W4 Theory Research Articles

W4 theory for computational thermochemistry: In pursuit of confident sub-kJ/mol predictions

In an attempt to improve on our earlier W3 theory [A. D. Boese et al., J. Chem. Phys. 120, 4129 (2004)] we consider such refinements as more accurate estimates for the contribution of connected quadruple excitations (T4), inclusion of connected quintuple excitations (T5), diagonal Born-Oppenheimer corrections (DBOC), and improved basis set extrapolation procedures. Revised experimental data for validation purposes were obtained from the latest version of the Active Thermochemical Tables thermochemical network. The recent CCSDT(Q) method offers a cost-effective way of estimating T4, but is insufficient by itself if the molecule exhibits some nondynamical correlation. The latter considerably slows down basis set convergence for T4, and anomalous basis set convergence in highly polar systems makes two-point extrapolation procedures unusable. However, we found that the CCSDTQ-CCSDT(Q) difference converges quite rapidly with the basis set, and that the formula 1.10[CCSDT(Q)cc-pVTZ+CCSDTQcc-pVDZ-CCSDT(Q)cc-pVDZ] offers a very reliable as well as fairly cost-effective estimate of the basis set limit T4 contribution. The T5 contribution converges very rapidly with the basis set, and even a simple double-zeta basis set appears to be adequate. The largest T5 contribution found in the present work is on the order of 0.5 kcal/mol (for ozone). DBOCs are significant at the 0.1 kcal/mol level in hydride systems. Post-CCSD(T) contributions to the core-valence correlation energy are only significant at that level in systems with severe nondynamical correlation effects. Based on the accumulated experience, a new computational thermochemistry protocol for first- and second-row main-group systems, to be known as W4 theory, is proposed. Its computational cost is not insurmountably higher than that of the earlier W3 theory, while performance is markedly superior. Our W4 atomization energies for a number of key species are in excellent agreement (better than 0.1 kcal/mol on average, 95% confidence intervals narrower than 1 kJ/mol) with the latest experimental data obtained from Active Thermochemical Tables. Lower-cost variants are proposed: the sequence W1-->W2.2-->W3.2-->W4lite-->W4 is proposed as a converging hierarchy of computational thermochemistry methods. A simple a priori estimate for the importance of post-CCSD(T) correlation contributions (and hence a pessimistic estimate for the error in a W2-type calculation) is proposed.

Heats of formation of perchloric acid, HClO 4, and perchloric anhydride, Cl 2O 7. Probing the limits of W1 and W2 theory

The heats of formation of HClO 4 and Cl 2O 7 have been determined to chemical accuracy for the first time by means of W1 and W2 theory. These molecules exhibit particularly severe degrees of inner polarization, and as such obtaining a basis-set limit SCF component to the total atomization energy becomes a challenge. (Adding high-exponent d functions to a standard spd basis set has an effect on the order of 100 kcal/mol for Cl 2O 7.) Wilson's aug-cc-pV(n+d)Z basis sets represent a dramatic improvement over the standard aug-cc-pVnZ basis sets, while the aug-cc-pVnZ+2d1f sequence converges still more rapidly. Jensen's polarization consistent basis sets still require additional high-exponent d functions: for smooth convergence we suggest the {aug-pc1+3d,aug-pc2+2d,aug-pc3+d,aug-pc4} sequence. The role of the tight d functions is shown to be an improved description of the Cl (3d) Rydberg orbital, enhancing its ability to receive back-bonding from the oxygen lone pairs. In problematic cases like this (or indeed in general), a single SCF/aug-cc-pV6Z+2d1f calculation may be preferable over empirically motivated extrapolations. Our best estimate heats of formation are Δ H f , 298 0 [ HClO 4 ( g ) ] = − 0.6 ± 1 kcal / mol and Δ H f, 298 0 [ Cl 2 O 7 ( g ) ] = 65.9 ± 2 kcal / mol , the largest source of uncertainty being our inability to account for post-CCSD(T) correlation effects. While G2 and G3 theory have fairly large errors, G3X theory reproduces both values to within 2 kcal/mol.

A Photoelectron Photoion Coincidence Study of the Vinyl Bromide and Tribromoethane Ion Dissociation Dynamics: Heats of Formation of C2H3+, C2H3Br, C2H3Br+, C2H3Br2+, and C2H3Br3

The threshold photoelectron photoion coincidence (TPEPICO) technique has been used to measure accurate dissociative photoionization onsets of vinyl bromide and 1,1,2-tribromoethane. The reactions investigated and their 0 K onsets are C2H3Br + hnu --> C2H3+ + Br (11.902 +/- 0.008 eV); C2H3Br3 + hnu --> C2H3Br2+ + Br (10.608 +/- 0.008 eV); and (C2H3Br3 + hnu --> C2H3Br+ + 2Br (12.301 +/- 0.035 eV). The vinyl ion heat of formation (Delta(f)H degrees 298K = 1116.1 +/- 3.0 kJ/mol) has been calculated using W1 theory and used as an anchor along with the measured dissociation energies to determine the heats of formation, Delta(f)H degrees 298K, in kJ/mol, of the following bromine-containing species: C2H3Br (74.1 +/- 3.1), C2H3Br+ (1021.9 +/- 3.1), C2H3Br2+ (967.1 +/- 4.0), and C2H3Br3 (53.5 +/- 4.3). These results represent accurate and consistent experimental determinations of heats of formation for these bromine-containing species, which serve to correct the discrepancies in the literature for C2H3Br and C2H3Br+ and provide the first experimental determination for the enthalpies of formation of C2H3Br2+ and C2H3Br3.

Thermodynamic Properties of C1 and C2 Bromo Compounds and Radicals. A Relativistic ab Initio Study

Heats of formation for a number of key C1 and C2 bromoalkanes and radicals have been calculated ab initio, both directly using an all-relativistic variant of W2 theory and indirectly using Douglas−Kroll relativistic CCSD(T)/Aug-VTZ reaction energies. For some of the bromoalkanes, our calculated values represent the first reliable data available. Bromine (3d) correlation contributes significantly to the molecular binding energies, but the effect of bromine (3s, 3p) correlation appears to be very small despite these orbitals lying above the carbon (1s) in energy. Thermodynamic functions have been obtained from molecular geometries and harmonic frequencies obtained at the B97-1/Aug-VTZ level and are given in the Supporting Information. These accurate thermodynamic parameters can be used to develop kinetic rate parameters.

W3 theory: robust computational thermochemistry in the kJ/mol accuracy range.

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 T3 (connected triple excitations) effects exhibit a basis set convergence behavior similar to the T3 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 T4 (connected quadruple excitations) effects are included that superior performance is achieved. T4 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): T5 (connected quintuple excitations) contributions reach 0.3 kcal/mol for the pathologically multireference X 1Sigmag+ state of C2 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.

The heats of formation of the haloacetylenes XCCY [X, Y = H, F, Cl]: basis set limit ab initio results and thermochemical analysis

The heats of formation of haloacetylenes are evaluated using the recent W1 and W2 ab initio computational thermochemistry methods. These calculations involve CCSD and CCSD(T) coupled cluster methods, basis sets of up to spdfgh quality, extrapolations to the one-particle basis set limit, and contributions of inner-shell correlation, scalar relativistic effects. and (where relevant) first-order spin-orbit coupling. The heats of formation determined using W2 theory are: δH1 298(HCCH) = 54.48 kcal mol−1, δHf 298(HCCH) = 25.15 kcal mol, δHf 298(FCCF) = 1.38 kcal mol−1, δHf 298(HCCC1) = 54.83 kcal mol−1, δHf 298(CICCC1) = 56.21 kcal mol−1, and δHf 298(FCCC1) = 28.47 kcal mo1−1. Enthalpies of hydrogenation and destabilization energies relative to acetylene were obtained at the WI level of theory. So doing we find the following destabilization order for acetylenes: FCCF > ClCCF > HCCF > ClCCCl > HCCCI > HCCH. By a combination of WI theory and isodesmic reactions. we show that the generally accepted heat of formation of 1,2-dichloroethane should be revised to −31.8 ± 0.6 kcal mol−1, in excellent agreement with a very recent critically evaluated review. The performance of compound thermochemistry schemes, such as G2, G3, G3X and CBS-QB3 theories, has been analysed.

Assessment of W1 and W2 theories for the computation of electron affinities, ionization potentials, heats of formation, and proton affinities

The performance of two recent ab initio computational thermochemistry schemes, W1 and W2 theory [J. M. L. Martin and G. de Oliveira, J. Chem. Phys. 111, 1843 (1999)], is assessed for an enlarged sample of thermochemical data consisting of the ionization potentials and electron affinities in the G2-1 and G2-2 sets, as well as the heats of formation in the G2-1 and a subset of the G2-2 set. We find W1 theory to be several times more accurate for ionization potentials and electron affinities than commonly used (and less expensive) computational thermochemistry schemes such as G2, G3, and CBS-QB3: W2 theory represents a slight improvement for electron affinities but no significant one for ionization potentials. The use of a two-point A+B/L5 rather than a three-point A+B/CL extrapolation for the self-consistent field (SCF) component greatly enhances the numerical stability of the W1 method for systems with slow basis set convergence. Inclusion of first-order spin–orbit coupling is essential for accurate ionization potentials and electron affinities involving degenerate electronic states: Inner-shell correlation is somewhat more important for ionization potentials than for electron affinities, while scalar relativistic effects are required for the highest accuracy. The mean deviation from experiment for the G2-1 heats of formation is within the average experimental uncertainty. W1 theory appears to be a valuable tool for obtaining benchmark quality proton affinities.

Triplectic quantization ofW2gravity

The role of one loop order corrections in the triplectic quantization is discussed in the case of W2 theory. This model illustrates the presence of anomalies and Wess Zumino terms in this quantization scheme where extended BRST invariance is represented in a completely anticanonical form.

A Definitive Heat of Vaporization of Silicon through Benchmark ab Initio Calculations on SiF4

To resolve a significant uncertainty in the heat of vaporization of silicona fundamental parameter in gas-phase thermochemistryΔH°f,0 [Si(g)] has been determined from a thermochemical cycle involving the precisely known experimental heats of formation of SiF4(g) and F(g) and a benchmark calculation of the total atomization energy (TAE0) of SiF4 using coupled-cluster methods. Basis sets up to [8s7p6d4f2g1h] on Si and [7s6p5d4f3g2h] on F have been employed, and extrapolations for residual basis set incompleteness applied. The contributions of inner-shell correlation (−0.08 kcal/mol), scalar relativistic effects (−1.88 kcal/mol), atomic spin−orbit splitting (−1.97 kcal/mol), and anharmonicity in the zero-point energy (+0.04 kcal/mol) have all been explicitly accounted for. Our benchmark TAE0 = 565.89 ± 0.22 kcal/mol leads to ΔH°f,0 [Si(g)] = 107.15 ± 0.38 kcal/mol (ΔH°f,298 [Si(g)] = 108.19 ± 0.38 kcal/mol): between the JANAF/CODATA value of 106.5 ± 1.9 kcal/mol and the revised value proposed by Grev and Schaefer [ J. Chem. Phys. 1992, 97, 8389], 108.1 ± 0.5 kcal/mol. The revision will be relevant for future computational studies on heats of formation of silicon compounds. Among standard computational thermochemistry methods, G2 and G3 theory exhibit large errors, while CBS-Q performs relatively well, and the very recent W1 theory reproduces the present calibration result to 0.1 kcal/mol.