Coupled-cluster theory based upon the fragment molecular-orbital method

The fragment molecular-orbital (FMO) method was combined with the single-reference coupled-cluster (CC) theory. The developed method (FMO-CC) was applied at the CCSD and CCSD(T) levels of theory, for the cc-pVnZ family of basis sets (n=D,T,Q) to water clusters and glycine oligomers (up to 32 molecules/residues using as large basis sets as possible for the given system). The two- and three-body FMO-CC results are discussed at length, with emphasis on the basis-set dependence and three-body effects. Two- and three-body approximations based on interfragment distances were developed and the values appropriate for their accurate application carefully determined. The error in recovering the correlation energy was several millihartree for the two-body FMO-CC method and in the submillihartree range for the three-body FMO-CC method. In the largest calculations, we were able to perform the CCSD(T) calculations of (H2O)32 with the cc-pVQZ basis set (3680 basis functions) and (GLY)32 with the cc-VDZ basis set (712 correlated electrons). FMO-CC was parallelized using the upper level of the two-layer parallelization scheme. The computational scaling of the two-body FMO-CC method was demonstrated to be nearly linear. As an example of timings, CCSD(T) calculations of (H2O)32 with cc-pVDZ took 13 min on an eight node 3.2-GHz Pentium4 cluster.     

Ab initio and density functional theory reinvestigation of gas-phase sulfuric acid monohydrate and ammonium hydrogen sulfate

We have calculated the thermochemical parameters for the reactions H(2)SO(4) + H(2)O <--> H(2)SO(4).H(2)O and H(2)SO(4) + NH(3) <--> H(2)SO(4).NH(3) using the B3LYP and PW91 functionals, MP2 perturbation theory and four different basis sets. Different methods and basis sets yield very different results with respect to, for example, the reaction free energies. A large part, but not all, of these differences are caused by basis set superposition error (BSSE), which is on the order of 1-3 kcal mol(-1) for most method/basis set combinations used in previous studies. Complete basis set extrapolation (CBS) calculations using the cc-pV(X+d)Z and aug-cc-pV(X+d)Z basis sets (with X = D, T, Q) at the B3LYP level indicate that if BSSE errors of less than 0.2 kcal mol(-1) are desired in uncorrected calculations, basis sets of at least aug-cc-pV(T+d)Z quality should be used. The use of additional augmented basis functions is also shown to be important, as the BSSE error is significant for the nonaugmented basis sets even at the quadruple-zeta level. The effect of anharmonic corrections to the zero-point energies and thermal contributions to the free energy are shown to be around 0.4 kcal mol(-1) for the H(2)SO(4).H(2)O cluster at 298 K. Single-point CCSD(T) calculations for the H(2)SO(4).H(2)O cluster also indicate that B3LYP and MP2 calculations reproduce the CCSD(T) energies well, whereas the PW91 results are significantly overbinding. However, basis-set limit extrapolations at the CCSD(T) level indicate that the B3LYP binding energies are too low by ca. 1-2 kcal/mol. This probably explains the difference of about 2 kcal mol(-1) for the free energy of the H(2)SO(4) + H(2)O <--> H(2)SO(4).H(2)O reaction between the counterpoise-corrected B3LYP calculations with large basis sets and the diffusion-based experimental values of S. M. Ball, D. R. Hanson, F. L Eisele and P. H. McMurry (J. Phys. Chem. A. 2000, 104, 1715). Topological analysis of the electronic charge density based on the quantum theory of atoms in molecules (QTAIM) shows that different method/basis set combinations lead to qualitatively different bonding patterns for the H(2)SO(4).NH(3) cluster. Using QTAIM analysis, we have also defined a proton transfer degree parameter which may be useful in further studies.     

Structural investigation of asymmetrical dimer radical cation system (H2O-H2S)+: proton-transferred or hemi-bonded?

Ab initio molecular orbital and hybrid density functional methods have been employed to characterize the structure and bonding of (H2O-H2S)+, an asymmetrical dimer radical cation system. A comparison has been made between the two-center three-electron (2c-3e) hemi-bonded system and the proton-transferred hydrogen-bonded systems of (H2O-H2S)+. Geometry optimization of these systems was carried out using unrestricted Hartree Fock (HF), density functional theory with different functionals, and second-order M?ller-Plesset perturbation (MP2) methods with 6-311++G(d,p) basis set. Hessian calculations have been done at the same level to check the nature of the equilibrium geometry. Energy data were further improved by calculating basis set superposition error for the structures optimized through MP2/6-311++G(d,p) calculations. The calculated results show that the dimer radical cation structure with H2O as proton acceptor is more stable than those structures in which H2O acts as a proton donor or the 2c-3e hemi-bonded (H2O thereforeSH2)+ system. This stability trend has been further confirmed by more accurate G3, G3B3, and CCSD(T) methods. On the basis of the present calculated results, the structure of H4OS+ can best be described as a hydrogen-bonded complex of H3O+ and SH with H2O as a proton acceptor. It is in contrast to the structure of neutral (H2O...H2S) dimer where H2O acts as a proton donor. The present work has been able to resolve the ambiguity in the nature of bonding between H2O and H2S in (H2O-H2S)+ asymmetrical dimer radical cation.     

Dimensional scaling treatment of stability of atomic anions induced by superintense, high-frequency laser fields

We show that dimensional scaling, combined with the high-frequency Floquet theory, provides useful means to evaluate the stability of gas phase atomic anions in a superintense laser field. At the large-dimension limit (D-->infinity), in a suitably scaled space, electrons become localized along the polarization direction of the laser field. We find that calculations at large D are much simpler than D=3, yet yield similar results for the field strengths needed to bind an "extra" one or two electrons to H and He atoms. For both linearly and circularly polarized laser fields, the amplitude of quiver motion of the electrons correlates with the detachment energy. Despite large differences in scale, this correlation is qualitatively like that found between internuclear distances and dissociation energies of chemical bonds.     

Density functional theory calculations for the hydrogen evolution reaction in an electrochemical double layer on the Pt(111) electrode

We present results of density functional theory calculations on a Pt(111) slab with a bilayer of water, solvated protons in the water layer, and excess electrons in the metal surface. In this way we model the electrochemical double layer at a platinum electrode. By varying the number of protons/electrons in the double layer we investigate the system as a function of the electrode potential. We study the elementary processes involved in the hydrogen evolution reaction, 2(H(+) + e(-)) --> H(2), and determine the activation energy and predominant reaction mechanism as a function of electrode potential. We confirm by explicit calculations the notion that the variation of the activation barrier with potential can be viewed as a manifestation of the Br?nsted-Evans-Polanyi-type relationship between activation energy and reaction energy found throughout surface chemistry.     

MP2, DFT and ab initio calculations on thioxanthone

Density functional theory (DFT), HF and MP2 calculations have been carried out to investigate thioxanthone molecule using the standard 6-31+G(d,p) basis set. The results of MP2 calculations show a butterfly structure for thioxanthone. The calculated results show that the predicted geometry can well reproduce the structural parameters. The predicted vibrational frequencies were assigned and compared with experimental IR spectra. A good harmony between theory and experiment is found. The theoretical electronic absorption spectra have been calculated using CIS method. ¹³C and ¹H NMR of the title compound have been calculated by means of B3LYP density functional method with 6-31+G(d,p) basis set. The comparison of the experimental and the theoretical results indicate that density functional B3LYP method is able to provide satisfactory results for predicting NMR properties.     

Ionized state of hydroperoxy radical-water hydrogen-bonded complex: (HO2-H2O)+

Ab initio molecular orbital calculations have been employed to characterize the structure and bonding of the (HO2-H2O)+ radical cation system. Geometry optimization of this system was carried out using unrestricted density functional theory in conjunction with the BHHLYP functional and 6-311++G(2df,2p) as well as 6-311++G(3df,3p) basis sets, the second-order M?ller-Plesset perturbation (MP2) method with the 6-311++G(3df,3p) basis set, and the couple cluster (CCSD) method with the aug-cc-pVTZ basis set. The effect of spin multiplicity on the stability of the (HO2-H2O)+ system has been studied and also compared with that of oxygen. The calculated results suggest a proton-transferred hydrogen bond between HO2 and H2O in H3O3+ wherein a proton is partially transferred to H2O producing the O2...H3O+ structure. The basis set superposition error and zero-point energy corrected results indicate that the H3O3+ system is energetically more stable in the triplet state; however, the singlet state of H3O3+ is more stable with respect to its dissociation into H3O+ and singlet O2. Since the resulting proton-transferred hydrogen-bonded complex (O2...H3O+) consists of weakly bound molecular oxygen, it might have important implications in various chemical processes and aquatic life systems.     

Monochlorogallane: physical properties and structure of the gaseous molecule H2Ga(mu-Cl)2GaH2 as determined by vibrational, electron diffraction, and ab initio studies

Monochlorogallane, synthesized by the metathesis of gallium(III) chloride with an excess of trimethylsilane at ca. 250 K, has been characterized by chemical analysis, by its IR, Raman, and 1H NMR spectra, and by the products of its reaction with trimethylamine. The vibrational spectra of the vapor species isolated in solid Ar, N2, or CH4 matrixes at ca. 12 K imply the presence of only one species, viz. the dimer with an equilibrium structure conforming to D2h symmetry. The structure of this molecule has been determined by gas-phase electron diffraction (GED) measurements augmented by the results of ab initio molecular orbital calculations. An equilibrium structure with D2h symmetry has been assumed in the analysis of the electron diffraction pattern. However, as the molecule has a very low frequency Ga(mu-Cl)2Ga ring-puckering mode, a dynamic model was used to describe it with the aid of a set of pseudoconformers spaced at even intervals (deltadelta = 5 degrees, deltamax, = 20 delta) around the ring-puckering angle delta and Boltzmann-weighted according to a quartic potential V(delta) = V4delta4 + V2delta2. The differences in bond distances and angles between the different pseudoconformers were constrained to the values derived from the ab initio calculations employing second-order Moller-Plesset (MP2) methods (with all the electrons included in the correlation calculations) and a 6-311G(d) basis set. The results for the weighted average of the principal distances (ralpha) and angles (相似文献   

Reactivity of C10H7+ and C10D7+ with H2 AND D2

We have investigated, both theoretically and experimentally, the reactions of naphthylium C10H7+ and d-naphthylium C10D7+ ions with H2 and D2. Cross sections as functions of the collision energy have been measured for a variety of reaction channels. Theoretical calculations have been carried out at the density functional theory level which utilizes the hybrid functional B3LYP and the split-valence 6-31G* basis set. The key features of the potential energy surfaces and the relevant thermochemical parameters have been calculated and they provide insights on the reaction mechanisms. The bimolecular reactivity of C10H7+ with H2 is dominated by the production of naphthalene cation C10H8+. The reaction is not a direct atom-abstraction process, but instead it proceeds via the formation of a stable intermediate complex C10H9+ of sigma type geometry, with a significant mobility of hydrogen along the ring. This mobility allows the scrambling of the hydrogen atoms and causes the successive statistical fragmentation of the complex into a variety of product channels. Elimination of one H(D) atom appears to be favored over elimination of one H2 or HD molecule. Alternatively, the intermediate complex can be stabilized either by collision with a third body or by emission of a photon.     

Grid‐based density functional calculations of many‐electron systems

Exploratory variational pseudopotential density functional calculations are performed for the electronic properties of many‐electron systems in the 3D cartesian coordinate grid (CCG). The atom‐centered localized gaussian basis set, electronic density, and the two‐body potentials are set up in the 3D cubic box. The classical Hartree potential is calculated accurately and efficiently through a Fourier convolution technique. As a first step, simple local density functionals of homogeneous electron gas are used for the exchange‐correlation potential, while Hay‐Wadt‐type effective core potentials are employed to eliminate the core electrons. No auxiliary basis set is invoked. Preliminary illustrative calculations on total energies, individual energy components, eigenvalues, potential energy curves, ionization energies, and atomization energies of a set of 12 molecules show excellent agreement with the corresponding reference values of atom‐centered grid as well as the grid‐free calculation. Results for three atoms are also given. Combination of CCG and the convolution procedure used for classical Coulomb potential can provide reasonably accurate and reliable results for many‐electron systems. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

An ab initio potential surface describing abstraction and exchange for H+CH4

We report an ab initio-based global potential energy surface for H+CH4 that describes the abstraction and exchange reactions. The PES, which is invariant with respect to any permutation of five H atoms, is a fit to 20,728 electronic energies calculated using the partially spin-restricted coupled-cluster method (RCCSD(T)) with a moderately large basis (aug-cc-pVTZ). A first set of quasiclassical trajectory calculations using this PES are reported for the H+CD4-->HD+CD3 reaction at collision energies of 0.65 and 1.52 eV and are compared to experiment and recent direct dynamics calculations done with density functional theory.     

On the sensitivity of f electrons to their chemical environment

Density functional calculations have been carried out on three families of lanthanide complexes of D3 or C4 symmetry, namely [Ln(H2O)9]3+, [Ln(DPA)3]3-, and [Ln(DOTAM)]3+ (Ln = Y, La, Lu; DPA = pyridine-2,6-dicarboxylate; DOTAM = 1,4,7,10-tetracarbamoylmethyl-1,4,7,10-tetraazacyclododecane), to get some insights concerning the sensitivity of 4f electrons to the surrounding ligands. We show that the electron density accumulations found within 0.7 A of the metal center, that precisely give the opposite image of the coordination sphere as they are located trans with respect to the Ln-ligand bonds, are almost exclusively due the f electrons. This polarization of the 4f electrons in lanthanides complexes has therefore to be considered as a general feature that plays a crucial role in some experimentally observed phenomenons such as the dependency of quadratic hyperpolarizability to the number of f electrons in [Ln(DPA)3]3- complexes that we have evidenced.     

Investigations with the finite element method on the Cyber 205

We are trying to investigate systematically the application of the finite element method (FEM) for solving the Schrödinger equation. The present paper is devoted to the calculation of vibrational transition probabilities for the collinear reactive system A + BC (i.e. H+H₂ and their isotopes). The calculations are fully two-dimensional and the results are compared with earlier FEM calculations and conventional basis set expansion methods using the the R-matrix or S-matrix propagation.We made extensive analysis of FEM on the vector-computer Cyber 205 and developed a vector code for the efficient use in two dimensions, so that in the near future applications even in three dimensions will be possible.For the hydrogen exchange reactions we investigated the following isotope combinations: (a) H + H₂, b) H + DH, D + HD and H + MuH (symmetric reaction), (c) D + HH, H + DD and Mu + DD (asymmetric reaction). We calculated the transition probabilities for up to five open vibrational channels and found excellent agreement with known exact values.     

Halogen‐Bonding Interactions with π Systems: CCSD(T), MP2, and DFT Calculations

Halogen bonding is a noncovalent interaction between a halogen atom and a nucleophilic site. Interactions involving the π electrons of aromatic rings have received, up to now, little attention, despite the large number of systems in which they are present. We report binding energies of the interaction between either NCX or PhX (X=F, Cl, Br, I) and the aromatic benzene system as determined with the coupled cluster with perturbative triple excitations method [CCSD(T)] extrapolated at the complete basis set limit. Results are compared with those obtained by Møller–Plesset perturbation theory to second order (MP2) and density functional theory (DFT) calculations by using some of the most common functionals. Results show the important role of DFT in studying this interaction.     

Application of standard DFT theory for nonbonded interactions in soft matter: prototype study of poly-para-phenylene

We present a detailed analysis of the application of density functional theory (DFT) methods to the study of structural properties of molecular and supramolecular systems, using as a paradigmatic example three para-phenylene-based systems: isolated biphenyl, single chain poly-para-phenylene, and crystalline biphenyl. We use different functionals for the exchange correlation potential, the local density (LDA), and generalized gradient approximations (GGA), and also different basis sets expansions, localized, plane waves (PW), and mixed (localized plus PW), within the reciprocal space formulation for the hamiltonian. We find that regardless of the choice of basis functions, the GGA calculations yield larger interring distances and torsion angles than LDA. For the same XC approximation, the agreement between calculations with different basis functions lies within 1% (LDA) or 0.5% (GGA) for distances, and while PW and mixed basis calculations agree within 1 degrees for torsion angles, the localized basis results show larger angles by approximately 8 degrees and a nonmonotonic dependence on basis size, with differences within 6 degrees. The most prominent features, namely the torsion between rings for isolated molecule and infinite chain, and planarity for the molecule in crystalline environment, are well reproduced by all DFT calculations.     

Accurate ab initio binding energies of alkaline earth metal clusters

The effects of basis set superposition error (BSSE) and core-correlation on the electronic binding energies of alkaline earth metal clusters Y(n) (Y = Be, Mg, Ca; n = 2-4) at the Moller-Plesset second-order perturbation theory (MP2) and the single and double coupled cluster method with perturbative triples correction (CCSD(T)) levels are examined using the correlation consistent basis sets cc-pVXZ and cc-pCVXZ (X = D, T, Q, 5). It is found that, while BSSE has a negligible effect for valence-electron-only-correlated calculations for most basis sets, its magnitude becomes more pronounced for all-electron-correlated calculations, including core electrons. By utilizing the negligible effect of BSSE on the binding energies for valence-electron-only-correlated calculations, in combination with the negligible core-correlation effect at the CCSD(T) level, accurate binding energies of these clusters up to pentamers (octamers in the case of the Be clusters) are estimated via the basis set extrapolation of ab initio CCSD(T) correlation energies of the monomer and cluster with only the cc-pVDZ and cc-pVTZ sets, using the basis set and correlation-dependent extrapolation formula recently devised. A comparison between the CCSD(T) and density functional theory (DFT) binding energies is made to identify the most appropriate DFT method for the study of these clusters.     

Efficient evaluation of Coulomb integrals in a mixed Gaussian and plane-wave basis using the density fitting and Cholesky decomposition

The objective of this paper is to show that the density fitting (resolution of the identity approximation) can also be applied to Coulomb integrals of the type (k(1)(1)k(2)(1)|g(1)(2)g(2)(2)), where k and g symbols refer to plane-wave functions and gaussians, respectively. We have shown how to achieve the accuracy of these integrals that is needed in wave-function MO and density functional theory-type calculations using mixed Gaussian and plane-wave basis sets. The crucial issues for achieving such a high accuracy are application of constraints for conservation of the number electrons and components of the dipole moment, optimization of the auxiliary basis set, and elimination of round-off errors in the matrix inversion.     

Ab initio configuration-interaction investigation of optical transitions in K+He and K+H2

The potassium resonance line (4s-->4p) centered around 770 nm is a major contributor to the optical extinction in the atmospheres of certain classes of brown dwarfs and extrasolar giant planets. The resonance line is significantly broadened by collisions with He and H2, and an accurate calculation of the line profile is needed for astrophysical models of these objects. As a first step, we report an accurate ab initio study of the K+He and K+H2 potential-energy curves correlating to the K 4s and 4p atomic energy levels, together with the dipole moments governing the transitions between these potential-energy curves. The molecular calculations have been carried out using a multireference configuration-interaction method, with the molecular orbitals expanded in a large Gaussian basis set. The transition dipole moments show significant variation with the molecular geometry. Calculations for the K+H2 system have been carried out for a range of H2 orientations and internuclear separations, so that the effect of H2 rotation and vibration may be explicitly included in future calculations of the pressure-broadened line profiles.     

Potential energy surfaces for the reaction of B+ (1S,3P) with H2 using spin-coupled VB theory: Asymptotic regions of the surfaces

We present spin-coupled VB calculations for the asymptotic regions of the potential surfaces for the (B + H₂)⁺ system. A large basis set is used and great care has been taken to ensure that all states lying within 13 eV of the BH⁺(X²Σ⁺) + H ground state are well described. A total of 592 spin-coupled structures (fully coupled configurations) was used. These calculations show a significant improvement over previous work. The present surfaces, at least in the regions studied here, appear to be of chemical accuracy. Having established the reliability of our calculations, further studies will concentrate on the inner regions of the surfaces - preferably in conjunction with dynamical studies.