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A more general way of combining ab initio quantum mechanical calculations and classical mechanical free energy perturbation method to measure the general energetics of enzyme-catalyzed reactions and the same reaction in solution is described. Estimating the free energy to assemble the reacting group was one of the more important conditions of the method for the accurate calculations of the reaction energies in solution. Moreover, the use of the RESP protocol was critical in calculating the charge distribution of the structures in the reaction pathway.

MNDO and ab initio SCF calculations predict a single energy minimum for each of the large fullerenes with Goldberg type I(sub h) symmetry, which corresponds to an icosahedrally shaped structure with facets obtained from nearly planar hexagonal sheets and vertices located at the pentagons. Higher energy shown by the spherically shaped structures disfavors spherically shaped fullerenes. The observed trends are explained on the basis of force field estimates and Huckel calculations.

A theoretical composite approach, termed ATOMIC for Ab initio Thermochemistry using Optimal-balance Models with Isodesmic Corrections, is introduced for the calculation of molecular atomization energies and enthalpies of formation. Care is taken to achieve optimal balance in accuracy and cost between the various components contributing to high-level estimates of the fully correlated energy at the infinite-basis-set limit. To this end, the energy at the coupled-cluster level of theory including single, double, and quasiperturbational triple excitations is decomposed into Hartree–Fock, low-order correlation (MP2, CCSD), and connected-triples contributions and into valence-shell and core contributions. Statistical analyses for 73 representative neutral closed-shell molecules containing hydrogen and at least three first-row atoms (CNOF) are used to devise basis-set and extrapolation requirements for each of the eight components to maintain a given level of accuracy. Pople’s concept of bond-separation reactions is implemented in an ab initio framework, providing for a complete set of high-level precomputed isodesmic corrections which can be used for any molecule for which a valence structure can be drawn. Use of these corrections is shown to lower basis-set requirements dramatically for each of the eight components of the composite model. A hierarchy of three levels is suggested for isodesmically corrected composite models which reproduce atomization energies at the reference level of theory to within 0.1 kcal/mol (A), 0.3 kcal/mol (B), and 1 kcal/mol (C). Large-scale statistical analysis shows that corrections beyond the CCSD(T) reference level of theory, including coupled-cluster theory with fully relaxed connected triple and quadruple excitations, first-order relativistic and diagonal Born–Oppenheimer corrections can normally be dealt with using a greatly simplified model that assumes thermoneutral bond-separation reactions and that reduces the estimate of these corrections to the simple task of adding up bond increments. Preliminary validation with experimental enthalpies of formation using the subset of neutral closed-shell (HCNOF) species contained in the G3/99 test set indicates that the ATOMIC protocol performs slightly better than the popular G3 approach. The newly introduced protocol does not require empirical calibration, however, and it is still efficient enough to be applied routinely to molecules with 10 or 20 nonhydrogen atoms. [ABSTRACT FROM AUTHOR]

A new two-point scheme is proposed for the extrapolation of electron correlation energies obtained with small basis sets. Using the series of correlation-consistent polarized valence basis sets, cc-pVXZ, the basis set truncation error is expressed as δEX∝(X+ξi)-γ. The angular momentum offset ξi captures differences in effective rates of convergence previously observed for first-row molecules. It is based on simple electron counts and tends to values close to 0 for hydrogen-rich compounds and values closer to 1 for pure first-row compounds containing several electronegative atoms. The formula is motivated theoretically by the structure of correlation-consistent basis sets which include basis functions up to angular momentum L=X-1 for hydrogen and helium and up to L=X for first-row atoms. It contains three parameters which are calibrated against a large set of 105 reference molecules (H, C, N, O, F) for extrapolations of MP2 and CCSD valence-shell correlation energies from double- and triple-zeta (DT) and triple- and quadruple-zeta (TQ) basis sets. The new model is shown to be three to five times more accurate than previous two-point schemes using a single parameter, and (TQ) extrapolations are found to reproduce a small set of available R12 reference data better than even (56) extrapolations using the conventional asymptotic limit formula δEX∝X-3. Applications to a small selection of boron compounds and to neon show very satisfactory results as well. Limitations of the model are discussed. [ABSTRACT FROM AUTHOR]

The electron correlation energy of two-electron atoms is known to converge asymptotically as ∼(L+1)-3 to the complete basis set limit, where L is the maximum angular momentum quantum number included in the basis set. Numerical evidence has established a similar asymptotic convergence ∼X-3 with the cardinal number X of correlation-consistent basis sets cc-pVXZ for coupled cluster singles and doubles (CCSD) and second order perturbation theory (MP2) calculations of molecules. The main focus of this article is to probe for deviations from asymptotic convergence behavior for practical values of X by defining a trial function X-β that for an effective exponent β=βeff(X,X+1,X+N) provides the correct energy EX+N, when extrapolating from results for two smaller basis sets, EX and EX+1. This analysis is first applied to “model” expansions available from analytical theory, and then to a large body of finite basis set results (X=D,T,Q,5,6) for 105 molecules containing H, C, N, O, and F, complemented by a smaller set of 14 molecules for which accurate complete basis set limits are available from MP2-R12 and CCSD-R12 calculations. βeff is generally found to vary monotonically with the target of extrapolation, X+N, making results for large but finite basis sets a useful addition to the limited number of cases where complete basis set limits are available. Significant differences in effective convergence behavior are observed between MP2 and CCSD (valence) correlation energies, between hydrogen-rich and hydrogen-free molecules, and, for He, between partial-wave expansions and correlation-consistent basis sets. Deviations from asymptotic convergence behavior tend to get smaller as X increases, but not always monotonically, and are still quite noticeable even for X=5. Finally, correlation contributions to atomization energies (rather than total energies) exhibit a much larger variation of effective convergence behavior, and extrapolations from small basis sets are found to be particularly erratic for molecules containing several electronegative atoms. Observed effects are discussed in the light of results known from analytical theory. A carefully calibrated protocol for extrapolations to the complete basis set limit is presented, based on a single “optimal” exponent βopt(X,X+1,∞) for the entire set of molecules, and compared to similar approaches reported in the literature. [ABSTRACT FROM AUTHOR]

TheATOMIC protocol is a quantum-chemical thermochemistry protocoldesigned to obtain accurate atomization energies and derived heatsof formation. It reduces errors of computationally tractable compositeschemes through the use of bond separation reactions, which are implementedin a consistent ab initio framework. The present work explores possiblesimplification of previously introduced ATOMIC models. While coupledcluster calculations with singles and doubles excitations and perturbationaltreatments of connected triples excitations [CCSD(T)] are still requiredfor high accuracy, basis-set truncations are possible in the CCSD-MP2and CCSD(T)-CCSD components. The resulting models B4, B5, and B6show root-mean-square (RMS) errors ofonly 0.21 to 0.46 kcal/mol for the AE set, which is a benchmark comprisingcomplete-basis-set CCSD(T)(full) atomization energies of 73 neutral,closed-shell molecules composed of H, C, N, O, and F atoms. The evaluationof connected triples excitations can be avoided at medium levels ofaccuracy if the complete-basis-set MP2 energy is augmented with anempirically calibrated fraction of the difference between MP3 (orCCSD) and MP2 energies, calculated with small basis sets. The correspondingEMP3and ECCSDmodels show RMS errors of 1.01and 0.70 kcal/mol, respectively. Spin-component scaling is an optionto rely entirely on the MP2 level of theory and still cut the RMSerror of 4.38 kcal/mol by roughly a factor of 2 and achieve an accuracycomparable to accurate density functionals, such as M05-2X. The proposednew models are additionally tested with the HOF benchmark, a subsetof G3/99 heats of formation that includes only neutral closed-shellmolecules composed of H, C, N, O, and F atoms. The assessment showsthat a number of experimental reference values are in error and shouldbe replaced with more recent data. Results obtained with the new modelsare compared to original HOF (G3/99) reference data, to updated referencedata, and to accurate ATOMIC/A theoretical data. [ABSTRACT FROM AUTHOR]

Research was conducted to examine the base-catalyzed hydrolysis of formamide in the gas phase and in aqueous solution by means of a combination of statistical mechanical and quantum chemical techniques. The main goal is to study the aqueous-phase reaction and to analyze the influence of bulk solvent. Results are in satisfactory agreement with available experimental data for the solution-phase reaction.

The recently proposed ATOMIC protocol is a fully ab initiothermochemicalprotocol that rests upon the concept of bond separation reactions(BSRs) to correct for systematic errors of composite wave functionapproaches. It achieves high accuracy for atomization energies andderived heats of formation if basis set requirements for all contributingcomponents are balanced carefully. The present work explores the potentialof density functionals as possible replacements of composite wavefunction approaches in the ATOMIC protocol. Twenty density functionalsare examined for their accuracy in thermochemical predictions basedon calculated bond-separation energies and precomputed high-leveldata for the small parent molecules entering BSRs. The best densityfunctionals outperform CCSD (coupled cluster with singles and doublesexcitations), but none reaches the accuracy of well-balanced compositewave function approaches that consider quasiperturbational connectedtriples excitations at least with small basis sets. Some functionalsshow unexpected problems with bond separation reactions and are analyzedfurther with a model of empirically calibrated bond additivity corrections.Finally, the benefit of adding empirical dispersion terms to commondensity functionals is analyzed in the context of BSR-corrected thermochemistry. [ABSTRACT FROM AUTHOR]