What have the XH4+ (X = C, Si, Ge) ions in common? An updated summary

A high level quantum mechanical study has been performed to explore the structural rearrangement and relative stability of the XH4+ (X = C, Si, Ge) radical cations at their X̃2T2 ground electronic states. All the stationary points located on the lowest adiabatic sheet of the Jahn-Teller (JT) split X̃2T2 state are fully optimized and characterized by performing harmonic vibrational frequency calculations. Five JT distorted stationary points with D2d(B22), C3v(A12), C2v(B22), and Cs(A'2) symmetries are located on the CH4+ ground state potential energy surface (PES), whereas four such structures are found on each of the SiH4+ and GeH4+ PESs. While the C2v(B22) isomer is found to be a global minimum and the Cs(A'2) one as a transition state for CH4+, the nature of them is reversed for SiH4+ and GeH4+. In particular, the Cs(A'2) stationary points are now global minima for the latter pair of radical cations, and C2v(B22) represents the transition state. Attempts are being made to understand such inconsistent findings via a combination of JT and epikernel principles. The barriers between equivalent C2v(B22) global minimum structures for CH4+ are found to be low, and thus CH4+ undergoes rapid interconversion along cyclic exchange of three hydrogen atoms via Cs transition state. The general features of the ground state PESs of SiH4+ and GeH4+ are similar. The pseudorotation between the Cs lowest energy structures undergoes along SiH2 and GeH2 wagging motions via C2v(B22) transition state for SiH4+ and GeH4+, respectively.

Efficient Method for Numerical Calculations of Molecular Vibrational Frequencies by Exploiting Sparseness of Hessian Matrix

Molecular vibrational frequency analysis plays an important role in theoretical and computational chemistry. However, in many cases, the analytical frequencies are unavailable, whereas frequency calculations using conventional numerical methods are very expensive. In this work, we propose an efficient method to numerically calculate the frequencies. Our main strategies are to exploit the sparseness of the Hessian matrix and to construct the N-fold two-variable potential energy surfaces to fit the parabola parameters, which are later used for the construction of Hessian matrices. A set of benchmark calculations is performed for typical molecules of different sizes and complexities using the proposed method. The obtained frequencies are compared to those calculated with the analytical methods and conventional numerical methods. It is shown that the results yielded with the new method are in very good agreement with corresponding accurate values (with a maximum error of ∼20 cm-1), while the required computation resource is largely reduced compared to that required by conventional numerical methods. For medium-sized molecules, the calculational scaling is lowered to O(N1.6) (this work) from that of O(N2) (conventional numerical methods). For even larger molecules, more computational savings can be achieved, and the scaling is estimated to be quasilinear with respect to the molecular size.

From six to eight Π-electron bare rings of group-XIV elements and beyond: can planarity be deciphered from the "quasi-molecules" they embed?

Ab initio molecular orbital theory is used to study the structures of six and eight π-electron bare rings of group-XIV elements, and even larger [n]annulenes up to C₁₈H₁₈, including some of their mono-, di-, tri-, and tetra-anions. While some of the above rings are planar, others are nonplanar. A much spotlighted case is cyclo-octatetraene (C₈H₈), which is predicted to be nonplanar together with its heavier group-XIV analogues Si₈H₈ and Ge₈H₈, with the solely planar members of its family having the stoichiometric formulas C₄Si₄H₈ and C₄Ge₄H₈. A similar situation arises with the six π-electron bare rings, where benzene and substituted ones up to C₃Si₃H₆ or so are planar, while others are not. However, the explanations encountered in the literature find support in ab initio calculations for such species, often rationalized from distinct calculated features. Using second-order Møller-Plesset perturbation theory and, when affordable (particularly tetratomics, which may allow even higher levels), the coupled-cluster method including single, double, and perturbative triple excitations, a common rationale is suggested based on a novel concept of quasi-molecules or the (3+4)-atom partition scheme. Any criticism of tautology is therefore avoided. The same analysis has also been successfully applied to even larger [n]annulenes, to their mixed family members involving silicon and germanium atoms, and to the C₁₈ carbon ring. Furthermore, it has been extended to annulene anions to check the criteria of the popular Hückel rule for planarity and aromaticity. Exploratory work on cycloarenes is also reported. Besides a partial study of the involved potential energy surfaces, equilibrium geometries and harmonic vibrational frequencies have been calculated anew, for both the parent and the actual prototypes of the quasi-molecules.

The effect of midbond functions on interaction energies computed using MP2 and CCSD(T)

In this article we use MP2 and CCSD(T) calculations for the A24 and S66 data sets to explore how midbond functions can be used to generate cost effective counterpoise corrected supramolecular interaction energies of noncovalent complexes. We use the A24 data set to show that the primary role of midbond functions is not to approach the complete basis set limit, but rather to ensure a balanced description of the molecules and the interaction region (unrelated to the basis set superposition error). The need for balance is a consequence of using atom centered basis sets. In the complete basis set limit, the error will disappear, but reaching the complete basis set limit is not feasible beyond small systems. For S66 we investigate the need for increasing the number of midbond centers. Results show that adding a second midbond center increases the accuracy, but the effect is secondary to changing the atom centered basis set. Further, by comparing calculations using the 3s3p2d1f1g midbond set with using aug-cc-pVDZ and aug-cc-pVTZ as midbond sets, we see that the requirements for the midbond set to be effective, is not just that it contains diffuse functions, but also that high angular momentum functions are included. By comparing two approaches for placing midbond centers we show that results are not particularly sensitive to placement as long as the placement is reasonable.

Optimized Structural Data at the Complete Basis Set Limit via Successive Quadratic Minimizations

Two variants of a successive quadratic minimization method (SQM and c-SQM) are suggested to calculate the structural properties of molecular systems at the complete basis set (CBS) limit. When applied to H₃⁺, H₂O, CH₂O, SH₂, and SO₂, they revealed CBS/(x₁, x₂) structural parameters that significantly surpass the raw ones calculated at the x₂ basis set level. Such a performance has also been verified for the intricate case of the water dimer. Because the c-SQM method is system specific, thus showing somewhat enhanced results relative to the general SQM protocol, it can be of higher cost depending on the level of calibration used. Yet, it hardly surpasses the general quality of the results obtained with the cost-effective SQM method. Since the number of cycles required to reach convergence is relatively small, both schemes are simple to use and easily adaptable to any of the existing extrapolation schemes for the Hartree-Fock and correlation energies.

Post-complete-basis-set extrapolation of conventional and explicitly correlated coupled-cluster energies: can the convergence to the CBS limit be diagnosed?

We assess benchmark correlation energies for 130 systems in test sets A24 and TS-106 both with the canonical CCSD(T) and explicitly correlated CCSD(T)-F12 methods. Aiming at enhanced accuracy, the calculated raw energies from both sets are CBS extrapolated to the complete basis set (CBS) limit and subsequently post-CBS extrapolated. Attention is focused at total energies, since their accuracy reflects on that of the interaction energies. Using up to triple-ζ basis sets for CBS and an additional quadruple-ζ for post-CBS, the mean and standard unsigned deviations with canonical CCSD(T) theory are 0.257 ± 0.25 kcal mol^-1, while the corresponding values for CCSD(T)-F12 in its F12a and F12b variants with specialized basis sets up to VQZ-F12 are 0.170 ± 0.13 kcal mol^-1 and 0.048 ± 0.04 kcal mol^-1. Although these show gains at post-CBS level that vary from 0.08 to 0.20 kcal mol^-1 relative to their CCSD(T)/VXZ analogues, the convergence is somewhat less clear when extending the basis up to V5Z-F12, the highest-rung available: 0.220 ± 0.17 kcal mol^-1 and 0.142 ± 0.08 kcal mol^-1, in the same order. An explanation for the up to one order of magnitude smaller deviations in energy differences is detailed. Based on energy differences involving basis set pairs employed for extrapolating to the CBS limit, a convergence diagnostic is also suggested. Arising from irregularities in the basis set that directly correlate with non-dynamical correlation, the new diagnostic may complement popular ones that feature other aspects of correlation.

Canonical and explicitly-correlated coupled cluster correlation energies of sub-kJ mol-1 accuracy via cost-effective hybrid-post-CBS extrapolation

Cost-effectiveness and accuracy are two basic pillars in electronic structure calculations. While cost-effectiveness enhances applicability, high accuracy is sustained when employing advanced computational tools. With the gold standard method of ab initio quantum chemistry at the focal point, canonical CCSD(T) and modern explicitly correlated CCSD(T)-F12 calculations are employed hand in hand to develop accurate hybrid post-CBS extrapolation schemes, which are validated using popular training sets involving a total of 130 molecules. By using raw valence-only calculations at CCSD(T)/VDZ and CCSD(T)/VQZ-F12 levels of theory, the novel scheme leads to the prediction of absolute energies that differ on average (-0.170 ± 0.224) kcal mol-1 from the highest affordable CCSD(T)-F12b/V(Q,5)Z-F12 extrapolations, but only (-0.048 ± 0.228) kcal mol-1 from the post-CBS extrapolated values based on CBS(D,T), CBS(D,Q) and CBS(T,Q) energies. From the cost-effectiveness standpoint, the approach is a kind of pseudo one-point extrapolation scheme since its cost is basically that of the highest-rung raw energy where it is based. Variants that imply no additional cost are also discussed, emerging h-pCBS(dt,dq)ab as the most effective. The approach can also be used with PNO-based local correlation methods that gained popularity due to allowing coupled-cluster calculations even for large molecules at reduced computational cost, namely local PNO-CCSD(T) and PNO-CCSD(T)-F12b. To gauge the approach performance, both the hydrogen molecule and the O-C2H5 torsion path of ethyl-methyl-ether, an extra molecule here considered with presupposed existence in astrophysical objects, are also studied. Additionally, the nonbonding interactions in the A24 test set are revisited per se. The results show that the title approach may be useful in high-accuracy quantum chemistry, with further improvements requiring the inclusion of contributions beyond the theory here employed such as the ones due to relativistic and nonadiabatic effects.

Extrapolation in quantum chemistry: Insights on energetics and reaction dynamics

Since there is no exact solution for problems in physics and chemistry, extrapolation methods may assume a key role in quantitative quantum chemistry. Two topics where it bears considerable impact are addressed, both at the heart of computational quantum chemistry: electronic structure and reaction dynamics. In the first, the problem of extrapolating the energy obtained by solving the electronic Schrödinger equation to the limit of the complete one-electron basis set is addressed. With the uniform-singlet-and-triplet-extrapolation (USTE) scheme at the focal point, the emphasis is on recent updates covering from the energy itself to other molecular properties. The second topic refers to extrapolation of quantum mechanical reactive scattering probabilities from zero total angular momentum to any of the values that it may assume when running quasiclassical trajectories, QCT/QM-[Formula: see text]J. With the extrapolation guided in both cases by physically motivated asymptotic theories, realism is seeked by avoiding unsecure jumps into the unknown. Although, mostly review oriented, a few issues are addressed for the first time here and there. Prospects for future work conclude the overview.

Reaction pathways and kinetics study on a syngas combustion system: CO + HO2 in an H2O environment

The reaction between CO and HO2 plays a significant role in syngas combustion. In this work, the catalytic effect of single-molecule water on this reaction is theoretically investigated at the CCSD(T)/aug-cc-pV(D,T,Q)Z and CCSD(T)-F12a/jun-cc-pVTZ levels in combination with the M062X/aug-cc-pVTZ level. Firstly, the potential energy surface (PES) of CO + HO2 (water-free) is revisited. The major products CO2 + OH are formed via a cis- or a trans-transition state (TS) channel and the formation of HCO + O2 is minor. In the presence of water, the title reaction has three different pre-reactive complexes (i.e., RC2: COHO2 + H2O, RC3: COH2O + HO2, and RC4: HO2H2O + CO), depending on the initial hydrogen bond formation. Compared to the water-free process, the reaction barriers of the water-assisted process are reduced considerably, due to more stable cyclic TSs and complexes. The rate constants for the bimolecular reaction pathways CO + HO2, RC2, RC3, and RC4 are further calculated using conventional transition state theory (TST) with Eckart asymmetric tunneling correction. For reaction CO + HO2, our calculations are in good agreement with the literature. In addition, the effective rate constants for the water-assisted process decrease by 1-2 orders of magnitude compared to the water-free one at a temperature below 600 K. In particular, the effective rate constants for the water-assisted and water-free processes are 1.55 × 10-28 and 3.86 × 10-26 cm3 molecule-1 s-1 at 300 K, respectively. This implies that the contribution of a single molecule water-assisted process is small and cannot accelerate the title reaction.

Kinetics and Thermodynamics of Reactions Involving Criegee Intermediates: An Assessment of Density Functional Theory and Ab Initio Methods Through Comparison with CCSDT(Q)/CBS Data

Reactions involving Criegee intermediates (CIs, R₁ R₂ COO) are important in atmospheric ozonolysis models. In recent years, density functional theory (DFT) and CCSD(T)-based ab initio methods are increasingly being used for modeling reaction profiles involving CIs. We obtain highly accurate CCSDT(Q)/CBS reaction energies and barrier heights for ring-closing reactions involving atmospherically important CIs (R₁ /R₂ = H, Me, OH, OMe, F, CN, cyclopropene, ethylene, acetaldehyde, and acrolein). We use this benchmark data to evaluate the performance of DFT, double-hybrid DFT (DHDFT), and ab initio methods for the kinetics and thermodynamics of these reactions. We find that reaction energies are more challenging for approximate theoretical procedures than barrier heights. Overall, taking both reaction energies and barrier heights into account, only one of the 58 considered DFT methods (the meta-GGA MN12-L) attains near chemical accuracy, with root-mean-square deviations (RMSDs) of 3.5 (barrier heights) and 4.7 (reaction energies) kJ mol^-1 . Therefore, MN12-L is recommended for investigations where CCSD(T)-based methods are not computationally feasible. For reaction barrier heights performance does not strictly follow Jacob's Ladder, for example, DHDFT methods do not perform better than conventional DFT methods. Of the ab initio methods, the cost-effective CCSD(T)/CBS(MP2) approach gives the best performance for both reaction energies and barrier heights, with RMSDs of 1.7 and 1.4 kJ mol^-1 , respectively. All the considered Gaussian-n methods show good performance with RMSDs below the threshold of chemical accuracy for both reaction energies and barrier heights, where G4(MP2) shows the best overall performance with RMSDs of 2.9 and 1.5 kJ mol^-1 , respectively. © 2019 Wiley Periodicals, Inc.

Optimal basis sets for CBS extrapolation of the correlation energy: oVxZ and oV(x+d)Z

We seek correlation consistent double- and triple-zeta basis sets that perform optimally for extrapolating the correlation energy to the one-electron complete basis set limit. Since the methods used are approximate, the novel basis sets become method specific in the sense of performing best for the chosen level of theory. Such basis sets are also shown to perform accurately for tensorial properties and do not significantly alter the Hartree-Fock energy. Quantitatively, the extrapolated correlation energies from (oVdZ, oVtZ) outperform typically by three- to fivefold those obtained from traditional ansatzes with similar flexibility, thus being (VtZ, VqZ) type or even better. They may even outperform explicitly correlated ones. Not surprisingly, the outperformance in relative energies (e.g., atomization and dissociation energies, and ionization potential) is somewhat downscaled, albeit consistently better than with traditional basis sets. As a case study, we also consider the polarizability of p-nitroaniline, a sizeable system for which complete basis set (CBS)(oVdZ, oVtZ) calculations are shown to outperform equally expensive CBS(VdZ, VtZ) results.

CBS extrapolation of Hartree-Fock energy: Pople and Dunning basis sets hand-to-hand on the endeavour

The Hartree-Fock (HF) energy is shown to be extrapolatable from subminimal, minimal, and extended basis sets. Unprecedentedly, it can be reliably extrapolated to the complete basis set limit (CBS) from as small as Pople's STO-2G up to the largest aug-cc-pVXZ basis sets of Dunning's correlation-consistent type and even more complete variants of such ansatzes. The approach is tested on a panoply of small, medium and large molecular systems. As a case study, extrapolation is shown to be particularly reliable and cost-effective (typically an order of magnitude more economical for similar accuracy) when employing a hybrid (STO-2G,extended) basis set pair. The additional cost relative to a single-point calculation with the extended basis set is of no significance. After training the novel scheme with a meager set of 18 systems (TS-18), four test sets covering from neutrals (TS-105) to neutrals plus cations (TS-26) and anions (TS-17), these involving up to third-row elements, as well as tetrapeptide conformers (TS-10) were utilized for its validation. Although the answer to the question of whether all basis sets converge to the same HF/CBS limit is a clear yes, that of whether they show the same convergence rate is open, an issue also examined in the present work. For systems involving atoms up to the second-row of the periodic table the answer seems to be a clear yes, at least when using correlation-consistent basis sets, but it is shown to be a no when the study is extended to anionic systems containing third-row elements. For the latter, augmented correlation consistent basis sets display a faster, perhaps optimal, convergence rate. The implications of this in practice can hardly be anticipated. For example, it cannot be predicted a priori which of such basis sets will yield the best relative energies for those anions, although a logical expectation suggests it to be the augmented ones which turn out to display the fastest convergence. As a blind-test type illustration, the novel scheme is applied to the conformational analysis of 2 tetrapeptides with 5 conformers each, using from subminimal up to extended basis sets as large as cc-pV5Z and aug-cc-pVQZ. The (STO-2G,extended) results so obtained are predicted to be in very good agreement with the best data reported thus far.

Dynamically adjustable spin component scaled second order Møller-Plesset perturbation theory for strongly correlated molecular systems

We present a novel spin-component scaled Møller-Plesset second order (MP2) perturbation theory [S. Grimme, J. Chem. Phys. 118, 9095 (2003)] in which the singlet and triplet correlation channels are dressed in a dynamical manner over the entire molecular potential energy surface. In order to strike the right balance between the short and long range correlation, the different correlation channels are scaled by two complementary functions without introducing any external parameter: while the singlet channel contribution to correlation energy is attenuated with increasing strong correlation of the system, the triplet channel contribution is amplified. We have justified our approach from physical reasoning as well as a few numerical examples with some difficult systems, like symmetric stretching of water and nitrogen molecules, which clearly demonstrate the efficacy of this method in describing the molecular potential energy surface, even in the strongly correlated regions where the conventional MP2 and its other variants disastrously fail.

Interatomic potentials for ground and excited states of Ar+He

The potential energy curves (PECs) of the ground and excited states that correlate in the atomic limit with Ar([Ne]3s ²3p ⁶,¹S), Ar([Ne]3s ²3p ⁵4s ¹, ³P, ¹P), and Ar([Ne]3s ²3p ⁵4p ¹, ³D, ³P, ³S, ¹D, ¹P, ¹S) are calculated at the multireference configuration interaction (MRCI+Q) theoretical level with extrapolations to the complete basis set limit using all-electron correlation consistent triple-, quadruple-, and quintuple-zeta basis sets. Scalar relativistic corrections are calculated using second-order Douglas-Kroll-Hess Hamiltonian with the corresponding basis sets contracted for scalar relativistic Hamiltonians. For these calculations, the 3s orbitals of the Ar atom are not included in the active space but are correlated through single and double excitations. Spin-orbit eigenstates are computed by diagonalizing the Breit-Pauli matrix between internal configurations with no electrons in external orbitals and added to the scalar relativistic results. A total of 32 molecular PECs are computed with spin-orbit contributions, which correlate with 1s₁, 1s_5-2, and 2p_10-1 atomic Ar energies in Paschen notation. Important features of the PECs and system crossings are discussed.