Coupled-cluster connected quadruples and quintuples corrections to the harmonic vibrational frequencies and equilibrium bond distances of HF, N2, F2, and CO

Potential energy curves for F2, Cl2, and Br2 with the i-DMFT method

The potential energy curves for dihalogens (F2, Cl2, and Br2) are calculated with the i-DMFT method proposed recently [Wang and Baerends, Phys. Rev. Lett. 128, 013001]. All electrons are correlated in a set of self-consistent-field eigenvalue equations, with the orbital occupation numbers obeying the Fermi-Dirac distribution. The only input is the dissociation energies of the molecules, which are usually available from an experimental database. The quality of the computed potential energy curve is examined by extracting spectroscopic parameters and rotation-vibration energy levels, which are compared with experiment data and other theoretical calculations.

Basis Set Requirements of σ-Functionals for Gaussian- and Slater-Type Basis Functions and Comparison with Range-Separated Hybrid and Double Hybrid Functionals

σ-Functionals belong to the class of Kohn-Sham (KS) correlation functionals based on the adiabatic-connection fluctuation-dissipation theorem and are technically closely related to the random phase approximation (RPA). They have the same computational demand as the latter, with the computational effort of an energy evaluation for both methods being lower than that of a preceding hybrid DFT calculation for typical systems but yield much higher accuracy, reaching chemical accuracy of 1 kcal/mol for quantities such as reactions and transition energies in main group chemistry. In previous work on σ-functionals, rather large Gaussian basis sets have been used. Here, we investigate the actual basis set requirements of σ-functionals and present three setups that employ smaller Gaussian basis sets ranging from quadruple-ζ (QZ) to triple-ζ (TZ) quality and represent a good compromise between accuracy and computational efficiency. Furthermore, we introduce an implementation of σ-functionals based on Slater-type basis sets and present two setups of QZ and TZ quality for this implementation. We test the accuracy of these setups on a large database of various physical properties and types of reactions, as well as equilibrium geometries and vibrational frequencies. As expected, the accuracy of σ-functional calculations becomes somewhat lower with a decreasing basis set size. However, for all setups considered here, calculations with σ-functionals are clearly more accurate than those within the RPA and even more so than those of the conventional KS methods. For the smallest setup using Gaussian-type basis functions and Slater-type basis functions, we introduce a reparametrization that reduces the loss in accuracy due to the basis set error to some extent. A comparison with the range-separated hybrid ωB97X-V and the double hybrid DSD-BLYP-D3 shows that σ functionals outperform in accuracy both of these accurate and, for their class, representative functionals.

Approximating large-basis coupled-cluster theory vibrational frequencies using focal-point approximations

The focal-point approximation can be used to estimate a high-accuracy, slow quantum chemistry computation by combining several lower-accuracy, faster computations. We examine the performance of focal-point methods by combining second-order Møller-Plesset perturbation theory (MP2) with coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] for the calculation of harmonic frequencies and that of fundamental frequencies using second-order vibrational perturbation theory (VPT2). In contrast to standard CCSD(T), the focal-point CCSD(T) method approaches the complete basis set (CBS) limit with only triple-ζ basis sets for the coupled-cluster portion of the computation. The predicted harmonic and fundamental frequencies were compared with the experimental values for a set of 20 molecules containing up to six atoms. The focal-point method combining CCSD(T)/aug-cc-pV(T + d)Z with CBS-extrapolated MP2 has mean absolute errors vs experiment of only 7.3 cm-1 for the fundamental frequencies, which are essentially the same as the mean absolute error for CCSD(T) extrapolated to the CBS limit using the aug-cc-pV(Q + d)Z and aug-cc-pV(5 + d)Z basis sets. However, for H2O, the focal-point procedure requires only 3% of the computation time as the extrapolated CCSD(T) result, and the cost savings will grow for larger molecules.

Quantum chemical rovibrational analysis of aminoborane and its isotopologues

Aminoborane, H₂ NBH₂ and its isotopologues, H₂ N¹⁰ BH₂ , D₂ NBD₂ , and D₂ N¹⁰ BD₂ , have been studied by high-level ab initio methods. All calculations rely on multidimensional potential energy surfaces and dipole moment surfaces including high-order mode coupling terms, which have been obtained from electronic structure calculations at the level of explicitly correlated coupled-cluster theory, CCSD(T)-F12, or the distinguishable cluster approximation, DCSD. Subsequent vibrational structure calculations based on second-order vibrational perturbation theory, VPT2, and vibrational configuration interaction theory, VCI, were used to determine rotational constants, centrifugal distortion constants, vibrationally averaged geometrical parameters and (an)harmonic vibrational frequencies. The impact of core-correlation effects is discussed in detail. Rovibrational VCI calculations were used to simulate the gas phase spectra of these species and an in-depth analysis of the ν₇ band of aminoborane is provided. Color-coding is used to reveal the identity of the individual progressions of the rovibrational transitions for this particular mode.

Geometries and vibrational frequencies with Kohn-Sham methods using σ-functionals for the correlation energy

Recently, Kohn-Sham (KS) methods with new correlation functionals, called σ-functionals, have been introduced. Technically, σ-functionals are closely related to the well-known random phase approximation (RPA); formally, σ-functionals are rooted in perturbation theory along the adiabatic connection. If employed in a post-self-consistent field manner in a Gaussian basis set framework, then, σ-functional methods are computationally very efficient. Moreover, for main group chemistry, σ-functionals are highly accurate and can compete with high-level wave-function methods. For reaction and transition state energies, e.g., chemical accuracy of 1 kcal/mol is reached. Here, we show how to calculate first derivatives of the total energy with respect to nuclear coordinates for methods using σ-functionals and then carry out geometry optimizations for test sets of main group molecules, transition metal compounds, and non-covalently bonded systems. For main group molecules, we additionally calculate vibrational frequencies. σ-Functional methods are found to yield very accurate geometries and vibrational frequencies for main group molecules superior not only to those from conventional KS methods but also to those from RPA methods. For geometries of transition metal compounds, not surprisingly, best geometries are found for RPA methods, while σ-functional methods yield somewhat less good results. This is attributed to the fact that in the optimization of σ-functionals, transition metal compounds could not be represented well due to the lack of reliable reference data. For non-covalently bonded systems, σ-functionals yield geometries of the same quality as the RPA or as conventional KS schemes combined with dispersion corrections.

Reduced-dimensional vibrational models of the water dimer

A model based on the finite-basis representation of a vibrational Hamiltonian expressed in internal coordinates is developed. The model relies on a many-mode, low-order expansion of both the kinetic energy operator and the potential energy surface (PES). Polyad truncations and energy ceilings are used to control the size of the vibrational basis to facilitate accurate computations of the OH stretch and HOH bend intramolecular transitions of the water dimer (H₂ ¹⁶O)₂. Advantages and potential pitfalls of the applied approximations are highlighted. The importance of choices related to the treatment of the kinetic energy operator in reduced-dimensional calculations and the accuracy of different water dimer PESs are discussed. A range of different reduced-dimensional computations are performed to investigate the wavenumber shifts in the intramolecular transitions caused by the coupling between the intra- and intermolecular modes. With the use of symmetry, full 12-dimensional vibrational energy levels of the water dimer are calculated, predicting accurately the experimentally observed intramolecular fundamentals. It is found that one can also predict accurate intramolecular transition wavenumbers for the water dimer by combining a set of computationally inexpensive reduced-dimensional calculations, thereby guiding future effective-Hamiltonian treatments.

The MOBH35 Metal–Organic Barrier Heights Reconsidered: Performance of Local-Orbital Coupled Cluster Approaches in Different Static Correlation Regimes

We have revisited the MOBH35 (Metal–Organic Barrier Heights, 35 reactions) benchmark [Iron, Janes, J. Phys. Chem. A, 2019, 123 ( (17), ), 3761−378130973722; ibid. 2019, 123, 6379–6380] for realistic organometallic catalytic reactions, using both canonical CCSD(T) and localized orbital approximations to it. For low levels of static correlation, all of DLPNO-CCSD(T), PNO-LCCSD(T), and LNO-CCSD(T) perform well; for moderately strong levels of static correlation, DLPNO-CCSD(T) and (T₁) may break down catastrophically, and PNO-LCCSD(T) is vulnerable as well. In contrast, LNO-CCSD(T) converges smoothly to the canonical CCSD(T) answer with increasingly tight convergence settings. The only two reactions for which our revised MOBH35 reference values differ substantially from the original ones are reaction 9 and to a lesser extent 8, both involving iron. For the purpose of evaluating density functional theory (DFT) methods for MOBH35, it would be best to remove reaction 9 entirely as its severe level of static correlation makes it just too demanding for a test. The magnitude of the difference between DLPNO-CCSD(T) and DLPNO-CCSD(T₁) is a reasonably good predictor for errors in DLPNO-CCSD(T₁) compared to canonical CCSD(T); otherwise, monitoring all of T₁, D₁, max|t_i^A|, and 1/(ε_LUMO – ε_HOMO) should provide adequate warning for potential problems. Our conclusions are not specific to the def2-SVP basis set but are largely conserved for the larger def2-TZVPP, as they are for the smaller def2-SV(P): the latter may be an economical choice for calibrating against canonical CCSD(T). Finally, diagnostics for static correlation are statistically clustered into groups corresponding to (1) importance of single excitations in the wavefunction; (2a) the small band gap, weakly separated from (2b) correlation entropy; and (3) thermochemical importance of correlation energy, as well as the slope of the DFT reaction energy with respect to the percentage of HF exchange. Finally, a variable reduction analysis reveals that much information on the multireference character is provided by T₁, I_ND/I_tot, and the exchange-based diagnostic A₁₀₀[TPSS].

How accurate is the determination of equilibrium structures for van der Waals complexes? The dimer N2O⋯CO as an example

Plausible methods for accurate determination of equilibrium structures of intermolecular clusters have been assessed for the van der Waals dimer N₂O⋯CO. In order to assure a large initial dataset of rotational parameters, we first measured the microwave spectra of the ¹⁵N₂O⋯¹²CO and ¹⁵N₂O⋯¹³CO isotopologs, expanding previous measurements. Then, an anharmonic force field was calculated ab initio and a semi-experimental equilibrium structure was determined. The dimer structure was also calculated at the coupled-cluster level of theory using very large basis sets with diffuse functions and counterpoise correction. It was found that the contributions of the diffuse functions and the counterpoise correction are not additive and do not compensate each other although they have almost the same value but opposite signs. The semi-experimental and ab initio structures were found to be in fair agreement, with the equilibrium distance between the centers of mass of both monomers being 3.825(13) Å and the intermolecular bond length r(C⋯O) = 3.300(9) Å. In this case, the mass-dependent method did not permit us to determine reliable intermolecular parameters. The combination of experimental rotational constants and results of ab initio calculations thus proves to be very sensitive to examine the accuracy of structural determinations in intermolecular clusters, offering insight into other aggregates.

High-Level Rovibrational Calculations on Ketenimine

From an astrochemical point of view ketenimine (CH₂CNH) is a complex organic molecule (COM) and therefore likely to be a building block for biologically relevant molecules. Since it has been detected in the star-forming region Sagittarius B2(N), it is of high relevance in this field. Although experimental data are available for certain bands, for some energy ranges such as above 1200 cm^-1 reliable data virtually do not exist. In addition, high-level ab initio calculations are neither reported for ketenimine nor for one of its deuterated isotopologues. In this paper, we provide for the first time data from accurate quantum chemical calculations and a thorough analysis of the full rovibrational spectrum. Based on high-level potential energy surfaces obtained from explicitly correlated coupled-cluster calculations including up to 4-mode coupling terms, the (ro)vibrational spectrum of ketenimine has been studied in detail by variational calculations relying on rovibrational configuration interaction (RVCI) theory. Strong Fermi resonances were found for all isotopologues. Rovibrational infrared intensities have been obtained from dipole moment surfaces determined from the distinguishable cluster approximation. A comparison of the spectra of the CH₂CNH molecule with experimental data validates our results, but also reveals new insight about the system, which shows very strong Coriolis coupling effects.

Quantifying and Understanding Errors in Molecular Geometries

Electronic structure calculations are ubiquitous in most branches of chemistry, but all have errors in both energies and equilibrium geometries. Quantifying errors in possibly dozens of bond angles and bond lengths is a Herculean task. A single natural measure of geometric error is introduced, the geometry energy offset (GEO). GEO links many disparate aspects of geometry errors: a new ranking of different methods, quantitative insight into errors in specific geometric parameters, and insight into trends with different methods. GEO can also reduce the cost of high-level geometry optimizations and shows when geometric errors distort the overall error of a method. Results, including some surprises, are given for both covalent and weak interactions.

Ab initio calculation of rovibrational states for non-degenerate double-well potentials: cis-trans isomerization of HOPO

The rovibrational spectra of metaphosphorous acid, HOPO, and its deuterated isotopologue have been studied by vibrational configuration interaction calculations, relying on the internal coordinate path Hamiltonian and the Watson Hamiltonian. Tunneling effects for the overtones of the torsional mode, which gives rise to the cis-trans isomerization, and its rovibrational transitions have been investigated in detail. Due to strong matrix effects, comparison with experimental data is hindered, and thus, the calculations provide accurate estimates for the fundamental modes of these species.

Equilibrium Structures of the Phosphorus Trihalides PF3 and PCl3, and the Phosphoranes PH3F2, PF5, PCl3F2, and PCl5

Among the title species, a reliable and accurate equilibrium geometry ( re structure) is available only for PF3, which has been determined experimentally more than 20 years ago. Here, we report accurate re structures for all title molecules, which were obtained using a composite computational approach based on explicitly correlated coupled-cluster theory (CCSD(T)-F12b) in conjunction with a large correlation-consistent basis set (cc-pCVQZ-F12) to take core-valence electron correlation into account. Additional terms were included to correct for the effects of iterative triple excitations (CCSDT), noniterative quadruple excitations (CCSDT(Q)), and scalar relativistic contributions (DKH2-CCSD(T)). The performance of this computational procedure was established through test calculations on selected small molecules (PH, PF, PCl, PH2, PF2, and PH3). For PF3, PCl3, PH3F2, and PF5 sufficiently accurate experimental ground-state rotational constants from the literature were used to determine semiexperimental re structures, which were found to be in excellent agreement with the corresponding best estimates from the current composite approach. The recommended equilibrium structural parameters are for PCl3, re(PCl) = 203.94 pm and θe(ClPCl) = 100.18°; for PH3F2, re(PHeq) = 138.38 pm and re(PFax) = 164.15 pm; for PF5, re(PFeq) = 153.10 pm and re(PFax) = 157.14 pm; for PCl3F2, re(PCleq) = 200.21 pm and re(PFax) = 159.37 pm; and for PCl5, re(PCleq) = 201.29 pm and re(PClax) = 211.83 pm. The associated uncertainties are estimated to be ±0.10 pm and ±0.10°, respectively.

State-of-the-art computation of the rotational and IR spectra of the methyl-cyclopropyl cation: hints on its detection in space

Recent measurements by the Cassini Ion Neutral Mass Spectrometer demonstrated the presence of numerous carbocations in Titan's upper atmosphere. In [Ali et al., Planet. Space Sci., 2013, 87, 96], an analysis of these measurements revealed the formation of the three-membered cyclopropenyl cation and its methyl derivatives. As a starting point of a future coordinated effort of laboratory experiments, quantum-chemical calculations, and astronomical observations, in the present work the molecular structure and spectroscopic properties of the methyl-cyclopropenyl cation have been investigated by means of state-of-the-art computational approaches in order to simulate its rotational and infrared spectra. Rotational parameters have been predicted with an expected accuracy better than 0.1% for rotational constants and on the order of 1-2% for centrifugal-distortion terms. As for the infrared spectrum, despite the challenge of a large amplitude motion, fundamental transitions have been computed to a good accuracy, i.e., the uncertainties are expected to be smaller than 5-10 wavenumbers.

Experiment and theory at the convergence limit: accurate equilibrium structure of picolinic acid by gas-phase electron diffraction and coupled-cluster computations

The accurate molecular structure of picolinic acid has been determined from experimental data and computed at the coupled cluster level of theory. Only one conformer with the O[double bond, length as m-dash]C-C-N and H-O-C[double bond, length as m-dash]O fragments in antiperiplanar (ap) positions, ap-ap, has been detected under conditions of the gas-phase electron diffraction (GED) experiment (Tnozzle = 375(3) K). The semiexperimental equilibrium structure, rsee, of this conformer has been derived from the GED data taking into account the anharmonic vibrational effects estimated from the ab initio force field. The equilibrium structures of the two lowest-energy conformers, ap-ap and ap-sp (with the synperiplanar H-O-C[double bond, length as m-dash]O fragment), have been fully optimized at the CCSD(T)_ae level of theory in conjunction with the triple-ζ basis set (cc-pwCVTZ). The quality of the optimized structures has been improved due to extrapolation to the quadruple-ζ basis set. The high accuracy of both GED determination and CCSD(T) computations has been disclosed by a correct comparison of structures having the same physical meaning. The ap-ap conformer has been found to be stabilized by the relatively strong NH-O hydrogen bond of 1.973(27) Å (GED) and predicted to be lower in energy by 16 kJ mol-1 with respect to the ap-sp conformer without a hydrogen bond. The influence of this bond on the structure of picolinic acid has been analyzed within the Natural Bond Orbital model. The possibility of the decarboxylation of picolinic acid has been considered in the GED analysis, but no significant amounts of pyridine and carbon dioxide could be detected. To reveal the structural changes reflecting the mesomeric and inductive effects due to the carboxylic substituent, the accurate structure of pyridine has been also computed at the CCSD(T)_ae level with basis sets from triple- to 5-ζ quality. The comprehensive structure computations for pyridine as well as for carbon dioxide have been used to examine the convergence with respect to the basis set size.

Trends in Strong Chemical Bonding in C2, CN, CN-, CO, N2, NO, NO+, and O2

The strong chemical bonds between C, N, and O play a central role in chemistry, and their formation and cleavage are critical steps in very many catalytic processes. The close-lying molecular orbital energies and large correlation effects pose a challenge to electronic structure calculations and have led to different bonding interpretations, most notably for C₂. One way to approach this problem is by strict benchmark comparison of related systems. This work reports reference electronic structures and computed bond dissociation enthalpies D₀ for C₂, CN, CN^-, CO, N₂, NO, NO⁺, O₂ and related systems C₂⁺ and C₂^- at chemical accuracy (∼1 kcal/mol or 4 kJ/mol) using CCSD(T)/aug-cc-pV5Z, with additional benchmarks of HF, MP2, CCSD, explicitly correlated F12 methods, and four density functionals. Very large correlation and basis set effects are responsible for up to 93% of total D₀. The order of the molecular orbitals 1π_u and 3σ_g changes, as seen in textbooks, depending on total and effective nuclear charge. Linear trends are observed in 2σ_u-2σ_g orbital splitting (R² = 0.91) and in D₀ of C₂, C₂^-, and C₂⁺ (R² = 0.99). The correlation component of D₀ of C₂ is by far the largest (∼93%) due to a poor HF description. Importantly, density functional theory fails massively in describing this series consistently in both limits of effective nuclear charge, and Hartree-Fock exchange or meta functionals do not remedy this 100 kJ/mol error, which should thus be addressed in future density functional developments as it affects very many studies involving cleavage or formation of these bonds.

An integrated experimental and quantum-chemical investigation on the vibrational spectra of chlorofluoromethane

The vibrational analysis of the gas-phase infrared spectra of chlorofluoromethane (CH2ClF, HCFC-31) was carried out in the range 200-6200 cm(-1). The assignment of the absorption features in terms of fundamental, overtone, combination, and hot bands was performed on the medium-resolution (up to 0.2 cm(-1)) Fourier transform infrared spectra. From the absorption cross section spectra accurate values of the integrated band intensities were derived and the global warming potential of this compound was estimated, thus obtaining values of 323, 83, and 42 on a 20-, 100-, and 500-year horizon, respectively. The set of spectroscopic parameters here presented provides the basic data to model the atmospheric behavior of this greenhouse gas. In addition, the obtained vibrational properties were used to benchmark the predictions of state-of-the-art quantum-chemical computational strategies. Extrapolated complete basis set limit values for the equilibrium geometry and harmonic force field were obtained at the coupled-cluster singles and doubles level of theory augmented by a perturbative treatment of triple excitations, CCSD(T), in conjunction with a hierarchical series of correlation-consistent basis sets (cc-pVnZ, with n = T, Q, and 5), taking also into account the core-valence correlation effects and the corrections due to diffuse (aug) functions. To obtain the cubic and quartic semi-diagonal force constants, calculations employing second-order Møller-Plesset perturbation (MP2) theory, the double-hybrid density functional B2PLYP as well as CCSD(T) were performed. For all anharmonic force fields the performances of two different perturbative approaches in computing the vibrational energy levels (i.e., the generalized second order vibrational treatment, GVPT2, and the recently proposed hybrid degeneracy corrected model, HDCPT2) were evaluated and the obtained results allowed us to validate the spectroscopic predictions yielded by the HDCPT2 approach. The predictions of the deperturbed second-order perturbation approach, DVPT2, applied to the computation of infrared intensities beyond the double-harmonic approximation were compared to the accurate experimental values here determined. Anharmonic DFT and MP2 corrections to CCSD(T) intensities led to a very good agreement with the absorption cross section measurements over the whole spectral range here analysed.

Accurate structure, thermodynamic and spectroscopic parameters from CC and CC/DFT schemes: the challenge of the conformational equilibrium in glycine

The structures, relative stabilities, and infrared spectra of the six low-energy conformers of glycine have been characterized using a state-of-the-art quantum-mechanical approach allowing the bond distances, conformational enthalpies and vibrational frequencies to be determined well within the chemical accuracy. Transition state structures governing interconversion among the different energy minima have also been characterized. In detail, the gas-phase thermodynamic properties (at 15 K and 410 K) of the glycine conformers considered have been obtained with a 1 kJ mol(-1) accuracy, and it has been shown that the employment of DFT geometries usually reduces such accuracy by at most 0.1 kJ mol(-1). Regarding molecular structures, the use of two different composite schemes allowed us to further confirm the suitability of a rather cost-effective approach and provide geometrical parameters with an overall accuracy better than 0.002 Å for distances and 1 degree for angles. Thanks to a hybrid CC/DFT approach, the infrared spectra of all conformers considered and of several deuterated isotopologues have been reproduced (when experimental data were available) or predicted with an accuracy of 10 cm(-1). Finally, the joint thermodynamic and spectroscopic investigation allowed us to shed some light on the possible observation of elusive conformers. On the whole, the high accuracy of the computational results allows us to draw a fully consistent interpretation of the available experimental data and to obtain a more complete characterization of the potential energy surface of glycine.

NOx Catalyzed Pathway of Stratospheric Ozone Depletion: A Coupled Cluster Investigation

We report a theoretical investigation on the NOx catalyzed pathways of stratospheric ozone depletion using highly accurate coupled cluster methods. These catalytic reactions represent a great challenge to state-of-the-art ab initio methods, while their mechanisms remain unclear to both experimentalists and theoreticians. In this work, we have used the so-called "gold standard of quantum chemistry," the CCSD(T) method, to identify the saddle points on NOx-based reaction pathways of ozone hole formation. Energies of the saddle points are calculated using the multireference variants of coupled cluster methods. The calculated activation energies and rate constants show good agreement with available experimental results. Tropospheric precursors to stratospheric NOx radicals have been identified, and their potential importance in stratospheric chemistry has been discussed. Our calculations resolve previous conflicts between ab initio and experimental results for a trans nitro peroxide intermediate, in the NOx catalyzed pathway of ozone depletion.

Implementation of the incremental scheme for one-electron first-order properties in coupled-cluster theory

A fully automated parallelized implementation of the incremental scheme for coupled-cluster singles-and-doubles (CCSD) energies has been extended to treat molecular (unrelaxed) first-order one-electron properties such as the electric dipole and quadrupole moments. The convergence and accuracy of the incremental approach for the dipole and quadrupole moments have been studied for a variety of chemically interesting systems. It is found that the electric dipole moment can be obtained to within 5% and 0.5% accuracy with respect to the exact CCSD value at the third and fourth orders of the expansion, respectively. Furthermore, we find that the incremental expansion of the quadrupole moment converges to the exact result with increasing order of the expansion: the convergence of nonaromatic compounds is fast with errors less than 16 mau and less than 1 mau at third and fourth orders, respectively (1 mau=10(-3)ea(0)(2)); the aromatic compounds converge slowly with maximum absolute deviations of 174 and 72 mau at third and fourth orders, respectively.