Monte Carlo configuration interaction applied to multipole moments,ionization energies,and electron affinities

The method of Monte Carlo configuration interaction (MCCI) (Greer, J. Chem. Phys. 1995a, 103, 1821; Tong, Nolan, Cheng, and Greer, Comp. Phys. Comm. 2000, 142, 132) is applied to the calculation of multipole moments. We look at the ground and excited state dipole moments in carbon monoxide. We then consider the dipole of NO, the quadrupole of N₂ and of BH. An octupole of methane is also calculated. We consider experimental geometries and also stretched bonds. We show that these nonvariational quantities may be found to relatively good accuracy when compared with full configuration interaction results, yet using only a small fraction of the full configuration interaction space. MCCI results in the aug‐cc‐pVDZ basis are seen to generally have reasonably good agreement with experiment. We also investigate the performance of MCCI when applied to ionisation energies and electron affinities of atoms in an aug‐cc‐pVQZ basis. We compare the MCCI results with full configuration interaction quantum Monte Carlo (Booth and Alavi, J. Chem. Phys. 2010, 132, 174104; Cleland, Booth, and Alavi, J. Chem. Phys. 2011, 134, 024112) and “exact” nonrelativistic results (Booth and Alavi, J. Chem. Phys. 2010, 132, 174104; Cleland, Booth, and Alavi, J. Chem. Phys. 2011, 134, 024112). We show that MCCI could be a useful alternative for the calculation of atomic ionisation energies however electron affinities appear much more challenging for MCCI. Due to the small magnitude of the electron affinities their percentage errors can be high, but with regards to absolute errors MCCI performs similarly for ionisation energies and electron affinities. © 2013 Wiley Periodicals, Inc.     

Efficient combination of Wang-Landau and transition matrix Monte Carlo methods for protein simulations

An efficient combination of the Wang-Landau and transition matrix Monte Carlo methods for protein and peptide simulations is described. At the initial stage of simulation the algorithm behaves like the Wang-Landau algorithm, allowing to sample the entire interval of energies, and at the later stages, it behaves like transition matrix Monte Carlo method and has significantly lower statistical errors. This combination allows to achieve fast convergence to the correct values of density of states. We propose that the violation of TTT identities may serve as a qualitative criterion to check the convergence of density of states. The simulation process can be parallelized by cutting the entire interval of simulation into subintervals. The violation of ergodicity in this case is discussed. We test the algorithm on a set of peptides of different lengths and observe good statistical convergent properties for the density of states. We believe that the method is of general nature and can be used for simulations of other systems with either discrete or continuous energy spectrum.     

Application of the unitary group approach to evaluate spin density for configuration interaction calculations in a basis of S2 eigenfunctions

We present an implementation of the spin‐dependent unitary group approach to calculate spin densities for configuration interaction calculations in a basis of spin symmetry‐adapted functions. Using S² eigenfunctions helps to reduce the size of configuration space and is beneficial in studies of the systems where selection of states of specific spin symmetry is crucial. To achieve this, we combine the method to calculate U(n) generator matrix elements developed by Downward and Robb (Theor. Chim. Acta 1977, 46, 129) with the approach of Battle and Gould to calculate U(2n) generator matrix elements (Chem. Phys. Lett. 1993, 201, 284). We also compare and contrast the spin density formulated in terms of the spin‐independent unitary generators arising from the group theory formalism and equivalent formulation of the spin density representation in terms of the one‐ and two‐electron charge densities.     

A comparative multi-reference configuration interaction study of the low-lying states of two thione isomers of thiophenol

Multi-reference configuration interaction, MR-CI (including extensivity corrections, named +Q), calculations were performed on the S₀–S₃ states of cyclohexa-2,4-diene-1-thione (thione 24 ) and cyclohexa-2,5-diene-1-thione (thione 25 ), which are thione isomers of thiophenol. Several types of uncontracted MR-CIS and MR-CISD wavefunctions were employed, comprising MR-CI expansions as large as ~365 × 10⁶ configuration state functions. The nature of the studied excited states was characterized. Vertical excitation energies (ΔE) and oscillator strengths (f) were computed. The most intense transitions (S₀ → S₂ for 24 and S₀ → S₃ for 25 ) did not change with the wavefunction, although a variation as large as ~1 eV was obtained for the S₃ state of 24 , at the highest (MR-CI+Q) level. On the other hand, ΔE changed at most by ~0.56 eV for 25 as the wavefunction changes, at the same level. The S₁ state of both thiones was found to have nπ* character and is in the visible region. For 24 , S₂ and S₃ are ππ* and nπ* states, respectively, while for 25 the reverse order is obtained. S₂ and S₃ are in the range ~3.5 to 5.2 eV, again at the highest level. It is the first time that the excited states of the title molecules are studied. The computed results agree with the experimental onset of photoreactions of thiones 24 and 25 found by Reva et al (Phys. Chem. Chem. Phys., 2015 , 17, 4888).     

应用Monte Carlo方法计算He原子包含电子相关作用的基态能量

应用Monte Carlo方法计算He原子包含电子相关波函数的基态能量,获得了与精确值非常接近的结果．实践表明,应用Monte Carlo方法有可能在多电子体系中直接采用包含任意2个电子间距离ry的函数作为变分函数来考虑电子相关作用．     

Configuration space partitioning and matrix buildup scaling for the vibrational configuration interaction method

The accurate computation of anharmonic vibrational states for medium to large molecules is a requirement for the detailed understanding of nonlinear multidimensional infrared spectra and the dynamical information encoded in them. The vibrational configuration interaction (VCI) method constitutes a particularly promising tool in this respect. It is generally hampered though by its unfavorable scaling with respect to system size. We analyze the scaling behavior of several well‐known as well as some new approximate VCI schemes in detail, which are complementary to the class of configuration selection schemes developed recently. We find that the combination of a configuration space partitioning, possibly based on configuration selection, with energetic thresholding and resonance screening provides an efficient scheme for the reduction of computational effort involved in VCI calculations while at the same time maintaining sufficient accuracy for the vibrational energies. © 2012 Wiley Periodicals, Inc.     

A comprehensive,self-contained derivation of the one-body density matrices from single-reference excited-state calculation methods using the equation-of-motion formalism

In this contribution, we review in a rigorous, yet comprehensive fashion the assessment of the one-body reduced density matrices derived from the most used single-reference excited-state calculation methods in the framework of the equation-of-motion formalism. Those methods are separated into two types: those which involve the coupling of a deexcitation operator to a single-excitation transition operator, and those which do not involve such a coupling. The case of many-body auxiliary wave functions for excited states is also addressed. For each of these approaches we were interested in deriving the elements of the one-body transition and difference density matrices, and to highlight their particular structure. This has been accomplished by applying a decomposition of integrals involving one-determinant quantum electronic states on which two or three pairs of second quantization operators can act. Such a decomposition has been done according to a corollary to Wick's theorem, which is brought in a comprehensive and detailed manner. A comment is also given about the consequences of using the equation-of-motion formulation in this context, and the two types of excited-state calculation methods (with and without coupling excitations to deexcitations) are finally compared from the point of view of the structure of their transition and difference density matrices.     

Monte Carlo Simulation of Polymers Confined Between Two Surfaces in the Presence of Diluent

Structure and surface properties of polymers confined between two surfaces are studied in the presence of diluent by using an off‐lattice Monte Carlo method. When the diluent–chain interaction is weak, the density of diluent beads near the surface increases sharply with increasing the diluent–surface interaction while the chain bead density near the surface decreases gradually. The total bead density near the surface increases with increasing the diluent–surface interaction until it exceeds the total bulk density. This is mainly due to a large increase in the diluent bead density near the surface. Because of the increase of diluent at the surface, chains near the surface change their conformation, i.e., long tails become abundant while short trains and loops are relatively depleted. On the other hand, when the diluent–chain interaction becomes strong, the total bead density near the surface increases slightly, but it exceeds the total bulk density only when the diluent–surface interaction is strong enough, because the diluents approaching the surface induce chain beads to move to the surface due to strong interaction between the chain and diluent.     

Monte Carlo simulation of polarizable systems: Early rejection scheme for improving the performance of adiabatic nuclear and electronic sampling Monte Carlo simulations

An early rejection scheme for trial moves in adiabatic nuclear and electronic sampling Monte Carlo simulation (ANES-MC) of polarizable intermolecular potential models is presented. The proposed algorithm is based on Swendsen–Wang filter functions for prediction of success or failure of trial moves in Monte Carlo simulations. The goal was to reduce the amount of calculations involved in ANES-MC electronic moves, by foreseeing the success of an attempt before making those moves. The new method was employed in Gibbs ensemble Monte Carlo (GEMC) simulations of the polarizable simple point charge-fluctuating charge (SPC-FQ) model of water. The overall improvement in GEMC depends on the number of swap attempts (transfer molecules between phases) in one Monte Carlo cycle. The proposed method allows this number to increase, enhancing the chemical potential equalization. For a system with 300 SPC-FQ water molecules, for example, the fractions of early rejected transfers were about 0.9998 and 0.9994 at 373 and 423 K, respectively. This means that the transfer moves consume only a very small part of the overall computing effort, making GEMC almost equivalent to a simulation in the canonical ensemble.     

Multicanonical Monte Carlo calculation of the free‐energy map of the base–amino acid interaction

The specific interactions between base pairs and amino acids were studied by the multicanonical Monte Carlo method. We sampled numerous interaction configurations and side‐chain conformations of the amino acid by the multicanonical algorithm, and calculated the free energies of the interactions between an amino acid at given C_α positions and a fixed base pair. The contour maps of free energy derived from this calculation represent the preferred C_α position of the amino acid around the base, and these maps of various combinations of bases and amino acids can be used to quantify the specificity of intrinsic base–amino acid interactions. Similarly, enthalpy and entropy maps will provide further details of the specific interactions. We have also calculated the free‐energy map of the orientations of the C_α C_β bond vector, which indicates the preferential orientation of the amino acid against the base. We compared the results obtained by the multicanonical method with those of the exhaustive sampling and canonical Monte Carlo methods. The free‐energy map of the base–amino acid interaction obtained by the multicanonical simulation method was nearly identical to the accurate result derived from the exhaustive sampling method. This indicates that a single multicanonical Monte Carlo simulation can produce an accurate free‐energy map. Multicanonical Monte Carlo sampling produced free‐energy maps that were more accurate than those produced by canonical Monte Carlo sampling. Thus, the multicanonical Monte Carlo method can serve as a powerful tool for estimating the free‐energy landscape of base–amino acid interactions and for elucidating the mechanism by which amino acids of proteins recognize particular DNA base pairs. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 954–962, 2000     

Shape and spin state in four-coordinate transition-metal complexes: the case of the d(6) configuration

Generalized polyhedral interconversion coordinates are defined within the framework of Avnir's continuous shape measures. The application of such interconversion coordinates to the study of the potential energy surfaces that define the stereochemical choice in four-coordinate transition metal complexes with different spin states is presented, and the correlation between potential energy curves and distribution of experimental structures along the tetrahedron to square interconversion path is shown for the case of the d(6) transition-metal complexes.     

Variational Monte Carlo calculations for some cations and anions of the first‐row atoms using explicitly correlated wave functions

The variational Monte Carlo method is applied to calculate ground‐state energies of some cations and anions of the first‐row atoms. Accurate values providing between 80 and 90% of the correlation energy are obtained. Explicitly correlated wave functions including up to 42 variational parameters are used. The nondynamic correlation due to the 2s ? 2p near degeneracy effect is included by using a multideterminant wave function. The variational free parameters have been fixed by minimizing the energy that has shown to be a more convenient functional than the variance of the local energy, which is the most commonly employed method in variational Monte Carlo calculations. The energies obtained improve previous works using similar wave functions. © 2002 Wiley Periodicals, Inc.; DOI 10.1002/qua.10125     

Investigation on the geometric and matrix effects and quantitative determination of K, Cl and S atomic fraction for biomass burning particles by Monte Carlo simulation

Using Monte Carlo simulation, the geometric and matrix effects on intensity and intensity ratio measured by EPMA were investigated for both synthetic particles and biomass burning particles. Three particulate standards, KCl, K₂SO₄, KHSO₄, were prepared and measured along with biomass burning particles. The modified CASINO program (University of Sherbrooke, Quebec, Canada) at the University of Antwerp, Belgium was used. The relative intensities obtained by the UA version of the CASINO program appear to be in line with those from experiments.The CASINO program and iterative procedures were applied to quantitatively determinate the atomic fraction of K, Cl and S in particulate standard and real samples. After correcting the geometric and matrix effects, the atomic fraction ratio of K to Cl in KCl sample was found to be 1.007±0.025, 0.996±0.013 and 1.011±0.019 for experiments with high voltages of 15, 20 and 25 keV, respectively. The same procedure was also applied to K₂SO₄ and KHSO₄ standard particle sample. The atomic fraction ratio of K to S was 1.945±0.049 (25 keV) for K₂SO₄ and 1.014±0.072 (20 keV) for KHSO₄. These ratios obtained are close to the theoretic values 1 or 2. Reasonable data were obtained for biomass burning particles, indicating that it is possible to perform chemical speciation.     

Monte Carlo simulation for the adsorption of symmetric triblock copolymers I. Configuration distribution and density profiles of adsorbed chains

Monte Carlo simulations for the adsorption of symmetric triblock copolymers from a nonselective solvent at a solid-liquid interface have been performed on a lattice model. In simulations, triblock copolymer molecules are modeled as self-avoiding linear chains composed of m segments of A and n segments of B arranged as A_m/2B_nA_m/2. Either segment A or segment B is attractive, while the other is non-attractive to the surface. The microstructure of the adsorbed layers, including the segment-density profiles and the size distribution of loops, tails and trains are presented. The effect of the adsorption energy, the bulk concentration, the chain composition, as well as the chain length on various adsorption properties has been studied. The results have shown that the size distribution of various configurations is dependent of the adsorption energy, the chain composition and the chain length. The mean length of the loops, trains and tails is insensitive to the bulk concentration. The mean length of the trains increases and that of the tails decreases as the adsorption energy and the length of the attractive segments increase. The mean length of the loops for the end-adsorbed copolymers appears a maximum and that for middle-adsorbed copolymers appears a minimum as the length of attractive segments increases. The length of the non-attractive segments affects mostly the size distribution of the tails. The longer the chain is, the larger the tail appears. The mean length of the tails and loops increases linearly as the length of the non-attractive segments increases, but that of the trains approximately is unchanged.     

Tuning the hydrogen storage capacity of MOF-650 by Mg2+/Ca2+ substitution and B,N co-doped atoms: Grand canonical Monte Carlo simulation and periodic density functional theory

This study used periodic density functional theory and grand canonical Monte Carlo simulations to investigate the effects of the co-doping of B and N atoms and substituting Zn²⁺ with Mg²⁺ or Ca²⁺ in the organic linker groups of MOF-650. The functionalization increased the polarity of the organic groups, stabilizing the interaction between the MOF and hydrogen molecules. The highest average binding energy of the adsorbed hydrogen in MOF-650 NB-C7-azulene-Mg was calculated to be −4.75 to 5.40 kcal/mol for the α adsorption sites. Using the substitution of NB azulene and metal cations being Mg²⁺ or Ca²⁺, The hydrogen storage capacity of functionalized MOF-650 was increased to 22 mg/g at 90 bar/298 K, implying the modification strategy of MOF-650 would strengthen the interaction between MOF frameworks and hydrogen molecules.     

分层性物质的组合取样误差与份样数目之间的关系及其Monte Carlo模拟

本文从理论上研究了分层性物质的组合取样误差与份样数目之间的定量关系，表明份样数目与组合取样相对标准偏差的平方之积为一常数，称为组合取样常数，它与Ｉｎｇａｍ ｅｌｌｓ 和Ｓｗ ｉｔｚｅｒ 提出的取样常数是相似的，表示６８％ 置信度下组合取样的相对标准偏差达到１％ 时的份样数目。应用Ｍｏｎｔｅ Ｃａｒｌｏ 模拟技术对该理论进行了验证，结果令人满意。     

Interaction of acetonitrile with alkaline metal cations: A density functional,coupled‐cluster,and quadratic configuration interaction study

A systematic quantum chemical study of CH₃CN and its CH₃CN?M⁺ 1:1 model adducts (M⁺∈{Li⁺, Na⁺}) is presented, with respect to binding energetics, structural and vibrational force field changes. Several gradient‐corrected density functional levels of theory were employed (of both “pure” and “hybrid” character), together with the coupled cluster including double substitutions from the Hartree–Fock determinant (CCD) and quadratic configuration interaction including single and double substitutions (QCISD) methods [with the rather large 6‐311G(d,p) basis set], and their performances compared. The binding energy decompositions according to the Kitaura–Morokuma scheme and the reduced variational space self‐consistent field (RVS‐SCF) method have shown that the electrostatic plus polarization interaction terms are primarily responsible for overall stabilization, while the charge‐transfer term is negligibly small and virtually identical for both adducts. The computed harmonic vibrational frequencies for acetonitrile correlate excellently with the experimental ones (r²>0.9998 for almost all cases, while for the BLYP level, r²=1). It is shown for the first time that the experimentally observed blue shifts of the ν_CN mode are caused even by formation of 1:1 adducts, contrary to the previously accepted opinions. The CCD and QCISD, as well as the BPW91 and BP86 levels of theory predict almost excellently the ν_CN mode blue shift upon adduct formation, while the BLYP and B3LYP levels perform significantly poorer. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001