Improved embedded molecular cluster model

We demonstrate that boundary effects (i.e., displacements of the cluster boundary atoms from their lattice sites and the difference between effective charges of the perfect crystal atoms and those of the cluster atoms in the case of a cluster with no point defect in it) in an embedded molecular cluster (EMC) model can be radically reduced. A new embedding scheme is proposed. It includes search for the structural elements (SE) of which perfect crystal is composed, use of corresponding to these SE expression for the total energy, and application of the degree of localization of equations consistent with the wave functions of the cluster. To get equations for the cluster wave functions, the problem of varied subsystem in the field of the frozen remaining part of the whole electron system” is investigated in the framework of a one-electron approximation. The consideration is general for every task of this type. Homogeneous equations resulting directly from variation of the total energy expression are obtained and transformed to the eigenvalue problem equations. Orthogonality constraints are not imposed during variation. A particular case of the equations describing mutually orthogonal one-electron wave functions of the cluster staying nonorthogonal to those of the remaining crystal is found. A proposed embedding scheme is realized in the CLUSTER code based on the calculation scheme of the semiempirical INDO method. Boundary effects both in the standard (cluster in the field of the infinite lattice of nonpoint spherical charges) and new embedding scheme are investigated, calculating the clusters of LiF, MgO, NaCl, KCl, and AgCl crystals. Significant reduction of the boundary effects in the new embedding scheme is achieved. Reasons for the boundary effects are discussed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Unlinked cluster effects in limited CI calculations of molecular properties

The unlinked cluster effects in limited CI calculations of dipole moments and polarizabilities are estimated by using the approximate corrections due to Davidson and Siegbahn. The results obtained for FH, H₂O, NH₃, and CH₄ indicate that the limited CI results for molecular electric properties need to be corrected for the erratic treatment of unlinked clusters.     

Madelung fields from optimized point charges for ab initio cluster model calculations on ionic systems

A simple procedure devised to obtain optimized point charges to represent the Madelung potential is reported and applied to six different crystal structures occurring in ionic systems. Their use in ab initio cluster model calculations is discussed through some selected examples and results compared with those arising from the use of the well-known Evjen method. © 1993 John Wiley & Sons, Inc.     

Multicenter point charge model for high-quality molecular electrostatic potentials from AM1 calculations

The natural atomic orbital/point charge (NAO-PC) model based upon the AM1 wave function has been developed to calculate molecular electrostatic potentials (MEPs). Up to nine point charges (including the core charge) are used to represent heavy atoms. The positions and magnitudes of the eight charges that represent the atomic electron cloud are calculated from the natural atomic orbitals (NAOs) and their occupations. Each hybrid NAO is represented by two point charges situated at the centroid of each lobe. The positions of the centroids and the magnitudes of the charges were obtained by numerical integration of the Slater-type hybrids and the results used to set up polynomials and look-up tables that replace the integration step in the actual MEP calculation. The MEPs calculated using this method are found to be in better agreement with those obtained using RHF/6-31G* than those obtained from the AM1 wave function using Coulson charges or with MOPAC-ESP. The MEP calculations are extremely fast and have, for instance, been incorporated into an interactive graphics package. © 1993 John Wiley & Sons, Inc.     

Differential correlation effects in chemisorption cluster model calculations: an FCI study

The interaction of atomic hydrogen with Cu₅ and Ag₅ cluster models simulating the Cu(100) and Ag(100) surfaces has been studied at the full configuration interaction (FCI) level in order to establish the transferability of differential correlation arising from the valence shell. It is shown that pseudopotentials that deal explicitly with one electron or eleven electrons lead to differential correlation effects which agree to within 1–2 mhartree when a localization procedure is used to separate d-shell MOs from the valence ones.     

Asymptotic extrapolation scheme for large-scale calculations with hybrid coupled cluster and molecular dynamics simulations

In this paper we discuss a simple extrapolation scheme based on the asymptotic behavior of the electronic energies considered as functions of cutoff factor for orbital energies corresponding to virtual orbitals. The performance of this approach is illustrated in the context of large-scale dynamic simulations for excitation energies of the cytosine molecule in its native DNA environment. We demonstrate that the extrapolation errors are significantly smaller than the excitation-energy fluctuations, due to the fluctuating environment.     

DFT and MO calculations of atomic and molecular chemisorption energies on surface cluster models

Summary Density functional theory (DFT) (including gradient corrections) and MCPF calculations have been performed for atomic (H, C, N, O) and molecular CH _x (x = 1–3) chemisorption on cluster models of different sites of the Cu(100) surface. The DFT and MCPF results are in good agreement once the important effects of core-valence correlation have been accounted for in the MCPF calculations by including contributions from a core polarization potential (CPP); in the DFT approach the core-valence correlation is obtained directly from the total density using the functional. Very large effects on the four-fold hollow site binding energy from core-valence correlation are found for C, N and CH. Several different DFT functionals were employed and compared in the calculations.     

Lattice-dynamical calculations for orthorhombic sulfur: a non-rigid molecular model

A lattice-dynamical calculation for orthorhombic (“α”) sulfur has been carried out with a non-rigid molecular model. A difference is observed for the lowest frequencies between the free and the packed molecule. For this reason the empirical force fields which have been fitted to the crystal should be modified, especially by lowering the torsional constants. If such a modified field is used, excellent agreement of calculated thermodynamic functions and crystallographic temperature factors with experimental data is obtained. An underestimation of nearly 2 cal mol^?1 K^?1 in the values which are currently reported for the entropy of the vapour at room temperature is also inferred.     

Prediction of polymer miscibility from molecular mechanics calculations

A new computational method is presented for the rapid estimation of polymer miscibility. The algorithm (coined FLEXIBLEND) uses molecular mechanics calculations on a pair of polymer segments and takes into account the effects of local chain flexibility to estimate heats of mixing. This paper shows miscibility predictions in agreement with experiment for blends of poly(ethyleneoxide) (PEO) with isotactic poly(propylene) (PP) as an immiscible system and of PEO with poly(acrylic acid) (PAA) as a miscible system.     

IMiCMO: a new integrated ab initio multicenter molecular orbitals method for molecular dynamics calculations in solvent cluster systems

A new computational scheme integrating ab initio multicenter molecular orbitals for determining forces of individual atoms in large cluster systems is presented. This method can be used to treat systems of many molecules, such as solvents by quantum mechanics. The geometry parameters obtained for three models of water clusters by the present method are compared with those obtained by the full ab initio MO method. The results agree very well. The scheme proposed in this article also intended for use in modeling cluster systems using parallel algorithms. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1107–1112, 2001     

Ab initio molecular orbital calculations on large lattice cluster models: Use of translational symmetry

Summary Translational symmetry has been shown to be useful in the calculation of electronic structures of large lattice models. The number of unique integrals has been derived for cases of different dimensionality. For the unique integrals zero screening and approximation methods are described. The method has been applied to arrays of hydrogen atoms and to a zincblende surface model. When the size of the system is increased the translationally unique integrals are shown to become either zero or they can be calculated by simple coulombic approximations.     

Ab initio compact group model potentials for describing environment effects in cluster calculations

A method for the determination of ab initio group model potentials within the Hartree–Fock framework is reported. Following the theory of separability of many electron systems, a new way to incorporate the effect of complete chemical entities by means of polycenter compact model potentials is presented. The interaction between active and frozen electrons is partitioned as a sum of long- and short-range terms. The long-range term is described as the effect of −2e charges placed in the center of the charge of the frozen group molecular orbitals; the short-range one, the exchange and Pauli repulsion, is developed as a spectral representation in a nonorthogonal basis set. An algorithm to solve the problem associated with the rotation of the polycenter model potential is presented and implemented in an all-purpose quantum chemical program. In order to check the method, a group model potential for H₂O was obtained and tested. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1145–1152, 1999     

Estimation of electron transfer parameters from AM1 calculations

The utility of AM1 calculations for estimation of the electron-transfer parameters lambda'(v) (the enthalpy part of the Marcus internal reorganization energy) and H(ab) (the electronic coupling between the charge-bearing units) is considered for some charge-localized intervalence bis(hydrazine) radical cations, for which these parameters have been experimentally determined from optical measurements. The Koopmans estimate of lambda'(v) that employs the orbital separation for the neutral compound at the radical cation geometry is far from that calculated from the enthalpies of the species involved (eq 1) and is not correct. The eq 1 lambda'(v) enthalpies estimated by AM1 are reasonably good for compounds with only alkyl substituents but are overestimated by 33-59% for aryl-substituted hydrazines. The Koopmans estimate of H(ab) as half the orbital separation for the neutral species at the transition state geometry requires adjustment for the twist angles to those of the relaxed ground state to produce useful H(ab) values. Symmetry breaking occurs for the electron-transfer transition states of the compounds with saturated bridges, and the Koopmans estimate predicts H(ab) values that are slightly less than half as large as the optical measurements.     

Using molecular dynamics and quantum mechanics calculations to model fluorescence observables

We provide a critical examination of two different methods for generating a donor-acceptor electronic coupling trajectory from a molecular dynamics (MD) trajectory and three methods for sampling that coupling trajectory, allowing the modeling of experimental observables directly from the MD simulation. In the first coupling method we perform a single quantum-mechanical (QM) calculation to characterize the excited state behavior, specifically the transition dipole moment, of the fluorescent probe, which is then mapped onto the configuration space sampled by MD. We then utilize these transition dipoles within the ideal dipole approximation (IDA) to determine the electronic coupling between the probes that mediates the transfer of energy. In the second method we perform a QM calculation on each snapshot and use the complete transition densities to calculate the electronic coupling without need for the IDA. The resulting coupling trajectories are then sampled using three methods ranging from an independent sampling of each trajectory point (the independent snapshot method) to a Markov chain treatment that accounts for the dynamics of the coupling in determining effective rates. The results show that the IDA significantly overestimates the energy transfer rate (by a factor of 2.6) during the portions of the trajectory in which the probes are close to each other. Comparison of the sampling methods shows that the Markov chain approach yields more realistic observables at both high and low FRET efficiencies. Differences between the three sampling methods are discussed in terms of the different mechanisms for averaging over structural dynamics in the system. Convergence of the Markov chain method is carefully examined. Together, the methods for estimating coupling and for sampling the coupling provide a mechanism for directly connecting the structural dynamics modeled by MD with fluorescence observables determined through FRET experiments.     

Strained ring carbonyl force constants from molecular orbital calculations

Molecular orbital theory is used to evaluate the carbonyl force constants in several compounds. The carbonyl force constants k_CO are found to be essentially unchanged in the series: acetone, cyclopentanone, and cyclobutanone; however, the value of k_CO is calculated to be 5% higher in the case of cyclopropanone.     

Molecular conformation of bilirubin from semiempirical molecular orbital calculations

Semiempirical methods were utilized in the computation of a fully optimized structure of bilirubin. Bond lengths and bond angles obtained using either AM1 or PM3 calculations showed excellent agreement with those obtained by X-ray diffraction. This indicated that molecular orbital methods satisfactory reproduced the complex conjugation found in bilirubin. Dihedral angles of the crucial “hinge” and the dihedral angles of the propionic acid side chains agreed well with those found by X-ray diffraction. Calculated hydrogen- bond parameters (distance and angles) showed substantial differences from experimental values, probably due to inherent weakness in the parameterization of the molecular orbital techniques. Conformational studies were carried out using AM1 by rotating the C9? C10 bond in 5° increments showed that the most stable structure exhibited a minimum at about 125° and exhibited a structure similar to those postulated from X-ray and NMR experiments. The hydrogen bonds showed remarkable tenacity during rotation of the C9? C10 bond and resisted breaking until the molecule was under extreme strain. © 1992 John Wiley & Sons, Inc.     

Charge calculations in molecular mechanics. Part 8 Partial atomic charges from classical calculations

Summary The CHARGE2 programme, which involves the classical calculation of both the inductive and resonance contributions to the partial atomic charges in molecules is described, and the charges and electrostatic potentials obtained presented for some illustrative examples.In substituted methanes (CH₃X, CF₃X, CCl₃X) the effects of varying the electronegativity of the substituents and the - and -substituent contributions are clearly illustrated for a variety of substituent groups X.The problems involved in the inclusion of silicon into this scheme are detailed, together with the methods of overcoming them. The partial atomic charges ( and contributions) and electrostatic potentials for some silicon oxygen compounds are presented and discussed.The partial atomic charges from CHARGE2 for all the natural amino acids as their N-acetyl, N-methyl-amides are given and compared with those obtained from the AMBER and ECEPP/2 force fields. Considerable differences in these figures are observed, with the AMBER charges consistently much larger than those from the other two methods.The CHARGE2 partial atomic charges and electrostatic potentials for the four common nucleic acids, adenine, cytosine, guanine and thymine, are given and compared with those derived from other calculations. Again there is general similarity but also there are considerable differences, with those from the AMBER force field somewhat larger than the other methods.For previous parts in this series, see Refs. 1-7.     

A new boundary treatment: HF surface potential model applied to solid-state cluster calculations

A new boundary treatment, a Hartree–Fock (HF ) surface potential model, is proposed to deal with the surface effect in the solid-state cluster calculations using the LCAO –MO –SCF ab initio method. The surface potential arises from one or more atoms, which have no basis function and are added to the calculated cluster system. These atoms are placed in such sites so that the HF potential field of the calculated system should possess a point-group symmetry. The surface potential could be found by the corresponding HF potential using a symmetry operator. The fact that a rather symmetric electronic structure of the asymmetric cluster YBa₂CuZn₂O₇ is obtained using the HF surface potential shows that the surface effect in the cluster calculations could be neutralized to a great extent. © 1995 John Wiley & Sons, Inc.     

Mesoscale model of polymer melt structure: self-consistent mapping of molecular correlations to coarse-grained potentials

Development and application of coarse-graining methods to condensed phases of macromolecules is an active area of research. Multiscale modeling of polymeric systems using coarse-graining methods presents unique challenges. Here we apply a coarse-graining method that self-consistently maps structural correlations from detailed molecular dynamics (MD) simulations of alkane oligomers onto coarse-grained potentials using a combination of MD and inverse Monte Carlo methods. Once derived, the coarse-grained potentials allow computationally efficient sampling of ensemble of conformations of significantly longer polyethylene chains. Conformational properties derived from coarse-grained simulations are in excellent agreement with experiments. The level of coarse graining provides a control over the balance of computational efficiency and retention of chemical identity of the underlying polymeric system. Challenges to extension and application of this and similar structure-based coarse-graining methods to model dynamics and phase behavior in polymeric systems are briefly discussed.     

A comparison of empirical force field parameters for molecular mechanics calculations on saturated hydrocarbons

Nine empirical force fields used in molecular mechanics calculations are tested for their abilities to reproduce experimental geometric and energy data on $\text{cis-syn-cis}$-perhydroanthracene.