Fifth-order constant denominator perturbation therory within a localized bond model: Contributions from single and double excitations

A Fifth-order constant denominator perturbation treatment of all single and double excitations occuring in the third-order perturbation wave function is presented for the perturbation configuration interaction using localized orbitals (PCILO ) method. Contributions from triple and quadruple excitations which decay back to singles and doubles at third order are automatically included in this theory. This method is computationally very fast, with an execution speed proportional to N³, Where N is the number of orbitals present. A [2,1] Padé approximate involving only singles and doubles contributions through to fifth order is shown to be remarkably accurate.     

Many-body perturbation theory,coupled-pair many-electron theory,and the importance of quadruple excitations for the correlation problem

Many-body (diagrammatic) perturbation theory (MBPT ), coupled-pair many-electron theory (CPMET ), and configuration interaction (CI ) are investigated with particular emphasis on the importance of quadruple excitations in correlation theories. These different methods are used to obtain single, double, and quadruple excitation contributions to the correlation energy for a series of molecules including CO₂, HCN, N₂, CO, BH₃, and NH₃. It is demonstrated that the sum of double and quadruple excitation diagrams through fourth-order perturbation theory is usually quite close to the CPMET result for these molecules at equilibrium geometries. The superior reliability of the CPMET model as a function of internuclear separation is illustrated by studying the ¹∑ potential curve of Be₂. This molecule violates the assumption common to nondegenerate perturbation theory that only a single reference function is important and this causes improper behavior of the potential curve as a function of R. This is resolved once the quadruple excitation terms are fully included by CPMET .     

VBSM: a solvation model based on valence bond theory

A new solvation model, called VBSM, is presented. The model combines valence bond (VB) theory with parameters determined for the SM6 solvation model (Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Chem. Theo. Comp. 2005, 1, 1133-1152). VBSM, like SM6, is based on the generalized Born (GB) approximation for bulk electrostatics and atomic surface tensions to account for cavitation, dispersion, and solvent structure (CDS). The solvation free energy of VBSM includes (i) a self-consistent polarization term obtained by using VB atomic charges in a GB reaction field with a VB self-consistent field procedure that minimizes the total energy of the system with respect to the valence bond orbitals and (ii) a geometry-dependent CDS term to account for deviations from bulk-electrostatic solvation. Test calculations for a few systems show that the liquid-phase partial atomic charges obtained by VBSM are in good agreement with liquid-phase charges obtained by charge model CM4 (Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Chem. Theo. Comp. 2005, 1, 1133-1152). Free energies of solvation are calculated for two prototype test cases, namely, for the degenerate S(N)2 reaction of Cl(-) with CH(3)Cl in water and for a Menshutkin reaction in water. These calculations show that the VBSM method provides a practical alternative to single-configuration self-consistent field theory for solvent effects in molecules and chemical reactions.     

Fluid-fluid and fluid-solid transitions in the Kern-Frenkel model from Barker-Henderson thermodynamic perturbation theory

We study the Kern-Frenkel model for patchy colloids using Barker-Henderson second-order thermodynamic perturbation theory. The model describes a fluid where hard sphere particles are decorated with one patch, so that they interact via a square-well potential if they are sufficiently close one another, and if patches on each particle are properly aligned. Both the gas-liquid and fluid-solid phase coexistences are computed and contrasted against corresponding Monte Carlo simulations results. We find that the perturbation theory describes rather accurately numerical simulations all the way from a fully covered square-well potential down to the Janus limit (half coverage). In the region where numerical data are not available (from Janus to hard-spheres), the method provides estimates of the location of the critical lines that could serve as a guideline for further efficient numerical work at these low coverages. A comparison with other techniques, such as integral equation theory, highlights the important aspect of this methodology in the present context.     

A reaction converting a w-w triple bond to a double bond: tetrakis-diethyldithiophosphate-disulfide-ditungsten,preparation and characterization

The reaction between W₂X₂(OR)₄ compounds [X = CH₂CMe₃ or OBu^t] and HS₂P(OEt)₂ (6 equivalents) in hydrocarbon solvents, produces a molecule of formula W₂S₂[S₂P(OEt)₂]₄ with corresponding elimination of alkane, alcohol and [(EtO)₂PS]₂. This tungsten compound has been characterized by IR,¹H,¹³C, and¹³P NMR spectroscopy, electronic absorption spectroscopy and single-crystal X-ray crystallography. The molecule adopts a structure based on an edge-shared bioctahedron, with two bridging sulfides, two chelating dithiophosphate ligands and two dithiophosphate ligands bridging the metal- metal double bond. The W-W distance of 2.5987(11)Åalong with the acute W—S—W angles of 67.74(8)dg, are consistent with the metalmetal double bond formulation Σ² π² . This structure is similar to the W₂S₂(S₂CNEt₂)₄ molecule prepared by Cotton et al. (Inorg. Chem. 1978,17, 2946).     

SrSn4: a superconducting stannide with localized and delocalized bond character

The title compound is the tin-richest phase in the system Sr-Sn and is obtained by stoichiometric combination of the elements. SrSn(4) peritecticly decomposes under formation of SrSn(3) and Sn at 340 degrees C. The structure determined from a single crystal shows a new structure type with a novel structure motive in tin chemistry. It can be described by a corrugated, distorted quadratic net of tin atoms as the only building unit. The nets intersect at common Sn atoms, and the resulting channels host the Sr atoms. The structure can alternatively be described as an intergrowth structure of the AlB(2)-type and W-type. The atoms that are connected by the two shortest Sn-Sn distances (2.900 and 3.044 A) form a two-dimensional net consisting of hexagons of tin atoms. The hexagons have boat conformation in contrast to the rather similar alpha-As structure type, where hexagons have a chair conformation. Further tin atoms connect the two-dimensional net of Sn hexagons. Temperature-dependent magnetic susceptibility measurements show that SrSn(4) is superconducting with T(c) = 4.8 K at 10 G. LMTO band structure and density of states calculations verify the metallic behavior of SrSn(4). An analysis of the electronic structure with the help of the electron localization function (ELF) shows that localized covalent bonds beside delocalized bonds coexist in SrSn(4).     

Thermodynamic properties of model solids with short-ranged potentials from Monte Carlo simulations and perturbation theory

Monte Carlo simulations have been performed to determine the excess energy and the equation of state of fcc solids with Sutherland potentials for wide ranges of temperatures, densities, and effective potential ranges. The same quantities have been determined within a perturbative scheme by means of two procedures: (i) Monte Carlo simulations performed on the reference hard-sphere system and (ii) second-order Barker-Henderson perturbation theory. The aim was twofold: on the one hand, to test the capability of the "exact" MC-perturbation theory of reproducing the direct MC simulations and, on the other hand, the reliability of the Barker-Henderson perturbation theory, as compared with direct MC simulations and MC-perturbation theory, to determine the thermodynamic properties of these solids depending on temperature, density, and potential range. We have found that the simulation data for the excess energy obtained from the two procedures are in close agreement with each other. For the equation of state, the results from the MC-perturbation procedure also agree well with the direct MC simulations except for very low temperatures and extremely short-ranged potentials. Regarding the Barker-Henderson perturbation theory, we have found that in general the second-order approximation does not provide significant improvement over the first-order one.     

Ground- and excited-state diatomic bond lengths, vibrational levels, and potential-energy curves from conventional and localized Hartree-Fock-based density-functional theory

Ground- and excited-state diatomic bond lengths, vibrational levels, and potential-energy curves are determined using conventional and localized Hartree-Fock (LHF)-based density-functional theory. Exchange only and hybrid functionals (with various fractions of exchange) are considered, together with a standard generalized gradient approximation (GGA). Ground-state bond lengths and vibrational wave numbers are relatively insensitive to whether orbital exchange is treated using the conventional or LHF approach. Excited-state calculations are much more sensitive. For a standard fraction of orbital exchange, N2 and CO vertical excitation energies at experimental bond lengths are accurately described by both conventional and LHF-based approaches, providing an asymptotic correction is present. Excited-state bond lengths and vibrational levels are more accurate with the conventional approach. The best quality, however, is obtained with an asymptotically corrected GGA functional. For the ground and lowest four singlet excited states, the GGA mean absolute errors in bond lengths are 0.006 A (0.5%) and 0.011 A (0.8%) for N2 and CO, respectively. Mean absolute errors in fundamental vibrational wavenumbers are 49 cm(-1) (2.7%) and 68 cm(-1) (5.0%), respectively. The GGA potential-energy curves are compared with near-exact Rydberg-Klein-Rees curves. Agreement is very good for the ground and first excited state, but deteriorates for the higher states.     

Ruthenium-catalyzed oxidation of a carbon-carbon triple bond: facile syntheses of alkenyl 1,2-diketones from alkynes

A new oxidation procedure of alkynes catalyzed by Tp(PPh(3))(CH(3)CN)Ru-Cl is presented, which provides an efficient way to obtain alkenyl 1,2-diketones via ruthenium alkenyl 1,2-diketone intermediates. In contrast, the analogous reactions with Tp(PPh(3))(PhCN)Ru-Cl gave rise to the ruthenium metallacycle complexes.     

Third-order Douglas-Kroll relativistic coupled-cluster theory through connected single, double, triple, and quadruple substitutions: applications to diatomic and triatomic hydrides

Coupled-cluster methods including through and up to the connected single, double, triple, and quadruple substitutions have been derived and implemented automatically for sequential and parallel executions by an algebraic and symbolic manipulation program TCE (TENSOR CONTRACTION ENGINE) for use in conjunction with a one-component third-order Douglas-Kroll approximation for relativistic corrections. A combination of the converging electron-correlation methods, the accurate relativistic reference wave functions, and the use of systematic basis sets tailored to the relativistic approximation has been shown to predict the experimental singlet-triplet separations within 0.02 eV (0.5 kcal/mol) for five triatomic hydrides (CH2, NH2+, SiH2, PH2+, and AsH2+), the experimental bond lengths (re or r0) within 0.002 angstroms, rotational constants (Be or B0) within 0.02 cm(-1), vibration-rotation constants (alphae) within 0.01 cm(-1), centrifugal distortion constants (De) within 2%, harmonic vibration frequencies (omegae) within 8 cm(-1) (0.4%), anharmonic vibrational constants (xomegae) within 2 cm(-1), and dissociation energies (D0(0)) within 0.02 eV (0.4 kcal/mol) for twenty diatomic hydrides (BH, CH, NH, OH, FH, AlH, SiH, PH, SH, ClH, GaH, GeH, AsH, SeH, BrH, InH, SnH, SbH, TeH, and IH) containing main-group elements across the second through fifth rows of the periodic table. In these calculations, spin-orbit effects on dissociation energies, which were assumed to be additive, were estimated from the measured spin-orbit coupling constants of atoms and diatomic molecules, and an electronic energy in the complete-basis-set, complete-electron-correlation limit has been extrapolated in two ways to verify the robustness of the results: One assuming Gaussian-exponential dependence of total energies on double through quadruple zeta basis sets and the other assuming n(-3) dependence of correlation energies on double through quintuple zeta basis sets.     

Raman scattering in crystalline oligothiophenes: a comparison between density functional theory and bond polarizability model

Raman intensity of intramolecular and lattice modes of crystalline alpha-bithiophene (alpha-2T) are investigated within density functional theory using a nonlinear response formalism. First, comparison between the calculated Raman spectrum and the experimental data allows the assignment of the main Raman lines over the whole frequency range. Then, a bond polarizability (BP) model, limited to first neighbors, is built. We show that, although the BP model cannot reproduce the changes of dielectric susceptibility under individual atomic displacements, it is accurate enough to reproduce the profile of the unpolarized nonresonant Raman spectrum of alpha-2T powder. Finally, the BP model, fitted on our first-principles results on alpha-2T, is applied with success to the alpha-quaterthiophene polymorph phases and alpha-sexithiophene, demonstrating on practical examples that first-principles and BP approaches are powerful complementary tools to calculate the nonresonant Raman spectrum of alpha-2T and make reasonable predictions on larger oligothiophenes.     

Density functionals from many-body perturbation theory: the band gap for semiconductors and insulators

Theoretically the Kohn-Sham band gap differs from the exact quasiparticle energy gap by the derivative discontinuity of the exchange-correlation functional. In practice for semiconductors and insulators the band gap calculated within any local or semilocal density approximations underestimates severely the experimental energy gap. On the other hand, calculations with an "exact" exchange potential derived from many-body perturbation theory via the optimized effective potential suggest that improving the exchange-correlation potential approximation can yield a reasonable agreement between the Kohn-Sham band gap and the experimental gap. The results in this work show that this is not the case. In fact, we add to the exact exchange the correlation that corresponds to the dynamical (random phase approximation) screening in the GW approximation. This accurate exchange-correlation potential provides band structures similar to the local density approximation with the corresponding derivative discontinuity that contributes 30%-50% to the energy gap. Our self-consistent results confirm substantially the results for Si and other semiconductors obtained perturbatively [R. W. Godby et al., Phys. Rev. B 36, 6497 (1987)] and extend the conclusion to LiF and Ar, a wide-gap insulator and a noble-gas solid.     

Valence bond calculations of hydrogen transfer reactions: a general predictive pattern derived from theory

Hydrogen abstraction reactions of the type X(*) + H-H' --> X-H + H'(*) (X = F, Cl, Br, I) are studied by ab initio valence bond methods and the VB state correlation diagram (VBSCD) model. The reaction barriers and VB parameters of the VBSCD are computed by using the breathing orbital valence bond and valence bond configuration interaction methods. The combination of the VBSCD model and semiempirical VB theory leads to analytical expressions for the barriers and other VB quantities that match the ab initio VB calculations fairly well. The barriers are influenced by the endo- or exothermicity of the reaction, but the fundamental factor of the barrier is the average singlet-triplet gap of the bonds that are broken or formed in the reactions. Some further approximations lead to a simple formula that expresses the barrier for nonidentity and identity hydrogen abstraction reactions as a function of the bond strengths of reactants and products. The semiempirical expressions are shown to be useful not only for the model reactions that are studied in this work, but also for other nonidentity and identity hydrogen abstraction reactions that have been studied in previous articles.     

Triple excitations in state-specific multireference coupled cluster theory: application of Mk-MRCCSDT and Mk-MRCCSDT-n methods to model systems

We report the first implementation with correct scaling of the Mukherjee multireference coupled cluster method with singles, doubles, and approximate iterative triples (Mk-MRCCSDT-n, n=1a,1b,2,3) as well as full triples (Mk-MRCCSDT). These methods were applied to the classic H4, P4, BeH(2), and H8 model systems to assess the ability of the Mk-MRCCSDT-n schemes to accurately account for triple excitations. In all model systems the inclusion of triples via the various Mk-MRCCSDT-n approaches greatly reduces the nonparallelism error (NPE) and the mean nonparallelism derivative diagnostics for the potential energy curves, recovering between 59% and 73% of the full triples effect on average. The most complete triples approximation, Mk-MRCCSDT-3, exhibits the best average performance, reducing the mean NPE to below 0.6 mE(h), compared to 1.4 mE(h) for Mk-MRCCSD. Both linear and quadratic truncations of the Mk-MRCC triples coupling terms are viable simplifications producing no significant errors. If the off-diagonal parts of the occupied-occupied and virtual-virtual blocks of the Fock matrices are ignored, the storage of the triples amplitudes is no longer required for the Mk-MRCCSDT-n methods introduced here. This proves to be an effective approximation that gives results almost indistinguishable from those derived from full consideration of the Fock matrices.     

A coupled cluster approach with a hybrid treatment of connected triple excitations: implementation and applications for open-shell systems

An implementation of the coupled cluster (CC) singles, doubles, and a hybrid treatment of connected triples [denoted as CCSD(T)-h], based on the unrestricted Hartree-Fock (UHF) reference, is presented. Based on the spin-integrated formulation, we have developed a computer program to achieve the automatic derivation and implementation of the CCSD(T)-h approach. The CCSD(T)-h approach computationally scales as the seventh power of the system size, and is affordable for many medium-sized systems. The present approach has been applied to study the equilibrium geometries and harmonic vibrational frequencies in a number of open-shell diatomic molecules and bond breaking potential energy profiles in several open-shell molecules, including CH(3), NH(2), and SiH(2). For all systems under study, the overall performance of the UHF-based CCSD(T)-h approach is very close to that of the corresponding CCSDT (CC singles, doubles, and triples), and much better than that of the UHF-based CCSD(T) (CC singles, doubles, and perturbative triples).     

Erratum: Thermodynamic perturbation theory of a dense fluid of polar and polarizable spheres

A method is described for determination of the dissociation energy D₀ for hydrogen bonded dimers B…H-A using only measurements of rotational transition intensities at a single temperature. Application in the particular case HCN…HF gives D₀ = 18.5 ± 1.1 kJ mol^?1. By taking account of the vibrational modes of HCN…HF in the harmonic oscillator approximation, D_e is estimated as 25.6 ± 1.6 kJ mol^?1.     

How to properly compute the resonance energy within the ab initio valence bond theory: a response to the ZHJVL paper

Valence bond (VB) theory describes a conjugated system by a set of electron-localized Lewis resonance structures. VB assumes that the magnitude of the intramolecular electron delocalization can be measured in terms of a resonance energy (RE), taken to be the energy difference between the real conjugated system (delocalized) and the corresponding most stable virtual resonance structure (localized). Proper RE estimates within VB theory require both delocalized and localized states to be defined at the same theoretical level, and the definition of the localized state to closely correspond to the intuitive picture of the corresponding VB structure. In contrast, the VB-delocal and VB-local computational approaches adopted by Zielinski, et al. [preceding paper in this issue] used definitions for either the delocalized or the localized states which, in our view, depart from the intuitive chemical picture. Consequently, their RE estimates are much lower than seemingly appropriate experimental evaluations with which they strongly disagree. Very large basis sets approaching completeness blur the boundaries among resonance structures and result in “basis set artifact” problems within any variant of VB theory. However, block-localized wavefunction (BLW) computations with mid-size basis sets not only exhibit insignificant variations with theoretical levels, but the resulting RE estimates also are justified by comparisons with those employing experimental data and MO computations. We stress that RE differs from the aromatic stabilization energy (ASE). The RE measures the total stabilization of an aromatic system, whereas ASE measures only the part of the RE that exceeds that of appropriate conjugated (but non-aromatic) reference molecules.