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Double hybrid density functional theory arguably sits on the seamline between wavefunction methods and DFT: it represents a special case of Rung 5 on the "Jacob's Ladder" of John P. Perdew. For large and chemically diverse benchmarks such as GMTKN55, empirical double hybrid functionals with dispersion corrections can achieve accuracies approaching wavefunction methods at a cost not greatly dissimilar to hybrid DFT approaches, provided RI‐MP2 and/or another MP2 acceleration techniques are available in the electronic structure code. Only a half‐dozen or fewer empirical parameters are required. For vibrational frequencies, accuracies intermediate between CCSD and CCSD(T) can be achieved, and performance for other properties is encouraging as well. Organometallic reactions can likewise be treated well, provided static correlation is not too strong. Further prospects are discussed, including range‐separated and RPA‐based approaches. [ABSTRACT FROM AUTHOR]

In an attempt to extend the applicability of the W1 and W2 ab initio computational thermochemistry methods, we propose explicitly correlated versions thereof, denoted W1-F12 and W2-F12. In W2-F12, we can 'save' one cardinal number (viz., angular momentum) in the basis set sequences without loss in accuracy; in W1-F12, we can do so for first-row compounds but not for second-row compounds. At a root mean square deviation (RMSD) = 0.19 kcal/mol for the first-row molecules in the W4-11 benchmark dataset, W1-F12 is in fact superior to ordinary W1 theory. For the entire W4-11 set, W2-F12 yields a RMSD = 0.20 kcal/mol, comparable to 0.19 kcal/mol from ordinary W2 theory. The extended applicability ranges of W1-F12 and W2-F12 are not just due to the lower computational cost but also to greatly reduced memory and especially storage requirements. They are illustrated through applications to nucleic acids and to polyacenes (with up to four rings), for which the following revised gas-phase heats of formation are found: ΔfH298° = 19.6 (benzene), 34.94 (naphthalene), 53.9, (anthracene), 73.9 (naphthacene/tetracene), 54.9 (adenine), -16.3 (cytosine), 5.1 (guanine), -80.6 (thymine), and -71.6 (uracil) kcal/mol. Our theoretical values for the DNA/RNA bases largely confirm recent predictions based on much lower-level calculations. The W1-F12 theoretical values for benzene, naphthalene, and anthracene are in very good to reasonable agreement with experiment. However, both W1-F12 and other computational estimates show that the accepted experimental value for naphthacene cannot be reconciled with those for the lower acenes: we suggest that ΔfH298°[naphthacene(g)] = 74.25 ± 1 kcal/mol is a more realistic estimate. [ABSTRACT FROM AUTHOR]

A density functional theory exchange-correlation functional for the exploration of reaction mechanisms is proposed. This functional, denoted BMK (Boese-Martin for Kinetics), has an accuracy in the 2 kcal/mol range for transition state barriers but, unlike previous attempts at such a functional, this improved accuracy does not come at the expense of equilibrium properties. This makes it a general-purpose functional whose domain of applicability has been extended to transition states, rather than a specialized functional for kinetics. The improvement in BMK rests on the inclusion of the kinetic energy density together with a large value of the exact exchange mixing coefficient. For this functional, the kinetic energy density appears to correct “back” the excess exact exchange mixing for ground-state properties, possibly simulating variable exchange. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We are proposing a new computational thermochemistry protocol denoted W3 theory, as a successor to W1 and W2 theory proposed earlier [Martin and De Oliveira, J. Chem. Phys. 111, 1843 (1999)]. The new method is both more accurate overall (error statistics for total atomization energies approximately cut in half) and more robust (particularly towards systems exhibiting significant nondynamical correlation) than W2 theory. The cardinal improvement rests in an approximate account for post-CCSD(T) correlation effects. Iterative T[sub 3] (connected triple excitations) effects exhibit a basis set convergence behavior similar to the T[sub 3] contribution overall. They almost universally decrease molecular binding energies. Their inclusion in isolation yields less accurate results than CCSD(T) nearly across the board: It is only when T[sub 4] (connected quadruple excitations) effects are included that superior performance is achieved. T[sub 4] effects systematically increase molecular binding energies. Their basis set convergence is quite rapid, and even CCSDTQ/cc-pVDZ scaled by an empirical factor of 1.2532 will yield a quite passable quadruples contribution. The effect of still higher-order excitations was gauged for a subset of molecules (notably the eight-valence electron systems): T[sub 5] (connected quintuple excitations) contributions reach 0.3 kcal/mol for the pathologically multireference X [sup 1]Σ[sub g][sup +] state of C[sub 2] but are quite small for other systems. A variety of avenues for achieving accuracy beyond that of W3 theory were explored, to no significant avail. W3 thus appears to represent a good compromise between accuracy and computational cost for those seeking a robust method for computational thermochemistry in the kJ/mol accuracy range on small systems. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The total atomization energy at absolute zero, (TAE[sub 0]) of benzene, C[sub 6]H[sub 6], was computed fully ab initio by means of W2h theory as 1306.6 kcal/mol, to be compared with the experimentally derived value 1305.7±0.7 kcal/mol. The computed result includes contributions from inner-shell correlation (7.1 kcal/mol), scalar relativistic effects (-1.0 kcal/mol), atomic spin–orbit splitting (-0.5 kcal/mol), and the anharmonic zero-point vibrational energy (62.1 kcal/mol). The largest-scale calculations involved are CCSD/cc-pV5Z and CCSD(T)/cc-pVQZ; basis set extrapolations account for 6.3 kcal/mol of the final result. Performance of more approximate methods has been analyzed. Our results suggest that, even for systems the size of benzene, chemically accurate molecular atomization energies can be obtained from fully first-principles calculations, without resorting to corrections or parameters derived from experiment. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The mechanistic details of the Meerwein-Schmidt-Ponndorf-Verley (MSPV) reduction of ketones to the corresponding alcohols are investigated both experimentally and computationally. The results demonstrate that a direct hydrogen transfer mechanism involving a concerted six-membered ring transition state is the most favorable pathway in all calculated models, including the experimental BINOLate/Al/Ho/MePhc=O system.

Scalar relativistic corrections to atomisation energies of first- and second-row molecules can be rationalised in terms of a simple additive model, linear in changes in atomic s populations. In a sample of 200 first-and second-row molecules, such a model can account for over 98% of the variance (99% for the first-row subset). The remaining error can be halved again by adding a term involving the change in atomic p populations: those coefficients need not be fitted but can be fixed from atomic electron affinity calculations. This model allows a fairly accurate a priori estimate for the importance of scalar relativistic corrections on a reaction energy, at essentially zero computational cost. While this is not a substitute for explicit calculation of Douglas–Kroll–Hess (DKH) or exact two-component (X2C) relativistic corrections, the model offers an interpretative tool for the chemical analysis of scalar relativistic contributions to reaction energies. [ABSTRACT FROM AUTHOR]

The inner-shell correlation contributions to the total atomisation energies of the W4-17 computational thermochemistry benchmark have been determined at the CCSD(T) level near the basis set limit using several families of core correlation basis sets, such as aug-cc-pCVnZ (n = 3–6), aug-cc-pwCVnZ (n = 3–5) and nZaPa-CV (n = 3–5). The three families of basis sets agree very well with each other (0.01 kcal/mol RMS) when extrapolating from the two largest available n: however, there are considerable differences in convergence behaviour for the smaller basis sets. nZaPa-CV is superior for the core-core term and awCVnZ for the core-valence term. While the aug-cc-pwCV(T+d)Z basis set of Yockel and Wilson is superior to aug-cc-pwCVTZ, further extension of this family proved unproductive. The best compromise between accuracy and computational cost, in the context of high-accuracy computational thermochemistry methods, is CCSD(T)/awCV{T,Q}Z, where the {T,Q} notation stands for extrapolation from the awCVTZ and awCVQZ basis set pair. For lower-cost calculations, we recommend a previously proposed combination of CCSD-F12b/cc-pCVTZ-F12 and CCSD(T)/pwCVTZ(no f). While in first-row molecules core-valence correlation on average accounts for over 90% of the inner-shell contribution, in second-row molecules core-core contributions may become important, particularly in systems like P4 and S4 with multiple adjacent second-row atoms. [ABSTRACT FROM AUTHOR]

The quartic force field of cyclic C4 has been computed using basis sets of spdf quality and augmented coupled cluster methods. The effect of core correlation and further basis set extension has been investigated. Vibrational energy levels have been obtained using perturbation theory and two different variational approaches. A severe Fermi resonance exists between the most intense vibration, ν6, and ν3+ν5 through an exceptionally large k356=-258.2 cm-1; a large k1356 =-54.8 cm-1 causes significant higher-order anharmonicity, including a shift in ν6 of +9 cm-1. C4 appears to be an excellent test case for methods for solving the vibrational Schrödinger equation, since perturbation theory breaks down even when the above resonances are accounted for. Our best estimate for ν6, 1320±10 cm-1, may suggest its assignment to a feature detected at 1284 cm-1 in argon and 1302 cm-1 in krypton matrix, but this would imply an unusually large matrix red shift in argon. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The quartic force field of ethylene, C2H4, has been calculated ab initio using augmented coupled cluster, CCSD(T), methods and correlation consistent basis sets of spdf quality. For the 12C isotopomers C2H4, C2H3D, H2CCD2, cis-C2H2D2, trans-C2H2D2, C2HD3, and C2D4, all fundamentals are reproduced to better than 10 cm-1, except for three cases where the error is 11 cm-1. Our calculated harmonic frequencies suggest a thorough revision of the accepted experimentally derived values. Our computed and empirically corrected re geometry differs substantially from experimentally derived values: Both the predicted rz geometry and the ground-state rotational constants are, however, in excellent agreement with experiment, suggesting revision of the older values. Anharmonicity constants agree well with experiment for stretches, but differ substantially for stretch–bend interaction constants, due to equality constraints in the experimental analysis that do not hold. Improved criteria for detecting Fermi and Coriolis resonances are proposed and found to work well, contrary to the established method based on harmonic frequency differences that fails to detect several important resonances for C2H4 and its isotopomers. Surprisingly good results are obtained with a small spd basis at the CCSD(T) level. The well-documented strong basis set effect on the ν8 out-of-plane motion is present to a much lesser extent when correlation-optimized polarization functions are used. Complete sets of anharmonic, rovibrational coupling, and centrifugal distortion constants for the isotopomers are available as supplementary material to the paper via the World-Wide Web. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The total atomization energies of the carbon clusters Cn (n=2–10) have been calculated ab initio using augmented coupled-cluster methods and basis sets of spdf and spdfg quality. The values agree to within experimental uncertainty with recent Knudsen effusion measurements for Cn (n=2–7), but suggest actual values on the high side of their experimental range. For the odd-numbered clusters, an additivity approximation holds very well, and extrapolated ∑D0 values are proposed for C11, C13, C15, C17, and C19. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The potential energy surface for the B2C molecule and the potential energy curve for the ground state of BC have been investigated using full-valence complete active space SCF (CASSCF), augmented coupled cluster [CCSD(T)] and multireference treatments. The ground state of B2C is an extraordinarily stable ring (∑ De=261.6±1 kcal/mol) with two 2-electron π systems. The first excited state is linear BCB (1Σ+g), which is essentially biconfigurational due to a (4σg)–(3σu) near degeneracy. Anharmonic spectroscopic constants were obtained from quartic force fields at the CCSD(T) level with a correlation-consistent basis set of [4s3p2d1f] quality. A severe Fermi resonance exists between the bending and symmetric stretching modes. All computed intensities are fairly weak. Spectroscopic constants for BC using elaborate multireference techniques were very well reproduced using the CCSD(T) method with a spin-restricted Hartree–Fock reference configuration, but not with an unrestricted Hartree–Fock reference. This suggests that even moderate levels of spin contamination that do not significantly affect relative energies may have a detrimental effect on computed spectroscopic constants. [ABSTRACT FROM AUTHOR]

The total atomization energies (∑De values), geometries, and harmonic frequencies for a number of experimentally well-described molecules have been calculated at the CCSD(T) (coupled cluster) level using Dunning’s correlation-consistent cc-pVDZ([3s2p1d]), cc-pVTZ([4s3p2d1f]), and cc-pVQZ([5s4p3d2f1g]) basis sets. Additivity correction are proposed for binding energies and geometries. Using a three-term additive correction of the form proposed by Martin [J. Chem. Phys. 97, 5012 (1992)] mean absolute errors in ∑De are 0.46 kcal/mol for the cc-pVQZ, 0.93 for the cc-pVTZ, and 2.59 for the c-pVDZ basis sets. The latter figure implies that, although unsuitable for quantitatively accurate work, three-term corrected CCSD(T)/cc-pVDZ binding energies can still be used for a rough estimate when the cost of larger basis set calculations would be prohibitive. CCSD(T)/cc-pVQZ calculations reproduce bond lengths to 0.001 Å for single bonds, and 0.003 Å for multiple bonds; remaining error is probably partly due to core–core and core–valence correlation. CCSD(T)/cc-pVTZ calculations result in additional overestimates of 0.001 Å for single, 0.003 Å for double, and 0.004 Å for triple bonds. CCSD(T)/cc-pVDZ calculations result in further overestimates of 0.01 Å for single bonds, and 0.02 Å for multiple bonds.CCSD(T)/cc-pVDZ harmonic frequencies are in surprisingly good agreement with experiment, except for pathological cases like the umbrella mode in NH3. Both CCSD(T)/cc-pVTZ and CCSD(T)/cc-pVQZ harmonic frequencies generally agree with experiment to 10 cm-1 or better; performance of cc-pVQZ is somewhat superior on multiple bonds or the umbrella mode in NH3. Again, a source of remaining error appears to be core correlation. The use of MP2/6-31G* reference geometries in the ∑De calculation can result in fairly substantial errors in the uncorrected ∑De values for systems with cumulated multiple bonds.... [ABSTRACT FROM AUTHOR]

Pulsed laser evaporation of pellets pressed from boron and graphite powder gave a new 1:4 doublet at 1232.5 and 1194.6 cm-1 in addition to the carbon cluster absorptions reported previously. The 1232.5 cm-1 band dominated boron-10 experiments. The new bands increased as carbon cluster bands decreased with increasing B/C ratio in the pellet and with increasing laser power. Augmented coupled cluster and full-valence complete active space SCF (CASSCF) calculations predict the global minimum BC2 structure to be an asymmetric triangle: however, the vibrationally averaged structure will be an isosceles triangle with a strong symmetric B–C2 stretching frequency near 1200 cm-1. The calculated boron-10/boron-11 frequency ratio (1.0323) is in excellent agreement with the observed ratio (1.0317), and confirms assignment of the 1194.6 cm-1 band to the BC2 ring. Calculations predict linear BCC to be less stable by 6.2±2 kcal/mol and to absorb in the 2000–2050 cm-1 range: the barrier towards rearrangement to the cyclic structure is very low (1.1 kcal/mol). Linear BCC was not detected in these experiments. Computed energetics explain why BC2 is abundant in B/C experiments, but absent in B+C2H2 experiments. [ABSTRACT FROM AUTHOR]

The energetics of the gas-phase S(sub N)2 reactions Y(super -) + CH3X right arrow CH3Y + X(super -) (X,Y = F,Cl, Br), were studied using the W1 and W2 ab initio computational thermochemistry methods. The nonidentity S(sub N)2 reactions and F/F identity reaction possess transition state structures below the reactants energy while Cl/Cl and Br/Br transition structures are above the reactants energy.

The reactivity of the H5PV2Mo10O40 polyoxometalate and its analogues as an electron transfer and electron transfer–oxygen transfer oxidant has been extensively studied in the past and has been shown to be useful in many transformations. One of the hallmarks of this oxidant is the possibility of its re-oxidation with molecular oxygen, thus enabling aerobic catalytic cycles. Although the re-oxidation reaction was known, the kinetics and mechanism of this reaction have not been studied in any detail. Experimentally, we show that both the one- and two-electron reduced polyoxometalate are reactive with O2, the two-electron one more so. The reactions are first-order in the polyoxometalate and O2. Solvents also have a considerable effect, protic solvents being preferred over aprotic ones. H5PV2Mo10O40 was reduced either by an electron transfer reaction (H2) or an electron transfer–oxygen transfer reaction (Ph3P). Similar rate constants and activation parameters were observed for both. DFT calculations carried out on the re-oxidation reactions strongly suggest an inner-sphere process. The process involves first the formation of a coordinatively unsaturated site (CUS) and subsequently the binding of O2 to form superoxo and then peroxo η2-O2 adducts. Most interestingly, although vanadium is the reactive redox centre as well as a necessary component for the oxidative activity of H5PV2Mo10O40, and a CUS can be formed at both Mo and V sites, O2 coordination occurs mostly at the Mo CUSs, preferably those where the vanadium centers are distal to each other. [ABSTRACT FROM AUTHOR]

The notoriously small X 3Π-a 1Σ+ excitation energy of the BN diatomic has been calculated using high-order coupled cluster methods. Convergence has been established in both the one-particle basis set and the coupled cluster expansion. Explicit inclusion of connected quadruple excitations T⁁4 is required for even semiquantitative agreement with the limit value, while connected quintuple excitations T⁁5 still have an effect of about 60 cm-1. Still higher excitations only account for about 10 cm-1. Inclusion of inner-shell correlation further reduces Te by about 60 cm-1 at the CCSDT, and 85 cm-1 at the CCSDTQ level. Our best estimate, Te=183±40 cm-1, is in excellent agreement with earlier calculations and experiment, albeit with a smaller (and conservative) uncertainty. The dissociation energy of BN(X 3Π) is De=105.74±0.16 kcal/mol and D0=103.57±0.16 kcal/mol. [ABSTRACT FROM AUTHOR]