents the LE state emission vanishes and only ICT emission is observed. This emission displays strong solvatochromism and analysis according to the Lippert–Mataga–Oshika formalism shows significant ICT for all the luminescent compounds with high efficiency even for the longer more conjugated systems. The excited‐state properties of the dyads in non‐polar solvents vary with the extent of conjugation. For more conjugated systems a fast non‐radiative route dominates the excited‐state decay and follows the Engelman–Jortner energy gap law. The data suggest that the non‐radiative decay is driven by the weak coupling limit.     

Kramers' unrestricted Hartree–Fock and second-order Møller–Plesset perturbation methods using relativistic effective core potentials with spin–orbit operators: Test calculations for HI and CH3I

The Kramers' restricted Hartree–Fock (KRHF) and second-order Møller–Plesset perturbation (KRMP2) methods using relativistic effective core potentials (RECP) with spin–orbit operators and two-component spinors are extended to the unrestricted forms, KUHF and KUMP2. As in the conventional unrestricted methods, the KUHF and KUMP2 methods are capable of qualitatively describing the bond breaking for a single bond. As a result, it is possible to estimate spin–orbit effects along the dissociation curve at the HF and MP2 levels of theory as is demonstrated by the test calculations on the ground states of HI and CH₃I. Since the energy lowering due to spin–orbit interactions is larger for the I atom than for the closed-shell molecules, dissociation energies are reduced and bond lengths are slightly elongated by the inclusion of the spin–orbit interactions. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 91–98, 1998     

Energy Landscape of Aptamer/Protein Complexes Studied by Single‐Molecule Force Spectroscopy

Aptamers are single‐stranded nucleic acid molecules selected in vitro to bind to a variety of target molecules. Aptamers bound to proteins are emerging as a new class of molecules that rival commonly used antibodies in both therapeutic and diagnostic applications. With the increasing application of aptamers as molecular probes for protein recognition, it is important to understand the molecular mechanism of aptamer–protein interaction. Recently, we developed a method of using atomic force microscopy (AFM) to study the single‐molecule rupture force of aptamer/protein complexes. In this work, we investigate further the unbinding dynamics of aptamer/protein complexes and their dissociation‐energy landscape by AFM. The dependence of single‐molecule force on the AFM loading rate was plotted for three aptamer/protein complexes and their dissociation rate constants, and other parameters characterizing their dissociation pathways were obtained. Furthermore, the single‐molecule force spectra of three aptamer/protein complexes were compared to those of the corresponding antibody/protein complexes in the same loading‐rate range. The results revealed two activation barriers and one intermediate state in the unbinding process of aptamer/protein complexes, which is different from the energy landscape of antibody/protein complexes. The results provide new information for the study of aptamer–protein interaction at the molecular level.     

Reformulating the entropic contribution in molecular docking scoring functions

We have derived, in the context of the Rigid Rotor Harmonic Approximation (RRHO), a general mass and Planck's constant h independent expression for the dissociation free energy in ligand–receptor systems, featuring a systematically (anti‐binding) additive negative entropic term depending on readily available ligand–receptor quantities. The proposed RRHO expression allows to straightforwardly compute the absolute standard dissociation free energy without resorting to expensive normal mode analysis or other dynamical matrix‐based techniques for evaluating the entropic contribution, hence providing an effective scoring function for assessing docking poses with no adjustable parameters. Our RRHO formula was tested on a set of 55 ligand–receptor systems obtaining correlation coefficients and unsigned mean errors comparable to or better than those obtained with computationally demanding techniques for the dissociation entropy assessment. The proposed compact reformulation of the RRHO entropy term could constitute the basis for new and more effective scoring functions in molecular docking‐based high‐throughput virtual screening for drug discovery. © 2016 Wiley Periodicals, Inc.     

Fully polarizable QM/MM calculations: An application to the nonbonded iodine–oxygen interaction in dimethyl‐2‐iodobenzoylphosphonate

The compound dimethyl‐2‐iodobenzoylphosphonate is unusual in that it forms well‐ordered crystals that clearly show short iodine‐oxygen interactions in which both the iodine and the oxygen are in their normal oxidation states. These interactions were studied using a new hybrid quantum mechanical–molecular mechanical approach that employs a polarizable molecular mechanics component. The electric field at the molecular mechanics atoms was calculated from a distributed multipole expansion of the wave function; this induced dipoles on the molecular mechanics atoms. The electrostatic potential in a spherical shell around the induced dipoles was reproduced through induced charges on the atomic center and those bonded to it using an analytical (rather than numerical) procedure. The new atomic charges (induced charges plus permanent charges) were then able to interact with the quantum mechanical entity and polarize the wave function. The procedure was iterated to convergence. The calculations show that the iodine atom becomes more positive in the crystal environment (modeled by a chain of three molecules of dimethyl‐2‐iodobenzoylphosphonate). Thus, while the cooperative effects of the crystal environment may not be the only feature stabilizing this unusual interaction, they do play a significant role in reducing the otherwise unfavourable iodine–oxygen monopole–monopole interaction. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 478–482, 2000     

Time‐Dependent Density Functional Theory Molecular Dynamics Simulations of Liquid Water Radiolysis

The early stages of the Coulomb explosion of a doubly ionized water molecule immersed in liquid water are investigated with time‐dependent density functional theory molecular dynamics (TD–DFT MD) simulations. Our aim is to verify that the double ionization of one target water molecule leads to the formation of atomic oxygen as a direct consequence of the Coulomb explosion of the molecule. To that end, we used TD–DFT MD simulations in which effective molecular orbitals are propagated in time. These molecular orbitals are constructed as a unitary transformation of maximally localized Wannier orbitals, and the ionization process was obtained by removing two electrons from the molecular orbitals with symmetry 1B₁, 3A₁, 1B₂ and 2A₁ in turn. We show that the doubly charged H₂O²⁺ molecule explodes into its three atomic fragments in less than 4 fs, which leads to the formation of one isolated oxygen atom whatever the ionized molecular orbital. This process is followed by the ultrafast transfer of an electron to the ionized molecule in the first femtosecond. A faster dissociation pattern can be observed when the electrons are removed from the molecular orbitals of the innermost shell. A Bader analysis of the charges carried by the molecules during the dissociation trajectories is also reported.     

Elastic scattering of low and intermediate-energy electrons by Kr and Xe atoms

The many-body correlation forces, which act between the impinging electron and the bound electrons of the two heaviest rare gas atoms, are treated here using a newly developed correlation-polarisation potential that originates from the calculation of correlation energies in electronic bound-states of atoms and molecules. The new formulation of such forces, already tested by us for the lighter atomic targets, is particularly effective for the present systems and can be implemented very easily even for heavy atomic targets. The calculations reported in this paper show clearly that very good accord is obtained with more sophisticated theoretical treatments and with several experimental data on integral cross sections, momentum transfer cross sections and angular distributions.Von Humboldt — Prize Awardee 1992     

The physics of the born–oppenheimer approximation

A new derivation of the Born–Oppenheimer separation of electronic and nuclear motion is presented. The arguments used differ from those in earlier works in not being specially designed for molecules. Instead they aim at an intuitive understanding of the qualitative behavior of the low energy bound states of any, real or hypothetical, Coulomb interacting system of particles. The virial theorem is the starting point of the discussion. After a brief explanation of how it can be used to understand atomic structure it is applied to molecules. It is found that coordinates of collective and individual motion are natural coordinates for the approximate separation, rather than nuclear and electronic. It is also shown that it is the form of the interaction between the particles that is responsible for the separation; the smallness of m_et/M_Nu is irrelevant.     

Dissociation energy of ekaplutonium fluoride E126F: the first diatomic with molecular spinors consisting of g atomic spinors

Our ab initio all-electron fully relativistic Dirac-Fock (DF) and nonrelativistic (NR) Hartree-Fock (HF) self-consistent field (SCF) calculations predict the superheavy diatomic ekaplutonium fluoride E126F to be bound with the calculated dissociation energy of 7.44 and 10.46 eV at the predicted E126-F bond lengths of 2.03 and 2.18 Angstroms, respectively. The antibinding effects of relativity to the dissociation energy of E126F are approximately 3 eV. The predicted dissociation energy with both our NR HF and relativistic DF SCF wave functions is fairly large and is comparable to that for very stable diatomics. This is the first case, where in a diatomic, an atom has g orbital (l = 4) occupied in its ground state electronic configuration and such superheavy diatomics would have occupied molecular spinors (orbitals) consisting of g atomic spinors (orbitals). This opens up a whole new field of chemistry where g atomic spinors (orbitals) may be involved in electronic structure and chemical bonding of systems of superheavy elements with Z> or =122.     

Charge Separation in Graphene‐Decorated Multimodular Tris(pyrene)–Subphthalocyanine–Fullerene Donor–Acceptor Hybrids

A new approach to probe the effect of graphene on photochemical charge separation in donor–acceptor conjugates is devised. For this, multimodular donor–acceptor conjugates, composed of three molecules of pyrene, a subphthalocyanine, and a fullerene C₆₀ ((Pyr)₃SubPc‐C₆₀), have been synthesized and characterized. These systems were hybridized on few‐layer graphene through π–π stacking interactions of the three pyrene moieties. The hybrids were characterized using Raman, HRTEM, and spectroscopic and electrochemical techniques. The energy levels of the donor–acceptor conjugates were fine‐tuned upon interaction with graphene and photoinduced charge separation in the absence and presence of graphene was studied by femtosecond transient absorption spectroscopy. Accelerated charge separation and recombination was detected in these graphene‐decorated conjugates suggesting that they could be used as materials for fast‐responding optoelectronic devices and in light energy harvesting applications.     

Relationship between structures and activities of silver salt–organic halide catalyst systems for styrene polymerization

The rate of bulk polymerization of styrene initiated by silver salt–organic halide systems was measured at 0°C. Neither of the catalyst components initiated the polymerization when used alone, while combined catalysts containing both components initiated the polymerization in the case that the components reacted with each other with precipitation of silver halide. The rate in the early stage of the polymerization increased with an increase in reaction time. Plots of yield against the second power of time gave a linear relation in the early stage of the polymerization. The slope of the line was taken as a measure of catalytic activity. The catalytic activity was markedly influenced by the kinds of the components. The activities of silver perchlorate–organic halide systems increased in the following order of halides: chloride < bromide < iodide in most cases. The activities of silver perchlorate–organic chloride systems increased with a decrease in ionization potentials of the organic groups of the chlorides. The activities of silver salt–benzyl bromide systems increased with a decrease in the pK_a values of conjugate acids of silver salts. From these results, it was concluded that the facility of ionic dissociation of the catalyst components determined the activities.