The barrier to linearity of water

"On-the-fly" Crystal : How to reliably and automatically characterize and construct potential energy surfaces

In this work, the Crystal  code, developed previously by the authors to find "holes" as well as legitimate transition states in existing potential energy surface (PES) functions [JPC Lett. 11, 6468 (2020)], is retooled to perform on-the-fly "direct dynamics"-type PES explorations, as well as automatic construction of new PES functions. In all of these contexts, the chief advantage of Crystal  over other methods is its ability to globally map the PES, thereby determining the most relevant regions of configuration space quickly and reliably-even when the dimensionality is rather large. Here, Crystal  is used to generate a uniformly spaced grid of density functional theory (DFT) or ab initio points, truncated over the relevant regions, which can then be used to either: (a) hone in precisely on PES features such as minima and transition states, or; (b) create a new PES function automatically, via interpolation. Proof of concept is demonstrated via application to three molecular systems: water (H2 O), (reduced-dimensional) methane (CH4 ), and methylene imine (CH2 NH).

Accurate ab initio potential energy surface, rovibrational energy levels and resonance interactions of triplet ( X ~ 3 B1 ) methylene

In this work, we report rovibrational energy levels for four isotopologues of methylene (CH2 , CHD, CD2 , and 13 CH2 ) in their ground triplet electronic state (X ~ 3 B1 ) from variational calculation up to ~10,000 cm-1 and using a new accurate ab initio potential energy surface (PES). Triplet methylene exhibits a large-amplitude bending vibration and can reach a quasilinear configuration due to its low barrier (~2000 cm-1 ). To construct the ab initio PES, the Dunning's augmented correlation-consistent core-valence orbital basis sets were employed up to the sextuple-ζ quality [aug-cc-pCVXZ, X = T, Q, 5, and 6] combined with the single- and double-excitation unrestricted coupled cluster approach with a perturbative treatment of triple excitations [RHF-UCCSD(T)]. We have shown that the accuracy of the ab initio energies is further improved by including the corrections due to the scalar relativistic effects, DBOC and high-order electronic correlations. For the first time, all the available experimental rovibrational transitions were reproduced with errors less than 0.12 cm-1 , without any empirical corrections. Unlike more "traditional" nonlinear triatomic molecules, we have shown that even the energies of the ground vibrational state (000) with rather small rotational quantum numbers are strongly affected by the very pronounced rovibrational resonance interactions. Accordingly, the polyad structure of the vibrational levels of CH2 and CD2 was analyzed and discussed. The comparison between the energy levels obtained from the effective Watson A-reduced Hamiltonian, from the generating-function approach and from a variational calculation was given.

Structure, energetics, and spectroscopy of the chromophores of HHe+n, H2He+n, and He+n clusters and their deuterated isotopologues

The linear molecular ions H₂He⁺, HHe+2, and He+3 are the central units (chromophores) of certain He-solvated complexes of the H₂He+n, HHe+n, and He+n families, respectively. These are complexes which do exist, according to mass-spectrometry studies, up to very high n values. Apparently, for some of the H₂He+n and He+n complexes, the linear symmetric tetratomic H₂He+2 and the diatomic He+2 cations, respectively, may also be the central units. In this study, definitive structures, relative energies, zero-point vibrational energies, and (an)harmonic vibrational fundamentals, and, in some cases, overtones and combination bands, are established mostly for the triatomic chromophores. The study is also extended to the deuterated isotopologues D₂He⁺, DHe+2, and D₂He+2. To facilitate and improve the electronic-structure computations performed, new atom-centered, fixed-exponent, Gaussian-type basis sets called MAX, with X = T(3), Q(4), P(5), and H(6), are designed for the H and He atoms. The focal-point-analysis (FPA) technique is employed to determine definitive relative energies with tight uncertainties for reactions involving the molecular ions. The FPA results determined include the 0 K proton and deuteron affinities of the ⁴He atom, 14 875(9) cm^-1 [177.95(11) kJ mol^-1] and 15 229(8) cm^-1 [182.18(10) kJ mol^-1], respectively, the dissociation energies of the He+2 → He⁺ + He, HHe+2 → HHe⁺ + He, and He+3 → He+2 + He reactions, 19 099(13) cm^-1 [228.48(16) kJ mol^-1], 3948(7) cm^-1 [47.23(8) kJ mol^-1], and 1401(12) cm^-1 [16.76(14) kJ mol^-1], respectively, the dissociation energy of the DHe+2 → DHe⁺ + He reaction, 4033(6) cm^-1 [48.25(7) kJ mol^-1], the isomerization energy between the two linear isomers of the [H, He, He]⁺ system, 3828(40) cm^-1 [45.79(48) kJ mol^-1], and the dissociation energies of the H₂He⁺ → H+2 + He and the H₂He+2 → H₂He⁺ + He reactions, 1789(4) cm^-1 [21.40(5) kJ mol^-1] and 435(6) cm^-1 [5.20(7) kJ mol^-1], respectively. The FPA estimates of the first dissociation energy of D₂He⁺ and D₂He+2 are 1986(4) cm^-1 [23.76(5) kJ mol^-1] and 474(5) cm^-1 [5.67(6) kJ mol^-1], respectively. Determining the vibrational fundamentals of the triatomic chromophores with second-order vibrational perturbation theory (VPT2) and vibrational configuration interaction (VCI) techniques, both built around the Eckart-Watson Hamiltonian, proved unusually challenging. For the species studied, VPT2 has difficulties yielding dependable results, in some cases even for the fundamentals of the H-containing molecular cations, while carefully executed VCI computations yield considerably improved spectroscopic results. In a few cases unusually large anharmonic corrections to the fundamentals, on the order of 15% of the harmonic value, have been observed.

Straightening the Hierarchical Staircase for Basis Set Extrapolations: A Low-Cost Approach to High-Accuracy Computational Chemistry

Because the one-electron basis set limit is difficult to reach in correlated post-Hartree-Fock ab initio calculations, the low-cost route of using methods that extrapolate to the estimated basis set limit attracts immediate interest. The situation is somewhat more satisfactory at the Hartree-Fock level because numerical calculation of the energy is often affordable at nearly converged basis set levels. Still, extrapolation schemes for the Hartree-Fock energy are addressed here, although the focus is on the more slowly convergent and computationally demanding correlation energy. Because they are frequently based on the gold-standard coupled-cluster theory with single, double, and perturbative triple excitations [CCSD(T)], correlated calculations are often affordable only with the smallest basis sets, and hence single-level extrapolations from one raw energy could attain maximum usefulness. This possibility is examined. Whenever possible, this review uses raw data from second-order Møller-Plesset perturbation theory, as well as CCSD, CCSD(T), and multireference configuration interaction methods. Inescapably, the emphasis is on work done by the author's research group. Certain issues in need of further research or review are pinpointed.

The INV24 test set: how well do quantum-chemical methods describe inversion and racemization barriers?

For years, there has been ongoing interest in experimentally and theoretically understanding inversion and racemization processes. However, to the best of our knowledge, there has been no computational study that systematically investigated how well low-level quantum-chemical methods predict inversion barriers. Herein, we provide an answer to this question and we present the INV24 benchmark set of 24 high-level, ab initio inversion barriers. INV24 covers inversion in triatomics, in pyramidal molecules, in one cyclic system, and in various helical and bowl-shaped compounds. Our results indicate that previously applied DFT approximations combined with small basis sets are not reliable enough and that at least a triple-ζ basis is needed for meaningful results. Moreover, we show that intramolecular London dispersion influences the barriers by 2 kcal/mol or more and that dispersion corrections should always be applied to DFT results. With our analysis of 34 DFT approximations, we can reproduce the well-known Jacob’s Ladder scheme with (meta-)generalized-gradient-approximation methods underestimating barriers and global-hybrid DFT functionals performing better. Range-separated hybrids or Minnesota-type hybrids are not particularly superior to more conventional methods, such as B3LYP-D3. The by far best results are achieved with dispersion-corrected double hybrids, which give results below the chemical accuracy target of 1 kcal/mol. They also outperform wave-function second-order perturbation theory approaches and we recommend using them whenever possible. Given that our systematic study of INV24 is the first of its kind, our findings have the potential to change common practice in this field and they will guide future investigations of inversion processes.

Global spectroscopy of the water monomer

Given the large energy required for its electronic excitation, the most important properties of the water molecule are governed by its ground potential energy surface (PES). Novel experiments are now able to probe this surface over a very extended energy range, requiring new theoretical procedures for their interpretation. As part of this study, a new, accurate, global spectroscopic-quality PES and a new, accurate, global dipole moment surface are developed. They are used for the computation of the high-resolution spectrum of water up to the first dissociation limit and beyond as well as for the determination of Stark coefficients for high-lying states. The water PES has been determined by combined ab initio and semi-empirical studies. As a first step, a very accurate, global, ab initio PES was determined using the all-electron, internally contracted multi-reference configuration interaction technique together with a large Gaussian basis set. Scalar relativistic energy corrections are also determined in order to move the energy determinations close to the relativistic complete basis set full configuration interaction limit. The electronic energies were computed for a set of about 2500 geometries, covering carefully selected configurations from equilibrium up to dissociation. Nuclear motion computations using this PES reproduce the observed energy levels up to 39 000 cm(-1) with an accuracy of better than 10 cm(-1). Line positions and widths of resonant states above dissociation show an agreement with experiment of about 50 cm(-1). An improved semi-empirical PES is produced by fitting the ab initio PES to accurate experimental data, resulting in greatly improved accuracy, with a maximum deviation of about 1 cm(-1) for all vibrational band origins. Theoretical results based on this semi-empirical surface are compared with experimental data for energies starting at 27 000 cm(-1), going all the way up to dissociation at about 41 000 cm(-1) and a few hundred wavenumbers beyond it.

CVRQD ab initio ground-state adiabatic potential energy surfaces for the water molecule

The high accuracy ab initio adiabatic potential energy surfaces (PESs) of the ground electronic state of the water molecule, determined originally by Polyansky et al. [Science 299, 539 (2003)] and called CVRQD, are extended and carefully characterized and analyzed. The CVRQD potential energy surfaces are obtained from extrapolation to the complete basis set of nearly full configuration interaction valence-only electronic structure computations, augmented by core, relativistic, quantum electrodynamics, and diagonal Born-Oppenheimer corrections. We also report ab initio calculations of several quantities characterizing the CVRQD PESs, including equilibrium and vibrationally averaged (0 K) structures, harmonic and anharmonic force fields, harmonic vibrational frequencies, vibrational fundamentals, and zero-point energies. They can be considered as the best ab initio estimates of these quantities available today. Results of first-principles computations on the rovibrational energy levels of several isotopologues of the water molecule are also presented, based on the CVRQD PESs and the use of variational nuclear motion calculations employing an exact kinetic energy operator given in orthogonal internal coordinates. The variational nuclear motion calculations also include a simplified treatment of nonadiabatic effects. This sophisticated procedure to compute rovibrational energy levels reproduces all the known rovibrational levels of the water isotopologues considered, H(2) (16)O, H(2) (17)O, H(2) (18)O, and D(2) (16)O, to better than 1 cm(-1) on average. Finally, prospects for further improvement of the ground-state adiabatic ab initio PESs of water are discussed.

On equilibrium structures of the water molecule

Equilibrium structures are fundamental entities in molecular sciences. They can be inferred from experimental data by complicated inverse procedures which often rely on several assumptions, including the Born-Oppenheimer approximation. Theory provides a direct route to equilibrium geometries. A recent high-quality ab initio semiglobal adiabatic potential-energy surface (PES) of the electronic ground state of water, reported by Polyansky et al. [ ibid. 299, 539 (2003)] and called CVRQD here, is analyzed in this respect. The equilibrium geometries resulting from this direct route are deemed to be of higher accuracy than those that can be determined by analyzing experimental data. Detailed investigation of the effect of the breakdown of the Born-Oppenheimer approximation suggests that the concept of an isotope-independent equilibrium structure holds to about 3 x 10(-5) A and 0.02 degrees for water. The mass-independent [Born-Oppenheimer (BO)] equilibrium bond length and bond angle on the ground electronic state PES of water is r(e) (BO)=0.957 82 A and theta e (BO)=104.48(5) degrees , respectively. The related mass-dependent (adiabatic) equilibrium bond length and bond angle of H2 (16)O is r(e) (ad)=0.957 85 A and theta e (ad)=104.50(0) degrees , respectively, while those of D2 (16)O are r(e) (ad)=0.957 83 A and theta e (ad)=104.49(0) degrees . Pure ab initio prediction of J=1 and 2 rotational levels on the vibrational ground state by the CVRQD PESs is accurate to better than 0.002 cm(-1) for all isotopologs of water considered. Elaborate adjustment of the CVRQD PESs to reproduce all observed rovibrational transitions to better than 0.05 cm(-1) (or the lower ones to better than 0.0035 cm(-1)) does not result in noticeable changes in the adiabatic equilibrium structure parameters. The expectation values of the ground vibrational state rotational constants of the water isotopologs, computed in the Eckart frame using the CVRQD PESs and atomic masses, deviate from the experimentally measured ones only marginally, especially for A0 and B0. The small residual deviations in the effective rotational constants are due to centrifugal distortion, electronic, and non-Born-Oppenheimer effects. The spectroscopic (nonadiabatic) equilibrium structural parameters of H2 16O, obtained from experimentally determined A'0 and B'0 rotational constants corrected empirically to obtain equilibrium rotational constants, are r(e) (sp)=0.957 77 A and theta e (sp)=104.48 degrees .

Correlation energy extrapolation by intrinsic scaling. IV. Accurate binding energies of the homonuclear diatomic molecules carbon, nitrogen, oxygen, and fluorine

The method of extrapolation by intrinsic scaling, recently introduced to obtain correlation energies, is generalized to multiconfigurational reference functions and used to calculate the binding energies of the diatomic molecules C2, N2, O2, and F2. First, accurate approximations to the full configuration interaction energies of the individual molecules and their constituent atoms are determined, employing Dunning's correlation consistent double-, triple- and quadruple zeta basis sets. Then, these energies are extrapolated to their full basis set limits. Chemical accuracy is attained for the binding energies of all molecules.

A new algorithm to handle finite nuclear mass effects in electronic calculations: The ISOTOPE program

We report the development of a simple algorithm to modify quantum chemistry codes based on the LCAO procedure, to account for the isotope problem in electronic structure calculations. No extra computations are required compared to standard Born-Oppenheimer calculations. An upgrade of the Gamess package called ISOTOPE is presented, and its applicability is demonstrated in some examples.

Toward subchemical accuracy in computational thermochemistry: Focal point analysis of the heat of formation of NCO and [H,N,C,O] isomers

In continuing pursuit of thermochemical accuracy to the level of 0.1 kcal mol(-1), the heats of formation of NCO, HNCO, HOCN, HCNO, and HONC have been rigorously determined using state-of-the-art ab initio electronic structure theory, including conventional coupled cluster methods [coupled cluster singles and doubles (CCSD), CCSD with perturbative triples (CCSD(T)), and full coupled cluster through triple excitations (CCSDT)] with large basis sets, conjoined in cases with explicitly correlated MP2-R12/A computations. Limits of valence and all-electron correlation energies were extrapolated via focal point analysis using correlation consistent basis sets of the form cc-pVXZ (X=2-6) and cc-pCVXZ (X=2-5), respectively. In order to reach subchemical accuracy targets, core correlation, spin-orbit coupling, special relativity, the diagonal Born-Oppenheimer correction, and anharmonicity in zero-point vibrational energies were accounted for. Various coupled cluster schemes for partially including connected quadruple excitations were also explored, although none of these approaches gave reliable improvements over CCSDT theory. Based on numerous, independent thermochemical paths, each designed to balance residual ab initio errors, our final proposals are DeltaH(f,0) ( composite function )(NCO)=+30.5, DeltaH(f,0) ( composite function )(HNCO)=-27.6, DeltaH(f,0) ( composite function )(HOCN)=-3.1, DeltaH(f,0) ( composite function )(HCNO)=+40.9, and DeltaH(f,0) ( composite function )(HONC)=+56.3 kcal mol(-1). The internal consistency and convergence behavior of the data suggests accuracies of +/-0.2 kcal mol(-1) in these predictions, except perhaps in the HCNO case. However, the possibility of somewhat larger systematic errors cannot be excluded, and the need for CCSDTQ [full coupled cluster through quadruple excitations] computations to eliminate remaining uncertainties is apparent.