On the rearrangement and dissociation mechanism of SiH4+ in its triply-degenerate ground state.

An ab initio molecular orbital study has been performed to explore the structural rearrangement and dissociation of SiH4+ radical cation at the X̃2T2 ground electronic state. All stationary points located on the lowest adiabatic sheet of Jahn-Teller (JT) split X̃2T2 state are fully optimized and characterized by performing harmonic vibrational frequency calculations. The structural rearrangement is predicted to start with JT distortions involving the doubly-degenerate (e) and triply-degenerate (t2) modes. The e mode reduces the initial Td symmetry of the SiH4+ ground state to a D2d saddle point, which eventually dissociates into the SiH3+(2A1) + H products via C3v local minimum. In turn, an e-type bending of αH-Si-H yields the SiH2+(2A1) + H2 products through the first C3v local minimum and then the Cs(2A') global minimum. In the alternative pathway, the t2 mode distorts the initial Td symmetry into a loosely bound C3v local minimum, which further dissociates into the SiH3+(2A1) + H asymptote via totally symmetric Si-H stretching mode, and SiH2+(2A1) + H2 products via H-Si-H bending (e) mode through the Cs(2A') global minimum. It is further predicted that the Cs global minimum interconverts equivalent structures via a C2v transition structure. In addition, the two dissociation products are found to be connected by a second C2v transition structure.

Carbon-[n]Triangulenes and Sila-[n]Triangulenes: Which Are Planar?

Using our recently suggested concept of a quasi-molecule ("tile") and, in the case of the planarity here at stake, its generalization to larger than tetratomics, we explain why carbon [n]triangulenes tend to be planar, while hybrids, where just a few or even all a- or b-type carbon atoms are silicon-substituted (sila-[n]triangulenes), tend to be planar/nonplanar when compared with the unsubstituted carbon-[n]triangulenes. Because other spin states of the parent carbon- and sila-[n]triangulenes tend to correlate with the same tiles, it is conjectured that no structural changes are expected to depend on their spin state. Other polycyclic and sila-compounds are also discussed.

Scale-free-modeling (harmonic) vibrational frequencies: Assessing accuracy and cost-effectiveness by CBS extrapolation.

Empirical scaling of calculated vibrational harmonic frequencies is a popular approach used in the field of molecular sciences. A nonempirical scheme that aims at reducing their basis set error is suggested here. Nearly as cost-effective as the scaled Kohn-Sham density functional theory (KS DFT), it consists of splitting the frequencies into Hartree-Fock and electron correlation contributions, followed by their extrapolation to the complete basis set (CBS) limit. Since the former converges exponentially, the overall cost may actually equal that of CBS extrapolation of the correlation part. Despite shifts in the molecular geometry during vibration, reasons are advanced to justify the approach, with extrapolation from the first two steps of the basis set ladder being effective in accelerating convergence. As benchmark data, a set of harmonic frequencies and zero-point energies for 15 molecules is employed at the second-order Moller-Plesset and coupled-cluster single double triple [CCSD(T)] levels of theory. The results outperform the optimized KS DFT scaled values. As a second test set, equilibrium structures and harmonic frequencies were computed for H2O2, CH2NH, C2H2O, and the trans-isomer of 1,2-C2H2F2. The results are also encouraging, particularly when improved for excess correlation at the CCSD(T)/VDZ level via the focal-point approach. In extreme cases, CBS extrapolation is done from two double-ζ calculations: one canonical and the other using explicit correlation theory. As a further case study, benzene is considered. While the CCSD(T) results show the smallest deviation from the best estimates, the MP2 results also attain good quality: When improved for excess correlation, they show 6-10 cm-1 errors relative to the best data, only slightly outperformed at the CCSD(T)/CBS level. Tentative results for the fundamental frequencies are also presented.

Reconciling spectroscopy with dynamics in global potential energy surfaces: The case of the astrophysically relevant SiC2.

SiC2 is a fascinating molecule due to its unusual bonding and astrophysical importance. In this work, we report the first global potential energy surface (PES) for ground-state SiC2 using the combined-hyperbolic-inverse-power-representation method and accurate ab initio energies. The calibration grid data are obtained via a general dual-level protocol developed afresh herein that entails both coupled-cluster and multi-reference configuration interaction energies jointly extrapolated to the complete basis set limit. Such an approach is specially devised to recover much of the spectroscopy from the PES, while still permitting a proper fragmentation of the system to allow for reaction dynamics studies. Besides describing accurately the valence strongly bound region that includes both the cyclic global minimum and isomerization barriers, the final analytic PES form is shown to properly reproduce dissociation energies, diatomic potentials, and long-range interactions at all asymptotic channels, in addition to naturally reflect the correct permutational symmetry of the potential. Bound vibrational state calculations have been carried out, unveiling an excellent match of the available experimental data on c-SiC2(A11). To further exploit the global nature of the PES, exploratory quasi-classical trajectory calculations for the endothermic C2 + Si → SiC + C reaction are also performed, yielding thermalized rate coefficients for temperatures up to 5000 K. The results hint for the prominence of this reaction in the innermost layers of the circumstellar envelopes around carbon-rich stars, hence conceivably playing therein a key contribution to the gas-phase formation of SiC, and eventually, solid SiC dust.

Quasiclassical Trajectory Study of the Si + SH Reaction on an Accurate Double Many-Body Expansion Potential Energy Surface.

An accurate potential energy surface (PES) for the HSiS system based on MRCI+Q calculations extrapolated to the complete basis set limit is presented. Modeled with the double many-body expansion (DMBE) method, the PES provides an accurate description of the long-range interactions, including electrostatic and dispersion terms decaying as R-4, R-5, R-6, R-8, R-10 that are predicted from dipole moments, quadrupole moments, and dipolar polarizabilities, which are also calculated at the MRCI+Q level. The novel PES is then used in quasiclassical trajectory calculations to predict the rate coefficients of the Si + SH → SiS + H reaction, which has been shown to be a major source of the SiS in certain regions of the interstellar medium. An account of the zero-point energy leakage based on various nonactive models is also given. It is shown that the reaction is dominated by long-range forces, with the mechanism Si + SH → SiSH → SSiH → SiS + H being the most important one for all temperatures studied. Although SSiH corresponds to the global minimum of the PES, the contribution from the direct reaction Si + SH → SSiH → SiS + H is less than 0.5% for temperatures higher than 500 K. The rovibrational distributions of the products are calculated using the momentum Gaussian binning method and show that as the temperature is increased the average vibrational quantum number decreases while the rotational distribution spreads up to larger values.

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.

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.

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.

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.

Accurate DMBE potential-energy surface for CNO(2A″) and rate coefficients in C(3P)+NO collisions.

A realistic double many-body expansion potential energy surface (PES) is developed for the 2A″ state of the carbon-nitrogen-oxygen (CNO) system based on MRCI-F12/cc-pVQZ-F12 ab initio energies. The new PES reproduces the fitted points with chemical accuracy (root mean square deviation up to 0.043 eV) and explicitly incorporates long range energy terms that can accurately describe the electrostatic and dispersion interactions. Thermal rate coefficients were computed for the C(3P) + NO(2Π) reaction for temperatures ranging from 15 K to 10 000 K, and the values are compared to previously reported results. The differences are rationalized, and the major importance of long range forces in predicting the rate coefficients for barrierless reactions is emphasized.

Accurate Potential Energy Surface for Quartet State HN2 and Interplay of N(4S) + NH(X̃3Σ-) versus H + N2(A3Σu+) Reactions.

A global potential energy surface for the lowest quartet state of HN2 is reported for the first time from accurate multireference ab initio calculations extrapolated to the complete basis set limit using the double many-body expansion method. All its stationary points are characterized, with the lowest quartet of HN2 predicted to have a bent global minimum 36 kcal mol-1 below the N(4S) + NH(X̃3Σ-) asymptote, from which it is barrierlessly achievable. The entire set of calculated ab initio points has been fitted for energies up to 1000 kcal mol-1 above the global minimum with an RMSD of 0.89 kcal mol-1, a gap comprising all identified stationary points. Special care is taken in modeling the involved long-range forces and cusps caused by crossing seams. The novel PES prompts for the calculation of rate constants for several unexplored reactions that are relevant for combustion, plasma, and atmospheric chemistry.

A global CHIPR potential energy surface for ground-state C3H and exploratory dynamics studies of reaction C2 + CH → C3 + H.

A full-dimensional global potential-energy surface (PES) is first reported for ground-state doublet C3H using the combined-hyperbolic-inverse-power-representation (CHIPR) method and accurate ab initio energies extrapolated to the complete basis set limit. The PES is based on a many-body expansion-type development where the two-body and three-body energy terms are from our previously reported analytic potentials for C2H(2A') and C3(1A',3A'), while the effective four-body one is calibrated using an extension of the CHIPR formalism for tetratomics. The final form is shown to accurately reproduce all known stationary structures of the PES, some of which are unreported thus far, and their interconversion pathways. Moreover, it warrants by built-in construction the appropriate permutational symmetry and describes in a physically reasonable manner all long-range features and the correct asymptotic behavior at dissociation. Exploratory quasi-classical trajectory calculations for the reaction C2 + CH → C3 + H are also performed, yielding thermalized rate coefficients for temperatures up to 4000 K.

Quasiclassical Study of the C(3P) + NO(X2Π) and O(3P) + CN(X2Σ+) Collisional Processes on an Accurate DMBE Potential Energy Surface.

The predicted rate constants for C + NO and O + CN collisions in three potential energy surfaces (PESs) for the 2A' state of the CNO molecule are compared using quasiclassical trajectories. Different temperature dependencies are obtained for the C + NO reaction, which are explained in terms of the long-range properties of the PESs. Recommended values and mechanistic details are also reported. For O + CN collisions, a better agreement between the theoretical results is found, except for temperatures below 100 K.

Accurate CHIPR Potential Energy Surface for the Lowest Triplet State of C3.

We report the first global ab initio-based potential energy surface (PES) for ground-state triplet C3(3A') based on accurate energies extrapolated to the complete basis set (CBS) limit, and using the combined-hyperbolic-inverse-power-representation method for the analytical modeling. By relying on a cost-effective CBS(D,T) protocol, we ensure that the final form reproduces all topographical features of the PES, including its cyclic-linear isomerization barrier, with CBS(5,6)-quality. To partially account for the incompleteness of the N-electron basis and other minor effects, the available accurate experimental data on the relevant diatomics were used to obtain direct-fit curves that replace the theoretical ones in the many-body expansion. Besides describing properly long-range interactions at all asymptotic channels and permutational symmetry by built-in construction, the PES reported here reproduces the proper exothermicities at dissociation regions as well as the spectroscopy of the diatomic fragments. Bound vibrational state calculations in both linear and cyclic isomers have also been carried out, unveiling a good match of the available data on C3(ã 3Πu), while assisting with IR band positions for C3(3A2') that may serve as a guide for its laboratory and astronomical detection.

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.

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.

Global Potential Energy Surface for HO2+ Using the CHIPR Method.

An analytical potential energy function for the title ion based on the combined hyperbolic inverse power representation (CHIPR) method and its characteristics are discussed at length in the present work. The curves of two diatomic ions, O2+ and OH+, are also obtained within the same approach. The model PES so obtained exhibits extraordinary flexibility in describing with subchemical accuracy even the weak topological features near the higher energy regions. Thus, structural properties predicted by the model may help spectroscopists who want to compare their experimental values with the ones from theory. The relaxed PESs in various coordinates have been calculated by relaxing the O2 bond distance using the present model, thus throwing light on all the possible isomers and their interconversions. The latest estimates of IR frequencies for three vibrational modes have been compared with the computed frequencies using the present model, and the agreement seems encouraging.

Difficulties and Virtues in Assessing the Potential Energy Surfaces of Carbon Clusters via DMBE Theory: Stationary Points of Cκ (κ = 2-10) at the Focal Point.

The previously reported potential energy surfaces (PESs) of ground-state singlet C3 and triplet C4 are here utilized as input for the construction of approximate cluster expansions for larger Cκ (κ = 5-10) species. Relying primarily on the double many-body expansion (DMBE) approach, global potentials are obtained by summing the total interaction energies of all atomic subclusters up to four-body terms. The notable capability of the final forms in predicting good estimates of the linear global minima and their thermochemical/structural properties may provide important insights into the structure-determining nature of the (2 + 3 + 4) terms. The main difficulties and virtues in assessing Cκ's via DMBE theory are analyzed and new prospects given for the construction of global reliable PESs for the target species.

CBS extrapolation in electronic structure pushed to the end: a revival of minimal and sub-minimal basis sets.

The complete basis set (CBS) limit is secluded in calculations of electronic structure, and hence CBS extrapolation draws immediate attention. Of the highest importance is the extremely slow-convergent correlation energy as obtained both from Møller-Plesset perturbation theory (MP2) and the gold standard coupled cluster singles, doubles, and perturbative triples method [CCSD(T)], both picked as the focal point. Because today's massive electronic structure calculations demand schemes for CBS extrapolation from the lowest rungs of the hierarchical staircase, the focus is also on how minimal and subminimal basis sets can help in the endeavour. The above has prompted, for the first time, the development of a reliable analytic variant of the unified singlet- and triplet-pair extrapolation (USTE) scheme, which is next utilized to hierarchize any arbitrary basis set. With all available basis set families for molecular orbital calculations systematized as subminimal, minimal and extended from the fraction of correlation energy that they can recover, the full approach is simple and general, yet reliable, and hereby illustrated for basis sets as small as Huzinaga MINI and as extended as the sophisticated ansatzes that are utilized in modern explicitly correlated MP2-F12 and CCSD(T)-F12 calculations. Extensively tested with up to 26 basis sets from various families, the reported results show that CBS extrapolation from a (subminimal, extended) basis-set pair yields correlation energies that outperform by far those obtained from Kohn-Sham density functional theory (KS DFT). When employing two subminimal basis sets, the results may still outperform KS-DFT but at a drastically smaller computational cost. To further gauge its performance, the new method is utilized to calculate the energies of all 45 isomers of C8H8 recently reported at a high ab initio level, with the present results showing excellent agreement with the available data. The present cost-effective approach may therefore be expected to have a broad impact on chemistry and even materials science.

The O + NO( v) Vibrational Relaxation Processes Revisited.

We have carried out a quasiclassical trajectory study of the O + NO( v) energy transfer process using DMBE potential energy surfaces for the ground-states of the 2A' and 2A″ manifolds. State-to-state vibrational relaxation rate constants have been computed over the temperature range 298 and 3000 K and initial vibrational states between v = 1 and 9. The momentum-Gaussian binning approach has been employed to calculate the probability of the vibrational transitions. A comparison of the calculated state-to-state rate coefficients with the results from experimental studies and previous theoretical calculations shows the relevance of the 1 2A″ potential energy surface to the title vibrational relaxation process.