Anharmonic Zero-point Energy Research Articles

Theoretical estimates of sulfoxyanion triple-oxygen equilibrium isotope effects and their implications

Triple-oxygen isotope (δ18O and Δ′17O) analysis of sulfate is becoming a common tool to assess several biotic and abiotic sulfur-cycle processes, both today and in the geologic past. Multi-step sulfur redox reactions often involve intermediate sulfoxyanions such as sulfite, sulfoxylate, and thiosulfate, which may rapidly exchange oxygen atoms with surrounding water. Process-based reconstructions therefore require knowledge of equilibrium oxygen-isotope fractionation factors (18α and 17α) between water and each individual sulfoxyanion. Despite this importance, there currently exist only limited experimental 18α data and no 17α estimates due to the difficulty of isolating and analyzing short-lived intermediate species. To address this, we theoretically estimate 18α and 17α for a suite of sulfoxyanions—including several sulfate, sulfite, sulfoxylate, and thiosulfate species—using quantum computational chemistry. We determine fractionation factors for sulfoxyanion “water droplets” using the B3LYP/6-31G+(d,p) method; we additionally calculate higher-order method (CCSD/aug-cc-pVTZ and MP2/aug-cc-pVTZ) scaling factors, and we qualitatively estimate the importance of anharmonic zero-point energy (ZPE) corrections using a suite of gaseous sulfoxy compounds. Methodological scaling factors greatly impact 18α predictions, whereas ZPE corrections are likely small (i.e., ⩽1‰) at Earth-surface temperatures; existing experimental data best agree with 18α predictions when including redox state-specific CCSD/aug-cc-pVTZ scaling factors. Theoretical pH- and temperature-specific bulk-solution (i.e., abundance-weighted average of all species) 18α values yield root-mean-square errors for sulfate/water, sulfite/water, and thiosulfate/water equilibrium of 4.5‰ (n=18 experimental conditions), 3.7‰ (n=27), and 2.2‰ (n=3), respectively. However, sulfate- and sulfite-system agreement improves considerably when comparing experimental results only to SO3(OH)−/H2O (RMSE = 1.6‰) and SO2(OH)−/H2O (RMSE = 2.2‰) predictions, rather than bulk solutions. This is particularly true for the sulfite system at high and low pH, when SO2(OH)− is not the dominant species. We discuss potential experimental and theoretical biases that may lead to this apparent improvement. By combining 18α and 17α predictions, we additionally estimate that sulfate, sulfite, sulfoxylate, and thiosulfate species can exhibit Δ′17O values as much as 0.199‰, 0.205‰, 0.101‰, and 0.186‰ more negative than equilibrated water at Earth-surface temperatures (reference line slope = 0.5305). This theoretical framework provides a foundation to interpret experimental and observational triple-oxygen isotope results of several sulfur-cycle processes including pyrite oxidation, microbial metabolisms (e.g., sulfate reduction, thiosulfate disproportionation), and hydrothermal anhydrite precipitation. We highlight this with several examples.

Multicomponent Orbital-Optimized Perturbation Theory with Density Fitting: Anharmonic Zero-Point Energies in Protonated Water Clusters.

Nuclear quantum effects such as zero-point energy are important in a wide range of chemical and biological processes. The nuclear-electronic orbital (NEO) framework intrinsically includes such effects by treating electrons and specified nuclei quantum mechanically on the same level. Herein, we implement the NEO scaled-opposite-spin orbital-optimized second-order Møller-Plesset perturbation theory with electron-proton correlation scaling (NEO-SOS'-OOMP2) using density fitting. This efficient implementation allows applications to larger systems with multiple quantum protons. Both the NEO-SOS'-OOMP2 method and its counterpart without orbital optimization predict proton affinities to within experimental precision and relative energies of protonated water tetramer isomers in agreement with previous NEO coupled cluster calculations. Applications to protonated water hexamers and heptamers illustrate that anharmonicity is critical for computing accurate relative energies. The NEO-SOS'-OOMP2 approach captures anharmonic zero-point energies at any geometry in a computationally efficient manner and hence will be useful for investigating reaction paths and dynamics in chemical systems.

Density Functional Geometries and Zero-Point Energies in Ab Initio Thermochemical Treatments of Compounds with First-Row Atoms (H, C, N, O, F).

Density functionals are often used in ab initio thermochemistry to provide optimized geometries for single-point evaluations at a high level and to supply estimates of anharmonic zero-point energies (ZPEs). Their use is motivated by relatively high accuracy at a modest computational expense, but a thorough assessment of geometry-related error seems to be lacking. We have benchmarked 53 density functionals, focusing on approximations of the first four rungs and on relatively small basis sets for computational efficiency. Optimized geometries of 279 neutral first-row molecules (H, C, N, O, F) are judged by energy penalties relative to the best available geometries, using the composite model ATOMIC/B5 as energy probe. Only hybrid functionals provide good accuracy with root-mean-square errors around 0.1 kcal/mol and maximum errors below 1.0 kcal/mol, but not all of them do. Conspicuously, first-generation hybrids with few or no empirical parameters tend to perform better than highly parameterized ones. A number of them show good accuracy already with small basis sets (6-31G(d), 6-311G(d)). As is standard practice, anharmonic ZPEs are estimated from scaled harmonic values. Statistics of the latter show less performance variation among functionals than observed for geometry-related error, but they also indicate that ZPE error will generally dominate. We have selected PBE0-D3/6-311G(d) for the next version of the ATOMIC protocol (ATOMIC-2) and studied it in more detail. Empirical expressions have been calibrated to estimate bias corrections and 95% uncertainty intervals for both geometry-related error and scaled ZPEs.

Analytical Gradients for Nuclear-Electronic Orbital Time-Dependent Density Functional Theory: Excited-State Geometry Optimizations and Adiabatic Excitation Energies.

The computational investigation of photochemical processes often entails the calculation of excited-state geometries, energies, and energy gradients. The nuclear-electronic orbital (NEO) approach treats specified nuclei, typically protons, quantum mechanically on the same level as the electrons, thereby including the associated nuclear quantum effects and non-Born-Oppenheimer behavior into quantum chemistry calculations. The multicomponent density functional theory (NEO-DFT) and time-dependent DFT (NEO-TDDFT) methods allow efficient calculations of ground and excited states, respectively. Herein, the analytical gradients are derived and implemented for the NEO-TDDFT method and the associated Tamm-Dancoff approximation (NEO-TDA). The programmable equations for these analytical gradients as well as the NEO-DFT analytical Hessian are provided. The NEO approach includes the anharmonic zero-point energy (ZPE) and density delocalization associated with the quantum protons as well as vibronic mixing in geometry optimizations and energy calculations of ground and excited states. The harmonic ZPE associated with the other nuclei can be computed via the NEO Hessian. This approach is used to compute the 0-0 adiabatic excitation energies for a set of nine small molecules with all protons quantized, exhibiting slight improvement over the conventional electronic approach. Geometry optimizations of two excited-state intramolecular proton-transfer systems, [2,2'-bipyridyl]-3-ol and [2,2'-bipyridyl]-3,3'-diol, are performed with one and two quantized protons, respectively. The NEO calculations for these systems produce electronically excited-state geometries with stronger intramolecular hydrogen bonds and similar relative stabilities compared to conventional electronic methods. This work provides the foundation for nonadiabatic dynamics simulations of fundamental processes such as photoinduced proton transfer and proton-coupled electron transfer.

A Molecular Candle Where Few Molecules Shine: HeHHe.

HeHHe is the only potential molecule comprised of atoms present in the early universe that is also easily observable in the infrared. This molecule has been known to exist in mass spectrometry experiments for nearly half-a-century and is likely present, but as-of-yet unconfirmed, in cold plasmas. There can exist only a handful of plausible primordial molecules in the epochs before metals (elements with nuclei heavier than He as astronomers call them) were synthesized in the universe, and most of these are both rotationally and vibrationally dark. The current work brings HeHHe into the discussion as a possible (and potentially only) molecular candle for probing high-z and any metal-deprived regions due to its exceptionally bright infrared feature previously predicted to lie at 7.43 m. Furthermore, the present study provides new insights into its possible formation mechanisms as well as marked stability, along with the decisive role of anharmonic zero-point energies. A new entrance pathway is proposed through the triplet state () of the HeH molecule complexed with a hydrogen atom and a subsequent 10.90 eV charge transfer/photon emission into the linear and vibrationally-bright HeHHe form.

Sparse low rank approximation of potential energy surfaces with applications in estimation of anharmonic zero point energies and frequencies

We propose a method that exploits sparse representation of potential energy surfaces (PES) on a polynomial basis set selected by compressed sensing. The method is useful for studies involving large numbers of PES evaluations, such as the search for local minima, transition states, or integration. We apply this method for estimating zero point energies and frequencies of molecules using a three step approach. In the first step, we interpret the PES as a sparse tensor on polynomial basis and determine its entries by a compressed sensing based algorithm using only a few PES evaluations. Then, we implement a rank reduction strategy to compress this tensor in a suitable low-rank canonical tensor format using standard tensor compression tools. This allows representing a high dimensional PES as a small sum of products of one dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate the product of sparse canonical low-rank representation of PES and Green’s function in the second-order diagrammatic vibrational many-body Green’s function theory (XVH2) for estimation of zero-point energies and frequencies. Numerical tests on molecules considered in this work suggest a more efficient scaling of computational cost with molecular size as compared to other methods.

Post-transition state dynamics and product energy partitioning following thermal excitation of the F⋯HCH2CN transition state: Disagreement with experiment.

Born-Oppenheimer direct dynamics simulations were performed to study atomistic details of the F + CH3CN → HF + CH2CN H-atom abstraction reaction. The simulation trajectories were calculated with a combined M06-2X/MP2 algorithm utilizing the 6-311++G** basis set. The experiments were performed at 300 K, and assuming the accuracy of transition state theory (TST), the trajectories were initiated at the F⋯HCH2CN abstraction TS with a 300 K Boltzmann distribution of energy and directed towards products. Recrossing of the TS was negligible, confirming the accuracy of TST. HF formation was rapid, occurring within 0.014 ps of the trajectory initiation. The intrinsic reaction coordinate (IRC) for reaction involves rotation of HF about CH2CN and then trapping in the CH2CN⋯HF post-reaction potential energy well of ∼10 kcal/mol with respect to the HF + CH2CN products. In contrast to this IRC, five different trajectory types were observed: the majority proceeded by direct H-atom transfer and only 11% approximately following the IRC. The HF vibrational and rotational quantum numbers, n and J, were calculated when HF was initially formed and they increase as potential energy is released in forming the HF + CH2CN products. The population of the HF product vibrational states is only in qualitative agreement with experiment, with the simulations showing depressed and enhanced populations of the n = 1 and 2 states as compared to experiment. Simulations with an anharmonic zero-point energy constraint gave product distributions for relative translation, HF rotation, HF vibration, CH2CN rotation, and CH2CN vibration as 5%, 11%, 60%, 7%, and 16%, respectively. In contrast, the experimental energy partitioning percentages to HF rotation and vibration are 6% and 41%. Comparisons are made between the current simulation and those for other F + H-atom abstraction reactions. The simulation product energy partitioning and HF vibrational population for F + CH3CN → HF + CH2CN resemble those for other reactions. A detailed discussion is given of possible origins of the difference between the simulation and experimental energy partitioning dynamics for F + CH3CN → HF + CH2CN. The F + CH3CN reaction also forms the CH3C(F)N intermediate, in which the F-atom adds to the C≡N bond. However, this intermediate and F⋯CH3CN and CH3CN⋯F van der Waals complexes are not expected to affect the F + CH3CN → HF + CH2CN product energy partitioning.

Ab Initio Computations and Active Thermochemical Tables Hand in Hand: Heats of Formation of Core Combustion Species.

The fidelity of combustion simulations is strongly dependent on the accuracy of the underlying thermochemical properties for the core combustion species that arise as intermediates and products in the chemical conversion of most fuels. High level theoretical evaluations are coupled with a wide-ranging implementation of the Active Thermochemical Tables (ATcT) approach to obtain well-validated high fidelity predictions for the 0 K heat of formation for a large set of core combustion species. In particular, high level ab initio electronic structure based predictions are obtained for a set of 348 C, N, O, and H containing species, which corresponds to essentially all core combustion species with 34 or fewer electrons. The theoretical analyses incorporate various high level corrections to base CCSD(T)/cc-pVnZ analyses (n = T or Q) using H2, CH4, H2O, and NH3 as references. Corrections for the complete-basis-set limit, higher-order excitations, anharmonic zero-point energy, core-valence, relativistic, and diagonal Born-Oppenheimer effects are ordered in decreasing importance. Independent ATcT values are presented for a subset of 150 species. The accuracy of the theoretical predictions is explored through (i) examination of the magnitude of the various corrections, (ii) comparisons with other high level calculations, and (iii) through comparison with the ATcT values. The estimated 2σ uncertainties of the three methods devised here, ANL0, ANL0-F12, and ANL1, are in the range of ±1.0-1.5 kJ/mol for single-reference and moderately multireference species, for which the calculated higher order excitations are 5 kJ/mol or less. In addition to providing valuable references for combustion simulations, the subsequent inclusion of the current theoretical results into the ATcT thermochemical network is expected to significantly improve the thermochemical knowledge base for less-well studied species.

Accurate Anharmonic Zero-Point Energies for Some Combustion-Related Species from Diffusion Monte Carlo.

Full-dimensional analytic potential energy surfaces based on CCSD(T)/cc-pVTZ calculations have been determined for 48 small combustion-related molecules. The analytic surfaces have been used in Diffusion Monte Carlo calculations of the anharmonic zero-point energies. The resulting anharmonicity corrections are compared to vibrational perturbation theory results based both on the same level of electronic structure theory and on lower-level electronic structure methods (B3LYP and MP2).

Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

ABSTRACTA new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm−1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.

Isotopomer-selective spectra of a single intact H2O molecule in the Cs(+)(D2O)5H2O isotopologue: Going beyond pattern recognition to harvest the structural information encoded in vibrational spectra.

We report the vibrational signatures of a single H2O molecule occupying distinct sites of the hydration network in the Cs(+)(H2O)6 cluster. This is accomplished using isotopomer-selective IR-IR hole-burning on the Cs(+)(D2O)5(H2O) clusters formed by gas-phase exchange of a single, intact H2O molecule for D2O in the Cs(+)(D2O)6 ion. The OH stretching pattern of the Cs(+)(H2O)6 isotopologue is accurately recovered by superposition of the isotopomer spectra, thus establishing that the H2O incorporation is random and that the OH stretching manifold is largely due to contributions from decoupled water molecules. This behavior enables a powerful new way to extract structural information from vibrational spectra of size-selected clusters by explicitly identifying the local environments responsible for specific infrared features. The Cs(+)(H2O)6 structure was unambiguously assigned to the 4.1.1 isomer (a homodromic water tetramer with two additional flanking water molecules) from the fact that its computed IR spectrum matches the observed overall pattern and recovers the embedded correlations in the two OH stretching bands of the water molecule in the Cs(+)(D2O)5(H2O) isotopomers. The 4.1.1 isomer is the lowest in energy among other candidate networks at advanced (e.g., CCSD(T)) levels of theoretical treatment after corrections for (anharmonic) zero-point energy. With the structure in hand, we then explore the mechanical origin of the various band locations using a local electric field formalism. This approach promises to provide a transferrable scheme for the prediction of the OH stretching fundamentals displayed by water networks in close proximity to solute ions.

Stochastic many-body perturbation theory for anharmonic molecular vibrations.

A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm(-1) and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.

Second-Order Many-Body Perturbation Theory: An Eternal Frontier

Second-order many-body perturbation theory [MBPT(2)] is the lowest-ranked member of a systematic series of approximations convergent at the exact solutions of the Schrödinger equations. It has served and continues to serve as the testing ground for new approximations, algorithms, and even theories. This article introduces this basic theory from a variety of viewpoints including the Rayleigh-Schrödinger perturbation theory, the many-body Green's function theory based on the Dyson equation, and the related Feynman-Goldstone diagrams. It also explains the important properties of MBPT(2) such as size consistency, its ability to describe dispersion interactions, and divergence in metals. On this basis, this article surveys three major advances made recently by the authors to this theory. They are a finite-temperature extension of MBPT(2) and the resolution of the Kohn-Luttinger conundrum, a stochastic evaluation of the correlation and self-energies of MBPT(2) using the Monte Carlo integration of their Laplace-transformed expressions, and an extension to anharmonic vibrational zero-point energies and transition frequencies based on the Dyson equation.

Second-order many-body perturbation expansions of vibrational Dyson self-energies

Second-order many-body perturbation theories for anharmonic vibrational frequencies and zero-point energies of molecules are formulated, implemented, and tested. They solve the vibrational Dyson equation self-consistently by taking into account the frequency dependence of the Dyson self-energy in the diagonal approximation, which is expanded in a diagrammatic perturbation series up to second order. Three reference wave functions, all of which are diagrammatically size consistent, are considered: the harmonic approximation and diagrammatic vibrational self-consistent field (XVSCF) methods with and without the first-order Dyson geometry correction, i.e., XVSCF[n] and XVSCF(n), where n refers to the truncation rank of the Taylor-series potential energy surface. The corresponding second-order perturbation theories, XVH2(n), XVMP2[n], and XVMP2(n), are shown to be rigorously diagrammatically size consistent for both total energies and transition frequencies, yield accurate results (typically within a few cm(-1) at n = 4 for water and formaldehyde) for both quantities even in the presence of Fermi resonance, and have access to fundamentals, overtones, and combinations as well as their relative intensities as residues of the vibrational Green's functions. They are implemented into simple algorithms that require only force constants and frequencies of the reference methods (with no basis sets, quadrature, or matrix diagonalization at any stage of the calculation). The rules for enumerating and algebraically interpreting energy and self-energy diagrams are elucidated in detail.

Isotopic Effects on the Dynamics of the CH3+ + H2 → CH5+ → CH3+ + H2 Reaction

Diffusion Monte Carlo is used to investigate the anharmonic zero-point energy corrected energies for the CH(3)(+) + H(2)→ CH(5)(+) → CH(3)(+) + H(2) process as a function of the center of mass separation of the two fragments. In addition to the title reaction, all possible deuterated and several tritiated (CH(4)T(+) and CH(3)T(2)(+)) analogues of this reaction are investigated. As anticipated, the replacement of one or more of the hydrogen atoms with deuterium or tritium atoms lowers the zero-point energy of the system. Further, in the partially deuterated or tritiated isotopologues, the lowest energy configuration generally has the heavy atoms in the CH(3)(+) fragment. Analysis of the wave functions allows us to study how zero-point energy influences the approach geometries sampled during low-energy collisions between CH(3)(+) and H(2), and to gain insights into how the dynamics is affected by the substitution of heavier isotopes for one or more of the hydrogen atoms. Differences between quantum and classical descriptions of the title reaction are also discussed.

Predicted thermochemistry and unimolecular kinetics of nitrous sulfide

The geometry of N(2)S was obtained at the CCSD(T)/aug-cc-pV(T + d)Z level of theory and energies with coupled-cluster single double triple (CCSD(T)) and basis sets up to aug-cc-pV(6 + d)Z. After correction for anharmonic zero-point energy, core-valence correlation, correlation up to CCSDT(Q) and relativistic effects, D(0) for the N-S bond is estimated as 71.9 kJ mol(-1), and the corresponding thermochemistry for N(2)S is Δ(f)H(0)(∘)=205.4 kJ mol(-1) and Δ(f)H(298)(∘)=202.6 kJ mol(-1) with an uncertainty of ±2.5 kJ mol(-1). Using CCSD(T)/aug-cc-pV(T + d) theory the minimum energy crossing point between singlet and triplet potential energy curves is found at r(N-N) ≈ 1.105 Å and r(N-S) ≈ 2.232 Å, with an energy 72 kJ mol(-1) above N(2) + S((3)P). Application of Troe's unimolecular formalism yields the low-pressure-limiting rate constant for dissociation of N(2)S k(0) = 7.6 × 10(-10) exp(-126 kJ mol(-1)/RT) cm(3) molecule(-1) s(-1) over 700-2000 K. The estimated uncertainty is a factor of 4 arising from unknown parameters for energy transfer between N(2)S and Ar or N(2) bath gas. The thermochemistry and kinetics were included in a mechanism for CO/H(2)/H(2)S oxidation and the conclusion is that little NO is produced via subsequent chemistry of NNS.

Accurate computational thermochemistry from explicitly correlated coupled-cluster theory

Explicitly correlated coupled-cluster theory has developed into a valuable computational tool for the calculation of electronic energies close to the limit of a complete basis set of atomic orbitals. In particular at the level of coupled-cluster theory with single and double excitations (CCSD), the space of double excitations is quickly extended towards a complete basis when Slater-type geminals are added to the wave function expansion. The purpose of the present article is to demonstrate the accuracy and efficiency that can be obtained in computational thermochemistry by a CCSD model that uses such Slater-type geminals. This model is denoted as CCSD(F12), where the acronym F12 highlights the fact that the Slater-type geminals are functions f(r 12) of the interelectronic distances r 12 in the system. The performance of explicitly correlated CCSD(F12) coupled-cluster theory is demonstrated by computing the atomization energies of 73 molecules (containing H, C, N, O, and F) with an estimated root-mean-square deviation from the values compiled in the Active Thermochemical Tables of σ = 0.10 kJ/mol per valence electron. To reach this accuracy, not only the frozen-core CCSD basis-set limit but also high-order excitations (connected triple and quadruple excitations), core–valence correlation effects, anharmonic vibrational zero-point energies, and scalar and spin–orbit relativistic effects must be taken into account.

Method and basis set dependence of anharmonic ground state nuclear wave functions and zero-point energies: Application to SSSH

One of the largest remaining errors in thermochemical calculations is the determination of the zero-point energy (ZPE). The fully coupled, anharmonic ZPE and ground state nuclear wave function of the SSSH radical are calculated using quantum diffusion Monte Carlo on interpolated potential energy surfaces (PESs) constructed using a variety of method and basis set combinations. The ZPE of SSSH, which is approximately 29 kJ mol(-1) at the CCSD(T)/6-31G* level of theory, has a 4 kJ mol(-1) dependence on the treatment of electron correlation. The anharmonic ZPEs are consistently 0.3 kJ mol(-1) lower in energy than the harmonic ZPEs calculated at the Hartree-Fock and MP2 levels of theory, and 0.7 kJ mol(-1) lower in energy at the CCSD(T)/6-31G* level of theory. Ideally, for sub-kJ mol(-1) thermochemical accuracy, ZPEs should be calculated using correlated methods with as big a basis set as practicable. The ground state nuclear wave function of SSSH also has significant method and basis set dependence. The analysis of the nuclear wave function indicates that SSSH is localized to a single symmetry equivalent global minimum, despite having sufficient ZPE to be delocalized over both minima. As part of this work, modifications to the interpolated PES construction scheme of Collins and co-workers are presented.

Accurate ab initio computation of thermochemical data for C 3H x[formula omitted] species

We have computed the atomization energies of nineteen C 3H x molecules and radicals using explicitly-correlated coupled-cluster theory including corrections for core–core and core–valence correlation, scalar and spin–orbit relativistic effects, and anharmonic vibrational zero-point energies. Equilibrium geometries were obtained at the coupled-cluster level [CCSD(T) model] in a correlation-consistent polarized core–valence quadruple-zeta basis set, using a spin-restricted Hartree–Fock reference wave function, and including all electrons in the correlation treatment. Applied to a set of selected CH x and C 2H x systems, our approach yields highly accurate atomization energies with a mean absolute deviation of 1.4 kJ/mol and a maximum deviation of 4.2 kJ/mol (for dicarbon) from the Active Thermochemical Tables (ATcT) values. The explicitly-correlated coupled-cluster approach provides energies near the basis-set limit of the CCSD(T) model, which is the coupled-cluster model with single and double excitations (CCSD) augmented with a perturbative correction for triple excitations (T). To obtain even more accurate atomization energies than those presented here, it would be required to include full triple excitations (CCSDT) and corrections for excitations beyond triples, as for instance done in the CCSDT(Q) model, which includes a perturbative correction for quadruple excitations (Q).

Efficiency considerations in the construction of interpolated potential energy surfaces for the calculation of quantum observables by diffusion Monte Carlo

A modified Shepard interpolation scheme is used to construct global potential energy surfaces (PES) in order to calculate quantum observables--vibrationally averaged internal coordinates, fully anharmonic zero-point energies and nuclear radial distribution functions--for a prototypical loosely bound molecular system, the water dimer. The efficiency of PES construction is examined with respect to (a) the method used to sample configurational space, (b) the method used to choose which points to add to the PES data set, and (c) the use of either a one- or two-part weight function. The most efficient method for constructing the PES is found to require a quantum sampling regime, a combination of both h-weight and rms methods for choosing data points and use of the two-part weight function in the interpolation. Using this regime, the quantum diffusion Monte Carlo zero-point energy converges to the exact result within addition of 50 data points. The vibrationally averaged O-O distance and O-O radial distribution function, however, converge more slowly and require addition of over 500 data points. The methods presented here are expected to be applicable to both other loosely bound complexes as well as tightly bound molecular species. When combined with high quality ab initio calculations, these methods should be able to accurately characterize the PES of such species.