Moller-Plesset Theory Research Articles

Infinite‐order functional for nonlinear parameters optimization in explicitly correlated coupled cluster theory

AbstractCoupled cluster (CC) calculations with Gaussian geminals rely heavily on extensive optimizations of nonlinear parameters (exponents and positions) defining the geminal basis functions. As the CC method is not a variational theory, it provides no functional for such an optimization. The nonlinear parameters must therefore be supplied by some other theory, giving pair functions that can be expected to be close to those of the CC method. The conventional approach thus far was to use the second‐order many‐body perturbation theory with Møller–Plesset partition of the Hamiltonian (MP2) for this purpose and to minimize the corresponding Hylleraas‐type functional. We present a new functional, which goes beyond the second order, and can be applied in situations when the Møller–Plesset theory converges slowly. This functional does take a partial account of infinite‐order terms in the MP theory, but neglects the interpair coupling in the spirit of the independent electron pair approximation approach. The pair functions minimizing this new functional include the most important infinite‐order contributions from the point of view of the MP theory and are much closer to the CC pair functions than the first‐order ones. The nonlinear parameters obtained using this infinite‐order functional are then better suited for coupled cluster calculations than those obtained using the MP2 functional. The effectiveness of the new functional is demonstrated by performing coupled cluster doubles (CCD) calculations for the Be atom and Li− ion. The obtained energies are much better than those based on the MP2 optimizations and represent the most accurate CCD energies for these systems obtained thus far. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Interaction Energies between Tetrahydrobiopterin Analogues and Aromatic Residues in Tyrosine Hydroxylase and Phenylalanine Hydroxylase

The phenylalanine residues 300 and 309 in the enzyme tyrosine hydroxylase are known to aid in the positioning and binding of tetrahydrobiopterin (BH4) to the enzyme active site. The residues phenylalanine 254 and tyrosine 325 similarly aid in binding BH4 in phenylalanine hydroxylase. BH4 is a cofactor necessary for enzyme function, and mutations in these residues have been shown to cause a decrease in enzyme function. We examine the pairwise interactions between each aromatic residue and BH4 using second-order Moller Plesset theory and density functional theory to determine the amount of binding due to these aromatic residues. Further, we perform in silico point mutations of these residues to determine if several likely mutations can cause a decrease in protein function. Our results show that dispersion dominates these interactions, and electrostatics alone is not enough to bind the BH4.

Theoretical Gas Phase Study of the Gauche and Trans Conformers of 1-Bromo-2-Iodoethane and Solvent Effects

This is a gas-phase study of the gauche and trans conformers of 1-bromo-2-iodoethane. The methods used are the second-order Moller-Plesset theory (MP2) and density functional theory (DFT). The functional used for the DFT method is B3LYP and the basis sets used are 6-311++G(d,p) for all atoms except that different basis sets, namely 3-21G, LANECP, CRENBL ECP, Stuttgart RLC ECP and 6-311G(d,p), have been explored for the iodine atom. The results indicate that the trans conformer is preferred. The energy difference between the gauche and trans conformers (ΔE g−t) and related thermodynamic parameters are reported. The ΔE g−t values are 12.50 kJ⋅mol−1 (B3LYP) and 10.00 kJ⋅mol−1 (MP2) with the basis sets being 6-311++G(d,p)[C,H,Br]/6-311G(d,p)[I]. The conformers of 1-bromo-2-iodoethane have also been subjected to vibrational analysis. The results from the two theoretical levels are in good agreement but they are not much affected by the basis set of the iodine atom. The study has been extended to explore solvent effects using Self-Consistent Reaction Field methods. The structural parameters of the conformers are little affected by the polarity of the solvent but ΔE g−t decreases and the solvation Gibbs energy increases with increasing polarity of the solvent.

Computational note on theoretical investigation of the molecular structure and vibrational spectra of 2,4-cyclopentadiene-1-one, 2,4-cyclopentadiene-1-thione and 2,4-cyclopentadiene-1-selenone

In this study, molecular geometry, harmonic vibrational frequencies and absolute intensities of 2,4-cyclopentadiene-1-one, 2,4-cyclopentadiene-1-thione and 2,4-cyclopentadiene-1-selenone are examined theoretically using density function theory B3LYP functional and second order Moller–Plesset theory with the standard 6-311++G(d,p) basis set. All calculations are carried out by Gaussian 03. The calculated vibrational frequencies of 2,4-cyclopentadiene-1-one are compared with available observed vibrational frequencies (2).

Substrate–protein interaction energy in the enzyme phenylalanine hydroxylase: DFT and ab initio results

The enzyme phenylalanine hydroxylase catalyzes the conversion of phenylalanine to tyrosine, which is in turn converted to a series of neurologically important compounds. These compounds can then inhibit the initial metabolism of phenylalanine by docking in the phenylalanine hydroxylase active site. We use second order Moller–Plesset theory (MP2) and several Density Functional Theory methods to estimate the contribution to the total substrate/protein interaction energy from the electrostatic and dispersion interactions between the substrate and Phe254 in the enzyme. We then study several mutations at the residue 254 site. Our results for one mutation, F254I, agree with an observed loss of function of phenylalanine hydroxylase. We predict several additional mutations that may also cause loss of function in the enzyme.

Femtosecond degenerate four-wave mixing of carbon disulfide: High-accuracy rotational constants

Femtosecond degenerate four-wave mixing (fs-DFWM) rotational coherence spectroscopy (RCS) has been used to determine the rotational and centrifugal distortion constants of the 00 (0)0 ground and 01 (1)0 vibrationally excited states of gas-phase CS(2). RCS transients were recorded over the 0-3300 ps optical delay range, allowing the observation of 87 recurrences. The fits yield rotational constants B(00 (0)0)=3.271 549 2(18) GHz for (12)C(32)S(2) and B(00 (0)0)=3.175 06(21) GHz for the (12)C(32)S(34)S isotopomer. The rotational constants of the degenerate 01 (1)0 bending level of (12)C(32)S(2) are B(01 (1)0)=3.276 72(40) and 3.279 03(40) GHz for the e and f substrates, respectively. These fs-DFWM rotational constants are ten times more accurate than those obtained by CO(2) laser/microwave heterodyne measurements and are comparable to those obtained by high-resolution Fourier transform infrared spectroscopy. Ab initio calculations were performed at two levels, second-order Moller-Plesset theory and coupled-cluster singles, doubles, and iterative triples [CCSD(T)]. The equilibrium and vibrationally averaged C=S distances were calculated using large Dunning basis sets. An extrapolation procedure combining the ab initio rotational constants with the experiment yields an equilibrium C=S bond length of 155.448 pm to an accuracy of +/-20 fm. The theoretical C=S bond length obtained by a complete basis set extrapolation at the CCSD(T) level is r(e)(C=S)=155.579 pm, or 0.13 pm longer than that in the experiment.

Density-functional calculation of methane adsorption on graphite (0001)

Methane adsorbed on graphite was studied using density-functional theory. The structure was fully optimized with strict energy and force convergence criteria. The methane converged to the preferred adsorption sites giving the vibrational frequencies, the energy of adsorption, charge distributions, and the electronic density of states. Under the two coverages studied ($\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ and $2\sqrt{3}\ifmmode\times\else\texttimes\fi{}2\sqrt{3}$) and a differing number of graphite layers (1--6), the methane molecules favored atop sites on the graphite surface with the hydrogen tripod down. We found the methane carbon $3.21\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ above the graphite carbon and the adsorption energy to be $118\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ for the lower coverage. The independent harmonic oscillator vibrational frequency perpendicular to the surface for the $\mathrm{C}{\mathrm{H}}_{4}$ molecule was computed to be $87\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{-1}$. The graphite surface contracted 5.0% and 4.1% for the first and second layers, respectively, from the spacing relative to their bulk values. To benchmark our frequency calculations, we also used second-order Moller-Plesset theory and the local spin density approximation (LSDA) in GAUSSIAN 03 for the molecule. All of our LDA results are in good agreement with corresponding experiments, while under the generalized gradient approximation approximation we get only qualitatively results.

Correlation corrections based on the Schrödinger equation with a local potential

A compromise version of calculation of the ground state electronic energy is proposed that combines both the density functional theory and the wave function formalism. Single-particle orbitals and energies are determined by solving the Kohn-Sham equations with a local effective potential, which depends on the parameters determined by the variational principle. Correlation corrections are calculated using the Rayleigh-Schrodinger perturbation theory in the zero-order approximation of the Moller-Plesset theory. The specific features of the expressions for the corrections to the wave function and the energy determined in terms of the Kohn-Sham orbitals are considered. This approach, in contrast to the well-known optimized effective potential method, can be applied with equal computational expenditures to both atoms and molecules. A comparative analysis for 20 helium-like atoms showed that the scheme proposed provides better agreement with the “exact” values of the energy in the second order of the perturbation theory in comparison with the results obtained using the conventional exchange-correlation potentials BLYP and PW91. A similar trend is also observed for diatomic hydrides (from LiH to FH), although, in contrast to the atoms, the deviations from the experimental estimates of the energy are less systematic.

The accuracy of ab initio molecular geometries for systems containing second-row atoms

The performance of the standard hierarchy of ab initio models--that is, Hartree-Fock theory, second-order Moller-Plesset theory, coupled-cluster singles-and-doubles theory, and coupled-cluster singles-doubles-approximate-triples theory--in combination with correlation-consistent basis sets is investigated for equilibrium geometries of molecules containing second-row elements. From an analysis on a collection of 31 molecules (yielding statistical samples of 41 bond distances and 13 bond angles), the statistical errors (mean deviation, mean absolute deviation, standard deviation, and maximum absolute deviation) are established at each level of theory. The importance of core correlation is examined by comparing calculations in the frozen-core approximation with calculations where all electrons are correlated.

Mechanistic and kinetic study of the CH3CO+O2 reaction

Potential-energy surface of the CH3CO + O2 reaction has been calculated by ab initio quantum chemistry methods. The geometries were optimized using the second-order Moller-Plesset theory (MP2) with the 6-311G(d,p) basis set and the coupled-cluster theory with single and double excitations (CCSD) with the correlation consistent polarized valence double zeta (cc-pVDZ) basis set. The relative energies were calculated using the Gaussian-3 second-order Moller-Plesset theory with the CCSD/cc-pVDZ geometries. Multireference self-consistent-field and MP2 methods were also employed using the 6-311G(d,p) and 6-311++G(3df,2p) basis sets. Both addition/elimination and direct abstraction mechanisms have been investigated. It was revealed that acetylperoxy radical [CH3C(O)OO] is the initial adduct and the formation of OH and alpha-lactone [CH2CO2(1A')] is the only energetically accessible decomposition channel. The other channels, e.g., abstraction, HO2 + CH2CO, O + CH3CO2, CO + CH3O2, and CO2 + CH3O, are negligible. Multichannel Rice-Ramsperger-Kassel-Marcus theory and transition state theory (E-resolved) were employed to calculate the overall and individual rate coefficients and the temperature and pressure dependences. Fairly good agreement between theory and experiments has been obtained without any adjustable parameters. It was concluded that at pressures below 3 Torr, OH and CH2CO2(1A') are the major nascent products of the oxidation of acetyl radicals, although CH2CO2(1A') might either undergo unimolecular decomposition to form the final products of CH2O + CO or react with OH and Cl to generate H2O and HCl. The acetylperoxy radicals formed by collisional stabilization are the major products at the elevated pressures. In atmosphere, the yield of acetylperoxy is nearly unity and the contribution of OH is only marginal.

Amino Acids and Small Peptides as Building Blocks for Proteins: Comparative Theoretical and Spectroscopic Studies

AbstractFor Abstract see ChemInform Abstract in Full Text.

Density-functional theory-symmetry-adapted intermolecular perturbation theory with density fitting: A new efficient method to study intermolecular interaction energies

The previously developed DFT-SAPT approach, which combines symmetry-adapted intermolecular perturbation theory (SAPT) with a density-functional theory (DFT) representation of the monomers, has been implemented by using density fitting of two-electron objects. This approach, termed DF-DFT-SAPT, scales with the fifth power of the molecular size and with the third power upon increase of the basis set size for a given dimer, thus drastically reducing the cost of the conventional DFT-SAPT method. The accuracy of the density fitting approximation has been tested for the ethyne dimer. It has been found that the errors in the interaction energies due to density fitting are below 10(-3) kcal/mol with suitable auxiliary basis sets and thus one or two orders of magnitude smaller than the errors due to the use of a limited atomic orbital basis set. An investigation of three prominent structures of the benzene dimer, namely, the T shaped, parallel displaced, and sandwich geometries, employing basis sets of up to augmented quadruple-zeta quality shows that DF-DFT-SAPT outperforms second-order Moller-Plesset theory (MP2) and gives total interaction energies which are close to the best estimates inferred from combining the results of MP2 and coupled-cluster theory with single, double, and perturbative triple excitations.

Analysis of the Tautomeric Properties of Substituted 3-Acryloyltetrahydrofuran-2,4-Dione According to the Data of IR Spectra and Ab Initio Quantum Chemical Calculations

The tautomerism and spectral properties of 3-[3-(4-methoxycarbonylphenyl-acryloyl]tetrahydrofuran-2,4-dione (MCPATD) have been investigated by the methods of nonempirical and semiempirical quantum chemistry (nonempirical calculations by the Moller–Plesset theory of 2nd-order perturbations, calculations by the AM1 and PM3 semiempirical methods), as well as by IR and 1H NMR spectroscopy. It has been shown that the presence of an additional chain of conjugation in the side chain of MCPATD substantially changes its tautomeric composition and spectral properties as compared to 3-formyl- and 3-acetyltetrahydrofuran-2,4-diones. The frequencies and forms of normal vibrations calculated for each cis-enolic tautomer differ substantially within the region of vibrations of keto groups and double bonds, which makes it possible to identify the tautomers present in the mixture. It is found that in CHCl3 solutions MCPATD exists as an equilibrium mixture of its exoenolic forms. The possible mechanisms underlying the enol-enolic conversions of MCPATD are discussed.

Barrier-free intermolecular proton transfer in the uracil-glycine complex induced by excess electron attachment

The photoelectron spectra (PES) of anions of uracil-glycine and uracil-phenylalanine complexes reveal broad features with maxima at 1.8 and 2.0 eV. The results of ab initio density functional B3LYP and second order Moller-Plesset theory calculations indicate that the excess electron occupies a π* orbital localized on uracil. The excess electron attachment to the complex can induce a barrier-free proton transfer (BFPT) from the carboxylic group of glycine to the O8 atom of uracil. As a result, the four most stable structures of the anion of uracil-glycine complex can be characterized as the neutral radical of hydrogenated uracil solvated by the anion of deprotonated glycine. The similarity between the PES spectra for the uracil complexes with glycine and phenylalanine suggests that the BFPT is also operative in the case of the latter anionic species. The BFPT to the O8 atom of uracil may be related to the damage of nucleic acid bases by low energy electrons because the O8 atom is involved in a hydrogen bond with adenine in the standard Watson-Crick pairing scheme.

Accurate relativistic Gaussian basis sets for H through Lr determined by atomic self-consistent field calculations with the third-order Douglas–Kroll approximation

Highly accurate relativistic Gaussian basis sets are developed for the 103 elements from H(Z=1) to Lr (Z=103). Orbital exponents are optimized by minimizing the atomic self-consistent field (SCF) energy with the scalar relativistic third-order Douglas–Kroll approximation. The basis sets are designed to have equal quality and to be appropriate for the incorporation of relativistic effects. The basis set performance is tested by calculations on prototypical molecules, hydrides, and dimers of copper, silver, and gold using SCF, Møller–Plesset theory, and the singles and doubles coupled-cluster methods with and without perturbative triples [CCSD, CCSD(T)]. Spectroscopic constants and dissociation energies are reported for the ground state of each species. The effects of relativity, electron correlation, and the basis set superposition error (BSSE) are investigated. At the BSSE corrected CCSD(T) level, the mean absolute error relative to experiment in De for three dimers (hydrides) is 0.13 (0.09) eV; for Re the error is 0.024 (0.003) Å, and for ωe it is 2 (13) cm−1. These illustrative calculations confirm that the present basis sets fulfill their design objectives.

Molecular modeling of the olefin metathesis by tungsten(0) carbene complexes

Density functional and second-order Moller–Plesset theory were used to model W(0) carbene mediated homogeneous metathesis reaction of propylene. The calculations show that the rate determining step of the metathesis is the initiation. After the initiation has been completed the rate determining step becomes dissociation of olefin–metallocarbene complex. The low stereoselectivity of the olefin metathesis reaction is due to the close matching of activation energies for cis and trans isomer formation and the fast cis– trans isomerization caused by the catalysts. The non-productive olefin metathesis reaction always dominates the reaction mixture owing to its very low activation energy. The electronic structure of metal carbene olefin complexes can be described as a combination of donor–acceptor interactions between HOMO of the olefin and LUMO of metal carbene located at carbene carbon on the one hand, and the Dewar, Chatt and Duncanson back donation scheme on the other.

Harmonic frequency scaling factors for Hartree-Fock, S-VWN, B-LYP, B3-LYP, B3-PW91 and MP2 with the Sadlej pVTZ electric property basis set

Scaling factors for obtaining fundamental vibrational frequencies from harmonic frequencies calculated at six of the most commonly used levels of theory have been determined from regression analysis for the polarized-valence triple-zeta (pVTZ) Sadlej electric property basis set. The Sadlej harmonic frequency scaling factors for first- and second-row molecules were derived from a comparison of a total of 900 individual vibrations for 111 molecules with available experimental frequencies. Overall, the best performers were the hybrid density functional theory (DFT) methods, Becke's three-parameter exchange functional with the Lee–Yang–Parr fit for the correlation functional (B3-LYP) and Becke's three-parameter exchange functional with Perdew and Wang's gradient-corrected correlation functional (B3-PW91). The uniform scaling factors for use with the Sadlej pVTZ basis set are 0.9066, 0.9946, 1.0047, 0.9726, 0.9674 and 0.9649 for Hartree–Fock, the Slater–Dirac exchange functional with the Vosko–Wilk–Nusair fit for the correlation functional (S-VWN), Becke's gradient-corrected exchange functional with the Lee–Yang–Parr fit for the correlation functional (B-LYP), B3-LYP, B3-PW91 and second-order Moller–Plesset theory with frozen core (MP2(fc)), respectively. In addition to uniform frequency scaling factors, dual scaling factors were determined to improve the agreement between computed and observed frequencies. The scaling factors for the wavenumber regions below 1800 cm−1 and above 1800 cm−1 are 0.8981 and 0.9097, 1.0216 and 0.9857, 1.0352 and 0.9948, 0.9927 and 0.9659, 0.9873 and 0.9607, 0.9844 and 0.9584 for Hartree–Fock, S-VWN, B-LYP, B3-LYP, B3-PW91 and MP2(fc), respectively. Hybrid DFT methods along with the Sadlej pVTZ basis set provides reliable theoretical vibrational spectra in a cost-effective manner.

Analytical energy gradients for local coupled-cluster methodsElectronic Supplementary Information available. See http://www.rsc.org/suppdata/cp/b1/b105126c/

Analytical expressions for evaluating energy gradients for local coupled-cluster wavefunctions are derived, and relations between the conventional and local coupled-cluster theories are elaborated. In the more general local case additional terms arise from the geometry dependence of the localization transformation and the non-orthogonality of the projected atomic orbitals (PAOs) which are used to span the virtual space. Furthermore, if the excitations from a given orbital pair are restricted to subsets (domains) of PAOs, new terms arise from the geometry dependence of these subspaces. The gradient theory is also generalized to the case in which weakly correlated electron pairs are treated by local second-order Moller–Plesset theory (LMP2) while the contributions of strong pairs are computed at the coupled-cluster level. A number of test calculations are presented in which optimized equilibrium structures are compared for local and conventional calculations, and it is concluded that the local approximations hardly affect the accuracy.

Structure of cationized glycine, gly.m (m = be, mg, ca, sr, ba), in the gas phase: intrinsic effect of cation size on zwitterion stability.

Interactions between divalent metal ions and biomolecules are common both in solution and in the gas phase. Here, the intrinsic effect of divalent alkaline earth metal ions (Be, Mg, Ca, Sr, Ba) on the structure of glycine in the absence of solvent is examined. Results from both density functional and Moller-Plesset theories indicate that for all metal ions except beryllium, the salt-bridge form of the ion, in which glycine is a zwitterion, is between 5 and 12 kcal/mol more stable than the charge-solvated structure in which glycine is in its neutral form. For beryllium, the charge-solvated structure is 5-8 kcal/mol more stable than the salt-bridge structure. Thus, there is a dramatic change in the structure of glycine with increased metal cation size. Using a Hartree-Fock-based partitioning method, the interaction between the metal ion and glycine is separated into electrostatic, charge transfer and deformation components. The charge transfer interactions are more important for stabilizing the charge-solvated structure of glycine with beryllium relative to magnesium. In contrast, the difference in stability between the charge-solvated and salt-bridge structure for magnesium is mostly due to electrostatic interactions that favor formation of the salt-bridge structure. These results indicate that divalent metal ions dramatically influence the structure of this simplest amino acid in the gas phase.

Structural analysis of the cyclic AlO2 and AlS2 systems in doublet and quartet states at density functional theory and the electron correlation levels

The geometries and the bonding properties have been predicted for cyclic AlO2 and AlS2 species in doublet and quartet states using density functional theory, the second, third, and fourth orders Moller–Plesset theory, quadric configuration interaction singles and doubles including a perturbational estimate of the triples and coupled cluster singles and doubles including a perturbational estimate of the triples all-electron correlation methods with 6-311+G* and aug-cc-pvtz basis sets. The geometrical optimizations and the harmonic vibrational frequency analysis are performed using density functional theory and coupled cluster singles and doubles methods. The relevant energy quantities are also determined using several high-order electron correlation methods (the second, third, and fourth orders Moller–Plesset theory, quadric configuration interaction, and coupled cluster theories) at both basis set levels (6-311+G* and aug-cc-pvtz). For the doublet state, each species possesses a A22 ground state with a higher energy level A12 state. The corresponding state–state separations are 11 kcal/mol for AlO2 species and 7.2 kcal/mol for AlS2 species at coupled cluster singles and doubles including a perturbational estimate of the triples and 6-311+G* level. The calculations using quadric configuration interaction and coupled cluster singles and doubles including a perturbational estimate of the triples yield dissociation energies in three dissociation mechanisms of ∼59, ∼190, and ∼294 kcal/mol for AlO2(2A2), and of ∼64, ∼167, and ∼272 kcal/mol for AlS2(2A2), respectively, and other methods [B3LYP, B3P86, B3PW91, Moller–Plesset (n=2,3,4), quadric configuration interaction and coupled cluster singles and doubles] yield dissociation energies within ∼4.5 kcal/mol. For the quartet states, the B14 state is more stable than the B24 state with energy separations of 43.5 kcal/mol for AlO2 and 29 kcal/mol for AlS2. The B14 and B24 states are significantly higher in energy than the ground states by 28.9 kcal/mol (B14) and 57.9 kcal/mol (B24) for AlS2, and 24.2 kcal/mol (B14) and 67.8 kcal/mol (B24) for AlO2. Result analysis has indicated that the cyclic AlO2 in the A22 and B24 states should be classified as superoxides, but they have different spin density distribution. However, AlO2 in the A12 state should not be, while AlO2 in the B14 state may be classified as the dioxide. The AlS2 species in the A22 state should be classified as a supersulfide. Although the A12 state has some supersulfide character, it should not be classified as such. The AlS2 in the B24 and B14 states should be classified as the weak interaction molecular complex and the disulfides, respectively. However, these superoxides and supersulfides are far less ionic than the corresponding alkali metal superoxides.