Correlation consistent basis sets for explicitly correlated wavefunctions: Pseudopotential-based basis sets for the post-d main group elements Ga–Rn

Anharmonic Vibrational Spectroscopy of Germanium-Containing Clusters, GexC4-x and GexSi4-x (x = 0-4), for Interstellar Detection

An extensive, high-level theoretical study on tetra-atomic germanium carbide/silicide clusters is presented. Accurate harmonic and anharmonic vibrational frequencies and rotational constants are calculated at the CCSD(T)-F12a(b)/cc-pVT(Q)Z-F12 levels of theory. With growing capabilities to discern more of the chemical composition of the interstellar medium (ISM), an accurate database of reference material is required. The presence of carbon is ubiquitous in the ISM, and silicon is known to be present in interstellar dust grains; however, germanium-containing molecules remain elusive. To begin understanding the presence and role of germanium in the ISM, we present this study of the vibrational and rotational spectroscopic properties of various germanium-containing molecules to aid in their potential identification in the ISM with modern observational tools such as the James Webb Space Telescope. Structures studied herein include rhomboidal (r-), diamond (d-), and trapezoidal (t-) tetra-atomic molecules of the form GexC4-x and GexSi4-x, where x = 0-4. The most promising structure for detection is r-Ge2C2 via the ν4 mode with a frequency of 802.7 cm-1 (12.5 μm) and an intensity of 307.2 km mol-1. Other molecules that are potentially detectable, i.e., through vibrational modes or rotational transitions, include r-Ge3C, r-GeSi3, d-GeC3, r-GeC3, and t-Ge2C2.

A new chapter in the never ending story of cycloadditions: The puzzling case of SO2 and acetylene

A comprehensive study of the different classes of cycloaddition reactions ([3+2], [2+2], and [2+1]) of SO2 to acetylene and ethylene has been performed using density functional theory (DFT) and composite wavefunction methods. The [3+2] cycloaddition reaction, that was previously explored in the context of the cycloaddition of thioformaldehyde S-methylide (TSM) to ethylene and acetylene, proceeds in a concerted way to the formation of stable heterocycles. In this paper, we extend our study to the [2+2] and [2+1] cycloadditions of SO2 to acetylene, which would produce 1,1-oxathiete-2-oxide and thiirene-1,1-dioxide, respectively. One of the main conclusions is that cyclic 1,1-oxathiete-2-oxide can open through a relatively easy breaking of the SO single bond and rearrange toward sulfinyl acetaldehyde (SA). The SA molecule can easily undergo several internal rearrangements, which eventually lead to sulfenic acid and sulfoxide derivatives of ethenone, 1,2,3-dioxathiole, and CO plus sulfinylmethane. The most probable path, however, produces 2-thioxoacetic acid, whose derivatives (or those of the corresponding acetate) are usually obtained by Willgerodt-Kindler-type sulfuration of acetates. This product can in turn decompose, leading to the final products CO2 and H2CS. Comparison of this decomposition path with that of 2-amino-2-thioxoacetic acid shows that the process occurs through different H-transfer processes.

Monohydrides of the Group 13 Elements M=B, Al and Ga: Axial Bi-Nucleophilicity and the Propensity to Form Both H-M⋅⋅⋅HX and M-H⋅⋅⋅HX Hydrogen Bonds (X=F, Cl, Br, I, CN, CCH, CP)

Equilibrium dissociation energies De of the hydrogen-bonded complexes HAl⋅⋅⋅HX and HGa⋅⋅⋅HX (X=F, Cl, Br, I, CN, CCH, and CP) were calculated ab initio at the CCSD(T)-(F12c)/cc-pVDZ-F12 level of theory. The gradients of graphs of De versus the electrophilicity EHX of the Lewis acids HX yielded the nucleophilicities NM-X of the Group 13 atoms M in these diatomic molecules. Molecular electrostatic surfaces potentials reveal that H-Al and H-Ga are bi-nucleophilic and that the H ends of these H-M molecules are more nucleophilic than the M ends for M=Al and Ga, but not when M=boron. Therefore, the complexes M-H⋅⋅⋅HX were investigated using the same approach. It was concluded for M=Al and Ga that, for a given X, the M-H⋅⋅⋅HX complexes were more strongly bound than the corresponding H-M⋅⋅⋅HX complexes for both M=Al and Ga but the reverse order applies for M = boron. The effects of substituting the H atoms in the M-H molecules by F atoms and by methyl groups were investigated to measure the -I and +I inductive effects relative to H, respectively, on the nucleophilicities of the molecules M-H when M is acting as hydrogen-bond acceptor in complexes H-M⋅⋅⋅H-X.

Efficient Exploitation of Numerical Quadrature with Distance-Dependent Integral Screening in Explicitly Correlated F12 Theory: Linear Scaling Evaluation of the Most Expensive RI-MP2-F12 Term

We present a linear scaling atomic orbital based algorithm for the computation of the most expensive exchange-type RI-MP2-F12 term by employing numerical quadrature in combination with CABS-RI to avoid six-center-three-electron integrals. Furthermore, a robust distance-dependent integral screening scheme, based on integral partition bounds [Thompson, T. H.; Ochsenfeld, C. J. Chem. Phys. 2019, 150, 044101], is used to drastically reduce the number of the required three-center-one-electron integrals substantially. The accuracy of our numerical quadrature/CABS-RI approach and the corresponding integral screening is thoroughly assessed for interaction and isomerization energies across a variety of numerical integration grids. Our method outperforms the standard density fitting/CABS-RI approach with errors below 1 μEh even for small grid sizes and moderate screening thresholds. The choice of the grid size and screening threshold allows us to tailor our ansatz to a desired accuracy and computational efficiency. We showcase the approach's effectiveness for the chemically relevant system valinomycin, employing a triple-ζ F12 basis set combination (C54H90N6O18, 5757 AO basis functions, 10,266 CABS basis functions, 735,783 grid points). In this context, our ansatz achieves higher accuracy combined with a 135× speedup compared to the classical density fitting based variant, requiring notably less computation time than the corresponding RI-MP2 calculation. Additionally, we demonstrate near-linear scaling through calculations on linear alkanes. We achieved an 817-fold acceleration for C80H162 and an extrapolated 28,765-fold acceleration for C200H402, resulting in a substantially reduced computational time for the latter─from 229 days to just 11.5 min. Our ansatz may also be adapted to the remaining MP2-F12 terms, which will be the subject of future work.

The p-block challenge: assessing quantum chemistry methods for inorganic heterocycle dimerizations

The elements of the p-block of the periodic table are of high interest in various chemical and technical applications like frustrated Lewis-pairs (FLP) or opto-electronics. However, high-quality benchmark data to assess approximate density functional theory (DFT) for their theoretical description are sparse. In this work, we present a benchmark set of 604 dimerization energies of 302 "inorganic benzenes" composed of all non-carbon p-block elements of main groups III to VI up to polonium. This so-called IHD302 test set comprises two classes of structures formed by covalent bonding and by weaker donor-acceptor (WDA) interactions, respectively. Generating reliable reference data with ab initio methods is challenging due to large electron correlation contributions, core-valence correlation effects, and especially the slow basis set convergence. To compute reference values for these dimerization reactions, after thorough testing, we applied a computational protocol using state-of-the-art explicitly correlated local coupled cluster theory termed PNO-LCCSD(T)-F12/cc-VTZ-PP-F12(corr.). It includes a basis set correction at the PNO-LMP2-F12/aug-cc-pwCVTZ level. Based on these reference data, we assess 26 DFT methods in combination with three different dispersion corrections and the def2-QZVPP basis set, five composite DFT approaches, and five semi-empirical quantum mechanical methods. For the covalent dimerizations, the r2SCAN-D4 meta-GGA, the r2SCAN0-D4 and ωB97M-V hybrids, and the revDSD-PBEP86-D4 double-hybrid functional are found to be the best-performing methods among the evaluated functionals of the respective class. However, since def2 basis sets for the 4th period are not associated to relativistic pseudo-potentials, we obtained significant errors in the covalent dimerization energies (up to 6 kcal mol-1) for molecules containing p-block elements of the 4th period. Significant improvements were achieved for systems containing 4th row elements by using ECP10MDF pseudopotentials along with re-contracted aug-cc-pVQZ-PP-KS basis sets introduced in this work with the contraction coefficients taken from atomic DFT (PBE0) calculations. Overall, the IHD302 set represents a challenge to contemporary quantum chemical methods. This is due to a large number of spatially close p-element bonds which are underrepresented in other benchmark sets, and the partial covalent bonding character for the WDA interactions. The IHD302 set may be helpful to develop more robust and transferable approximate quantum chemical methods in the future.

Weak hydrogen bonding to halogens and chirality communication in propanols: Raman and microwave spectroscopy benchmark theory

Constitutional and conformational isomers of bromopropanol are vibrationally and rotationally characterised with parallels drawn to the structural chlorine analogues. A previous microwave spectroscopic study of the chloropropanols is re-examined and all systems are explored by Raman jet spectroscopy. For bromine, the entire nuclear quadrupole coupling tensors are accurately determined and compared to their chlorine counterparts. Tensor asymmetry parameters are determined and linked with the hydrogen bond strength as indicated by the downshift of the OH-stretching frequency. The spectroscopic constants derived from the observed transitions are used as benchmarks for a large variety of electronic structure methods followed by harmonic and anharmonic rovibrational treatments. The CCSD(T) electronic structure calculations provide the best performance, in particular once anharmonic and relativistic corrections are applied or implied. Standard DFT approaches vary substantially with respect to their systematic error cancellation across the investigated species, and cost-effective compromises for the different observables are proposed.

Electronic excited states of monobromosilylene molecules including the spin-orbit-coupling

We employ the internally contracted multireference configuration interaction (icMRCI-F12) with Davidson corrections to explore the electronic states of monobromosilylene molecules (HSiBr). A total of 20 states with energy up to 8.7 eV and the corresponding 50 states after taking the spin-orbit coupling (SOC) effects into account are investigated. The spectroscopic constants of the low-lying states, as well as oscillator strengths, vertical transition energies and potential energy curves (PECs) for all the 20 spin-free states and the 50 spin-orbit-coupled states of HSiBr are presented. The results indicate that the SOC effect significantly affects the dissociation pathways and the PECs of electronic excited states of HSiBr. Based on our calculation results, the interactions between the states and the dissociation of HSiBr in the UV region are discussed. Our study sheds some light on the complex interactions and dynamics of the electronic excited states of HSiBr, which would provide valuable information for future experimental investigations.

Correlation Consistent Basis Sets for Explicitly Correlated Theory: The Transition Metals

We present correlation consistent basis sets for explicitly correlated (F12) calculations, denoted VnZ(-PP)-F12-wis (n = D,T), for the d-block elements. The cc-pVDZ-F12-wis basis set is contracted to [8s7p5d2f] for the 3d-block, while its ECP counterpart for the 4d and 5d-blocks, cc-pVDZ-PP-F12-wis, is contracted to [6s6p5d2f]. The corresponding contracted sizes for cc-pVTZ(-PP)-F12-wis are [9s8p6d3f2g] for the 3d-block elements and [7s7p6d3f2g] for the 4d and 5d-block elements. Our VnZ(-PP)-F12-wis basis sets are evaluated on challenging test sets for metal-organic barrier heights (MOBH35) and group-11 metal clusters (CUAGAU-2). In F12 calculations, they are found to be about as close to the complete basis set limit as the combination of standard cc-pVnZ-F12 on main-group elements with the standard aug-cc-pV(n+1)Z(-PP) basis sets on the transition metal(s). While our basis sets are somewhat more compact than aug-cc-pV(n+1)Z(-PP), the CPU time benefit is negligible for catalytic complexes that contain only one or two transition metals among dozens of main-group elements; however, it is somewhat more significant for metal clusters.

An ab initio study on the electronic excited states and photodissociation mechanism of bromocarbene molecule

We used the internally contracted explicitly correlated multireference configuration interaction (icMRCI-F12) method combined with Davidson correction to conduct a high-precision ab initio study of CHBr. The spin-orbit coupling (SOC) is incorporated into the calculation. The 21 spin-free states split into 53 spin-coupled states of CHBr. The vertical transition energies and oscillator strengths are obtained of these states. The SOC effect on the equilibrium structures and the harmonic vibrational frequencies of the ground state X¹A', the lowest triplet state a³A'' and the first excited singlet state A¹A'' is investigated. The results reveal a significant effect of the SOC on the bond angle and the frequency of the bending mode of a³A''. The potential energy curves of electronic states of CHBr as functions of the H-C-Br bond angle, C-H bond length, and C-Br bond length, respectively, are also investigated. Based on the calculated results, the interactions between electronic states and photodissociation mechanism involved in CHBr in the ultraviolet region are explored. Our theoretical studies will shed light on the complicated interactions and dynamics of the electronic states of bromocarbenes.

The Importance of Tight f Basis Functions for Heavy p-Block Oxides and Halides: A Parallel With Tight d functions in the Second Row

It is well-known that both wave function ab initio and DFT calculations on second-row compounds exhibit anomalously slow basis set convergence unless the basis sets are augmented with additional "tight" (high-exponent) d functions, as in the cc-pV(n+d)Z and aug-cc-pV(n+d)Z basis sets. This has been rationalized as being necessary for a better description of the low-lying 3d orbital, which as the oxidation state increases sinks low enough to act as a back-donation acceptor from chalcogen and halogen lone pairs. This prompts the question whether a similar phenomenon exists for the isovalent compounds of the heavy p-block. We show that for the fourth and fifth row, this is the case, but this time for tight f functions enhancing the description of the low-lying 4f and 5f Rydberg orbitals, respectively. In the third-row heavy p block, the 4f orbitals are too far up, while the 4d orbitals are adequately covered by the basis functions already present to describe the 3d subvalence orbitals.

Reduced Nucleophilicities ИB of Lewis Bases B: Is ИB Independent of Whether B is Involved in a Hydrogen Bond or a Halogen Bond?

Reduced nucleophilicities И_B of axially symmetric molecules B were determined from , where D_e is the equilibrium dissociation energy of the complexes B⋅⋅⋅XY, N_B is the nucleophilicity of B, E_XY is the electrophilicity of the halogen-bond donor XY and σ min ${{\sigma }_{{\rm { min}}}{\rm \ }}$ is the minimum electrostatic surface potential of B. The series B⋅⋅⋅ClY, B⋅⋅⋅BrY, B⋅⋅⋅IY (Y=F, Cl, Br, I, CN, and CCH) as well as (B⋅⋅⋅XY, XY=F₂ , Cl₂ , Br₂ ,and BrCl) of complexes were investigated. Molecules B were grouped so that the terminal atom involved in the halogen bond was fixed within the group. Groups having N as the terminal atom were RCN (R=CH₃ , H, and F) or RN (R=N and P), those with C as the terminal atom were RNC (R=H and F) and RC (R=O, S and Se), and those with a terminal O atom were R=C=O (R=O or S). Graphs of D e ${{D}_{{\rm { e}}}}$ versus E_XY for each group were straight lines through the origin, with generally different gradients, hence implying different N_B . By contrast, when D e / σ min ${{D}_{{\rm { e}}}/{\sigma }_{{\rm { min}}}}$ was the ordinate the lines conflated to give a single straight line, which then defines a common (reduced) nucleophilicity И_B for that group of B. Hence it was concluded that И_B is an intrinsic property of the terminal atom, independent of the remainder of B, and only weakly dependent on the type (C, N or O) of the terminal atom. Moreover, И_B for each B was the same as determined previously from the hydrogen-bonded series B⋅⋅⋅HX, (X=F, Cl, Br, I, CN, CCH, and CP).

Active Thermochemical Tables: Enthalpies of Formation of Bromo- and Iodo-Methanes, Ethenes and Ethynes

The thermochemistry of halocarbon species containing iodine and bromine is examined through an extensive interplay between new Feller-Peterson-Dixon (FPD) style composite methods and a detailed analysis of all available experimental and theoretical determinations using the thermochemical network that underlies the Active Thermochemical Tables (ATcT). From the computational viewpoint, a slower convergence of the components of composite thermochemistry methods is observed relative to species that solely contain first row elements, leading to a higher computational expense for achieving comparable levels of accuracy. Potential systematic sources of computational uncertainty are investigated, and, not surprisingly, spin-orbit coupling is found to be a critical component, particularly for iodine containing molecular species. The ATcT analysis of available experimental and theoretical determinations indicates that prior theoretical determinations have significantly larger uncertainties than originally reported, particularly in cases where molecular spin-orbit effects were ignored. Accurate and reliable heats of formation are reported for 38 halogen containing systems, based on combining the current computations with previous experimental and theoretical work via the ATcT approach.

Reduced-Scaling Double Hybrid Density Functional Theory with Rapid Basis Set Convergence through Localized Pair Natural Orbital F12

Following earlier work [Mehta, N.; Martin, J. M. L. J. Chem. Theory Comput.2022, 10.1021/acs.jctc.2c00426] that showed how the slow basis set convergence of the double hybrid density functional theory can be obviated by the use of F12 explicit correlation in the GLPT2 step (second order Görling-Levy perturbation theory), we demonstrate here for the very large and chemically diverse GMTKN55 benchmark suite that the CPU time scaling of this step can be reduced (asymptotically linearized) using the localized pair natural orbital (PNO-L) approximation at negligible cost in accuracy.

Automatic generation of complementary auxiliary basis sets for explicitly correlated methods

Explicitly correlated calculations, aside from the orbital basis set, typically require three auxiliary basis sets: Coulomb‐exchange fitting (JK), resolution of the identity MP2 (RI‐MP2), and complementary auxiliary basis set (CABS). If unavailable for the orbital basis set and chemical elements of interest, the first two can be auto‐generated on the fly using existing algorithms, but not the third. In this paper, we present a quite simple algorithm named autoCABS; a Python implementation under a free software license is offered at Github. For the cc‐pVnZ‐F12 (n = D,T,Q,5), the W4‐08 thermochemical benchmark, and the HFREQ2014 set of harmonic frequencies, we demonstrate that autoCABS‐generated CABS basis sets are comparable in quality to purpose‐optimized OptRI basis sets from the literature, and that the quality difference becomes entirely negligible as n increases.

Highly Efficient and Accurate Computation of Multiple Orbital Spaces Spanning Fock Matrix Elements on Central and Graphics Processing Units for Application in F12 Theory

We employ our recently published highly efficient seminumerical exchange (sn-LinK) [Laqua, H.; Thompson, T. H.; Kussmann, J.; Ochsenfeld, C. J. Chem. Theory Comput. 2020, 16, 1456-1468] and integral-direct resolution of the identity Coulomb (RI-J) [Kussmann, J.; Laqua, H.; Ochsenfeld, C. J. Chem. Theory Comput. 2021, 17, 1512-1521] methods to significantly accelerate the computation of the demanding multiple orbital spaces spanning Fock matrix elements present in R12/F12 theory on central and graphics processing units. The errors introduced by RI-J and sn-LinK into the RI-MP2-F12 energy are thoroughly assessed for a variety of basis sets and integration grids. We find that these numerical errors are always below "chemical accuracy" (∼1 mH) even for the coarsest settings and can easily be reduced below 1 μH by employing only moderately large integration grids and RI-J basis sets. Since the number of basis functions of the multiple orbital spaces is notably larger compared with conventional Hartree-Fock theory, the efficiency gains from the superior basis scaling of RI-J and sn-LinK (O(N_bas²) instead of O(N_bas⁴) for both) are even more significant, with maximum speedup factors of 37 000 for RI-J and 4500 for sn-LinK. In total, the multiple orbital spaces spanning Fock matrix evaluation of the largest tested structure using a triple-ζ F12 basis set (5058 AO basis functions, 9267 CABS basis functions) is accelerated over 1575× using CPUs and over 4155× employing GPUs.

Nucleophilicity of the boron atom in compounds R-B, (R = F, Cl, Br, I, CN, NC, CH3, SiH3, CF3, H): a new look at the inductive effects of the group R

Nucleophilicities N_R-B of molecules R-B (R = F, Cl, Br, I, CN, NC, CH₃, SiH₃, CF₃, H) are determined from the equilibrium dissociation energies D_e of 70 hydrogen-bonded complexes R-B⋯HX (X = F, Cl, Br, I, HCN. HCCH, HCP). The change in N_R-B relative to N_H-B of H-B allows a quantitative measure of the inductive effect I_R of each group R because only the group R affects the electron density associated with the axial non-bonding electron pair carried by the boron in R-B. An alternative definition of I_R, suggested by the strong correlation of the N_R-B values with the minimum value σ_min of the molecular electrostatic surface potential on the 0.001 e Bohr^-3 iso-surface along the R-B axis leads to excellent agreement between the two definitions.

Theoretical Study on the Structure and Dissociation Mechanism of Electronic Excited States of Nitrosyl Bromide Molecules

High-level ab initio calculations have been presented on nitrosyl bromide, BrNO, which are performed by the internally contracted explicitly correlated multireference configuration interaction (icMRCI-F12) method with Davidson correction. A total of 17 electronic states of BrNO from the ground state to the excited states at energy below 7 eV have been investigated. The energies and transitions of the states have been obtained, along with potential energy curves along the Br-N-O angle and the N-Br and N-O bond lengths. The photodissociation mechanism of the excited state involved in the UV-vis energy region has been discussed based on our calculation results. Our study would be of value to understand the interaction and dynamics of the electronic excited states and thus the photochemical processes of the BrNO molecules.

A Benchmark Protocol for DFT Approaches and Data-Driven Models for Halide-Water Clusters

Dissolved ions in aqueous media are ubiquitous in many physicochemical processes, with a direct impact on research fields, such as chemistry, climate, biology, and industry. Ions play a crucial role in the structure of the surrounding network of water molecules as they can either weaken or strengthen it. Gaining a thorough understanding of the underlying forces from small clusters to bulk solutions is still challenging, which motivates further investigations. Through a systematic analysis of the interaction energies obtained from high-level electronic structure methodologies, we assessed various dispersion-corrected density functional approaches, as well as ab initio-based data-driven potential models for halide ion-water clusters. We introduced an active learning scheme to automate the generation of optimally weighted datasets, required for the development of efficient bottom-up anion-water models. Using an evolutionary programming procedure, we determined optimized and reference configurations for such polarizable and first-principles-based representation of the potentials, and we analyzed their structural characteristics and energetics in comparison with estimates from DF-MP2 and DFT+D quantum chemistry computations. Moreover, we presented new benchmark datasets, considering both equilibrium and non-equilibrium configurations of higher-order species with an increasing number of water molecules up to 54 for each F, Cl, Br, and I anions, and we proposed a validation protocol to cross-check methods and approaches. In this way, we aim to improve the predictive ability of future molecular computer simulations for determining the ongoing conflicting distribution of different ions in aqueous environments, as well as the transition from nanoscale clusters to macroscopic condensed phases.

Reduced nucleophilicity: an intrinsic property of the Lewis base atom interacting with H in hydrogen-bonds with Lewis acids HX (X = F, Cl, Br, I, CN, CCH, CP)

Equilibrium hydrogen-bond dissociation energies De for the process B⋯HX = B + HX are calculated at the CCSD(T)(F12c)/cc-pVDZ-F12 level for ∼190 complexes B⋯HX. Reduced nucleophilicities of Lewis bases B are determined.

A reduced electrophilicity for simple Lewis acids A involved in non-covalent interactions with Lewis bases B

Dissociation energies De for B⋯A = B +A can be written De = c′NBEA, where NB and EA are the nucleophilicities and electrophilicities of the Lewis base B and the Lewis acid A, respectively.

Correlation consistent basis sets for explicitly correlated wavefunctions: Pseudopotential-based basis sets for the group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) elements

New correlation consistent basis sets for the group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) elements have been developed specifically for use in explicitly correlated F12 calculations. This includes orbital basis sets for valence only (cc-pVnZ-PP-F12, n = D, T, Q) and outer core-valence (cc-pCVnZ-PP-F12) correlation, along with both of these augmented with additional high angular momentum diffuse functions. Matching auxiliary basis sets required for density fitting and resolution-of-the-identity approaches to conventional and F12 integrals have also been optimized. All of the basis sets are to be used in conjunction with small-core relativistic pseudopotentials [Figgen et al., Chem. Phys. 311, 227 (2005)]. The accuracy of the basis sets is determined through benchmark calculation at the explicitly correlated coupled-cluster level of theory for various properties of atoms and diatomic molecules. The convergence of the properties with respect to the basis set is dramatically improved compared to conventional coupled-cluster calculations, with cc-pVTZ-PP-F12 results close to conventional estimates of the complete basis set limit. The patterns of convergence are also greatly improved compared to those observed from the use of conventional correlation consistent basis sets in F12 calculations.

Size-consistent explicitly correlated triple excitation correction

A new approach is proposed to reduce the basis set incompleteness error of the triple excitation correction in explicitly correlated coupled-cluster singles and doubles with perturbative triples calculations. Our method is similar to the intuitive triples correction approach of Knizia et al. [J. Chem. Phys. 130, 054104 (2009)] but, in contrast to the latter, is size-consistent. The new approximation is easy to implement, and its overhead is negligible with respect to the conventional (T) correction. The performance of the approach is assessed for atomization, reaction, and interaction energies as well as for bond lengths and harmonic vibrational frequencies. The advantages of its size consistency are also demonstrated.

The Electrophilicities of XCF3 and XCl (X=H, Cl, Br, I) and the Propensity of These Molecules To Form Hydrogen and Halogen Bonds with Lewis Bases: An Ab Initio Study

Equilibrium dissociation energies, De , of four series of halogen- and hydrogen-bonded complexes B⋅⋅⋅XCF3 (X=H, Cl, Br and I) are calculated ab initio at the CCSD(T)(F12c)/cc-pVDZ-F12 level. The Lewis bases B involved are N2 , CO, PH3 , C2 H2 , C2 H4 , H2 S, HCN, H2 O and NH3 . Plots of De versus NB , where the NB are the nucleophilicities assigned to the Lewis bases previously, are good straight lines through the origin, as are those for the corresponding set of complexes B⋅⋅⋅XCl. The gradients of the De versus NB plots define the electrophilicities EXCF3 and EXCl of the various Lewis acids. The determined values are: EXCF3 =2.58(22), 1.40(9), 2.15(2) and 3.04(9) for X=H, Cl, Br and I, respectively, and EXCl =4.48(22), 2.31(9), 4.37(27) and 6.06(37) for the same order of X. Thus, it is found that, for a given X, the ratio EXCl / EXCF3 is 2 within the assessed errors, and therefore appears to be independent of the atom X and of the type of non-covalent interaction (hydrogen bond or different varieties of halogen bond) in which it is involved. Consideration of the molecular electrostatic surface potentials shows that De and the maximum positive electrostatic potential σmax (the most electrophilic region of XCF3 and XCl, which lies on the symmetry axes of these molecules, near to the atom X) are strongly correlated.

A test of ab initio-generated, radial intermolecular potential energy functions for five axially-symmetric, hydrogen-bonded complexes BHF, where B = N2, CO, PH3, HCN and NH3

The radial potential energy functions for five axially symmetric, hydrogen-bonded complexes BHF (B = N₂, CO, PH₃, HCN and NH₃) have been calculated ab initio at the explicitly correlated level of theory CCSD(T)(F12c)/cc-pVTZ-F12 as a function of the hydrogen-bond distance r(ZH), where Z is the hydrogen-bond acceptor atom of B. The remaining geometric parameters were optimised at each point in the calculation. The functions so generated were then used to estimate the spectroscopic constants ω_σ, ω_σx_σ,α_σ, and the v_σ = 1 ← 0 transition wavenumber associated with the intermolecular stretching mode ν_σ of each BHF by using two equivalent approaches. Both involved the assumption that the vibrational modes of the B and HF molecules were sufficiently stiff relative to the intermolecular stretching mode that BHF could be treated in a pseudo-diatomic approximation. One approach used derivatives of the potential evaluated at the distance r = r_e while the other used the potential constants obtained by non-linear regression fits of three analytical functions (Morse, Rydberg and Hulburt-Hirschfelder) to the ab initio calculated points. The two approaches would give exactly the same results if the functions were a perfect fit. The H-H function gave the best fit. The determined spectroscopic constants were found to be in reasonable agreement with the limited number available by experiment. The efficacy of the approach was tested for the diatomic molecule H³⁵Cl by taking advantage of both an accurate RKR-type potential and an accurate set of spectroscopic constants. It was also established that the relationship D_e = k_σ/(2a²) between two measures (D_e and k_σ, both calculated ab initio) of the strength of the hydrogen bond in the BHF complexes (and required if the H-H function were an accurate representation of the BHF potential functions) holds to an excellent level of approximation, and supports the conclusion that this function is appropriate to represent the hydrogen bond in the complexes investigated.

A scaled explicitly correlated F12 correction to second-order Møller-Plesset perturbation theory

An empirically scaled version of the explicitly correlated F12 correction to second-order Møller-Plesset perturbation theory (MP2-F12) is introduced. The scaling eliminates the need for many of the most costly terms of the F12 correction while reproducing the unscaled explicitly correlated F12 interaction energy correction to a high degree of accuracy. The method requires a single, basis set dependent scaling factor that is determined by fitting to a set of test molecules. We present factors for the cc-pVXZ-F12 (X = D, T, Q) basis set family obtained by minimizing interaction energies of the S66 set of small- to medium-sized molecular complexes and show that our new method can be applied to accurately describe a wide range of systems. Remarkably good explicitly correlated corrections to the interaction energy are obtained for the S22 and L7 test sets, with mean percentage errors for the double-zeta basis of 0.60% for the F12 correction to the interaction energy, 0.05% for the total electron correlation interaction energy, and 0.03% for the total interaction energy, respectively. Additionally, mean interaction energy errors introduced by our new approach are below 0.01 kcal mol^-1 for each test set and are thus negligible for second-order perturbation theory based methods. The efficiency of the new method compared to the unscaled F12 correction is shown for all considered systems, with distinct speedups for medium- to large-sized structures.

Canonical and DLPNO-Based Composite Wavefunction Methods Parametrized against Large and Chemically Diverse Training Sets. 2: Correlation-Consistent Basis Sets, Core-Valence Correlation, and F12 Alternatives

A hierarchy of wavefunction composite methods (cWFT), based on G4-type cWFT methods available for elements H through Rn, was recently reported by the present authors [J. Chem. Theor. Comput.2020, 16, 4238]. We extend this hierarchy by considering the inner-shell correlation energy in the second-order Møller–Plesset correction and replacing the Weigend–Ahlrichs def2-mZVPP(D) basis sets used with complete basis set extrapolation from augmented correlation-consistent core–valence triple-ζ, aug-cc-pwCVTZ(-PP), and quadruple-ζ, aug-cc-pwCVQZ(-PP), basis sets, thus creating cc-G4-type methods. For the large and chemically diverse GMTKN55 benchmark suite, they represent a substantial further improvement and bring WTMAD2 (weighted mean absolute deviation) down below 1 kcal/mol. Intriguingly, the lion’s share of the improvement comes from better capture of valence correlation; the inclusion of core–valence correlation is almost an order of magnitude less important. These robust correlation-consistent cWFT methods approach the CCSD(T) complete basis limit with just one or a few fitted parameters. Particularly, the DLPNO variants such as cc-G4-T-DLPNO are applicable to fairly large molecules at a modest computational cost, as is (for a reduced range of elements) a different variant using MP2-F12/cc-pVTZ-F12 for the MP2 component.

The rotational spectrum of H2S⋯HI and an investigation by ab initio calculations of the origins of the observed doubling of rotational transitions in both H2S⋯HI and H2S⋯F2

The rotational spectrum of the complex H₂S⋯HI observed with a pulsed-jet, Fourier-transform microwave spectrometer shows that each rotational transition is split into a closely spaced doublet, a pattern similar to that observed earlier for the halogen-bonded complex H₂S⋯F₂. The origin of the doubling has been investigated by means of ab initio calculations conducted at the CCSD(T)(F12^*)/cc-pVDZ-F12 level. Two paths were examined by calculating the corresponding energy as a function of two angles. One path involved inversion of the configuration at S through a planar transition state of C_2v symmetry via changes in the angle ϕ between the C₂ axis of H₂S and the line joining the H and I nuclei [the potential energy function V(ϕ)]. The other was a torsional oscillation θ about the local C₂ axis of H₂S that also exchanges the equivalent H nuclei [the potential energy function V(θ)]. The inversion path is slightly lower in energy and much shorter in arc length and is therefore the favored tunneling pathway. In addition, calculation of V(ϕ) for the series of hydrogen- and halogen-bonded complexes H₂S⋯HX (X = F, Cl, or Br) and H₂S⋯XY (XY = Cl₂, Br₂, ClF, BrCl, or ICl) at the same level of theory revealed that doubling is unlikely to be resolved in these, in agreement with experimental observations. The barrier heights of the V(ϕ) of all ten complexes examined were found to be almost directly proportional to the dissociation energies D_e.

Chemical reactivity from the vibrational ground-state level. The role of the tunneling path in the tautomerization of urea and derivatives

Recent developments of low-temperature techniques are providing valuable knowledge about chemical processes that manifest in the quantum regimen. The tunneling effect from the vibrational ground-state is the main mechanism of these reactions, which usually involves the motion or transfer of hydrogen atoms. Theoretical methods can enrich the information supplied by these experimental methods through an insightful analysis of the tunneling process. In this context, canonical variational transition state theory with multidimensional tunneling corrections (CVT/MT) can handle this type of reaction, and it has been applied to several systems within the small-curvature approximation for tunneling (SCT). This method is of proven reliability for polyatomic reactions occurring at room temperature and above, but no tests have been performed to check its performance when only the lowest energy level is populated. In this work, we compare SCT against the least-action tunneling (LAT) method to study the tautomerization and cis-trans interconversion reactions in the enol forms of urea, thiourea, and selenourea. To the best of our knowledge, this is the first time that the LAT method is applied to a polyatomic reaction occurring in the deep-tunneling region. The theoretical results indicate that the reaction mechanisms are controlled by tunneling. The SCT and LAT tautomerization reaction times are in good agreement with the experimental values; however, LAT seems superior to SCT for reactions (tautomerizations) that involve moderate reaction path curvature, whereas the opposite is true for reactions with small curvature (interconversions). These results led us to introduce and recommend the microcanonically optimized tunneling path that selects the tunneling probability as the maximum between the SCT and LAT tunneling probabilities.

The Molpro quantum chemistry package

Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework.

A Simple Model for Halogen Bond Interaction Energies

Halogen bonds are prevalent in many areas of chemistry, physics, and biology. We present a statistical model for the interaction energies of halogen-bonded systems at equilibrium based on high-accuracy ab initio benchmark calculations for a range of complexes. Remarkably, the resulting model requires only two fitted parameters, X and B—one for each molecule—and optionally the equilibrium separation, R e , between them, taking the simple form E = X B / R e n . For n = 4 , it gives negligible root-mean-squared deviations of 0.14 and 0.28 kcal mol - 1 over separate fitting and validation data sets of 60 and 74 systems, respectively. The simple model is shown to outperform some of the best density functionals for non-covalent interactions, once parameters are available, at essentially zero computational cost. Additionally, we demonstrate how it can be transferred to completely new, much larger complexes and still achieve accuracy within 0.5 kcal mol - 1 . Using a principal component analysis and symmetry-adapted perturbation theory, we further show how the model can be used to predict the physical nature of a halogen bond, providing an efficient way to gain insight into the behavior of halogen-bonded systems. This means that the model can be used to highlight cases where induction or dispersion significantly affect the underlying nature of the interaction.

A variationally computed room temperature line list for AsH3

Calculations are reported on the rotation–vibration energy levels of the arsine molecule with associated transition intensities.

Gaussian basis sets for use in correlated molecular calculations. XI. Pseudopotential-based and all-electron relativistic basis sets for alkali metal (K-Fr) and alkaline earth (Ca-Ra) elements

New correlation consistent basis sets based on pseudopotential (PP) Hamiltonians have been developed from double- to quintuple-zeta quality for the late alkali (K-Fr) and alkaline earth (Ca-Ra) metals. These are accompanied by new all-electron basis sets of double- to quadruple-zeta quality that have been contracted for use with both Douglas-Kroll-Hess (DKH) and eXact 2-Component (X2C) scalar relativistic Hamiltonians. Sets for valence correlation (ms), cc-pVnZ-PP and cc-pVnZ-(DK,DK3/X2C), in addition to outer-core correlation [valence + (m-1)sp], cc-p(w)CVnZ-PP and cc-pwCVnZ-(DK,DK3/X2C), are reported. The -PP sets have been developed for use with small-core PPs [I. S. Lim et al., J. Chem. Phys. 122, 104103 (2005) and I. S. Lim et al., J. Chem. Phys. 124, 034107 (2006)], while the all-electron sets utilized second-order DKH Hamiltonians for 4s and 5s elements and third-order DKH for 6s and 7s. The accuracy of the basis sets is assessed through benchmark calculations at the coupled-cluster level of theory for both atomic and molecular properties. Not surprisingly, it is found that outer-core correlation is vital for accurate calculation of the thermodynamic and spectroscopic properties of diatomic molecules containing these elements.

Computational Comparison of Different Reagent Ions in the Chemical Ionization of Oxidized Multifunctional Compounds

High pressure anion chemical ionization is commonly used for the detection of neutral molecules in the gas phase. The detection efficiency in these measurements depends on how strongly the reagent ion binds to the neutral target molecule. We have calculated the binding strength of nitrate (NO₃^-), acetate (CH₃C(O)O^-), lactate (CH₃CH(OH)C(O)O^-), trifluoroacetate (CF₃C(O)O^-), trifluoromethanolate (CF₃O^-), bromide (Br^-), and iodide (I^-) reagent ions to ten different products derived from the OH radical-initiated oxidation of butadiene. We found that the binding of these oxidation products to the reagent ions depends almost linearly on the number of oxygen atoms in the target molecule, with the precise chemical identity of the compound (e.g., the number and relative position of hydroxyl or hydroperoxy groups) playing a more minor role. For acetate, the formation free energy decreases on average by around 4 kcal/mol when the number of oxygen atoms in the sample molecule increases by one. For the other reagent ions the corresponding decrease is around 3 kcal/mol. For all of the molecules studied, acetate forms the most stable clusters and I^- the least stable. We also investigated the effect of humidity on the chemical ionization by calculating how strongly water molecules bind to both the reagent ions and the ion-molecule clusters. Water binds much more strongly to the reagent ion monomers compared to the reagent ion "dimers" (defined here as a cluster of the reagent anion with the corresponding neutral conjugate acid, e.g., HNO₃(NO₃^-)) or the ion-molecule clusters. This likely leads to a stronger humidity dependence when using reagent ions that are not able to form reagent ion dimers (such as CF₃C(O)O^-, CF₃O^-, Br^-, and I^-).

UV photodissociation dynamics of CHI2Cl and its role as a photolytic precursor for a chlorinated Criegee intermediate

Photolysis of geminal diiodoalkanes in the presence of molecular oxygen has become an established route to the laboratory production of several Criegee intermediates, and such compounds also have marine sources. Here, we explore the role that the trihaloalkane, chlorodiiodomethane (CHI₂Cl), may play as a photolytic precursor for the chlorinated Criegee intermediate ClCHOO. CHI₂Cl has been synthesized and its UV absorption spectrum measured; relative to that of CH₂I₂ the spectrum is shifted to longer wavelength and the photolysis lifetime is calculated to be less than two minutes. The photodissociation dynamics have been investigated using DC slice imaging, probing ground state I and spin-orbit excited I* atoms with 2 + 1 REMPI and single-photon VUV ionization. Total translational energy distributions are bimodal for I atoms and unimodal for I*, with around 72% of the available energy partitioned in to the internal degrees of freedom of the CHICl radical product, independent of photolysis wavelength. A bond dissociation energy of D₀ = 1.73 ± 0.11 eV is inferred from the wavelength dependence of the translational energy release, which is slightly weaker than typical C-I bonds. Analysis of the photofragment angular distributions indicate dissociation is prompt and occurs primarily via transitions to states of A'' symmetry. Complementary high-level MRCI calculations, including spin-orbit coupling, have been performed to characterize the excited states and confirm that states of A'' symmetry with highly mixed singlet and triplet character are predominantly responsible for the absorption spectrum. Transient absorption spectroscopy has been used to measure the absorption spectrum of ClCHOO produced from the reaction of CHICl with O₂ over the range 345-440 nm. The absorption spectrum, tentatively assigned to the syn conformer, is at shorter wavelengths relative to that of CH₂OO and shows far weaker vibrational structure.

C(sp3 )-H Bond Activation by Vinylidene Gold(I) Complexes: A Concerted Asynchronous or Stepwise Process?

A detailed analysis of the C(sp³ )-H activation process by vinylidene Au^I complexes is described based on an intrinsic bond orbital analysis. Based on our analysis this event can be divided into three phases: (i) hydride transfer, (ii) C-C bond formation, and (iii) σ to π rearrangement of the lone pair coordinated to Au. Small perturbations of the system lead to either a concerted asynchronous reaction, or a stepwise reaction featuring an intermediate with a C-H-C three-centre two-electron (3c-2e) bond. The role of π-donating substituents is highlighted and provides a way of controlling reactions of this type in future experimental studies.

Exploring the structure and photodissociation mechanism of the electronic states of iodocarbene, CHI: a theoretical contribution

Interactions between the electronic states of CHI were investigated and the dissociation mechanism was explored in the ultraviolet region.

Ab initio studies of the Rg-NO(+)(X(1)Σ(+)) van der Waals complexes (Rg = He, Ne, Ar, Kr, and Xe)

We used the explicitly correlated variant of the coupled clusters method with single, double, and noniterative triple excitations [CCSD(T)-F12] to compute two-dimensional potential energy surfaces of van der Waals complexes formed by rare gas atoms (Rg) and NO(+)(X(1)Σ(+)) cations. We used the correlation-consistent, triple-zeta (cc-pVTZ-F12) atomic basis sets, and for Kr and Xe rare gases, we employed corresponding pseudopotential cc-pVTZ-PP-F12 atomic basis sets. These basis sets were additionally augmented with mid-bond functions. The complexes are all of skewed T-shape type with Rg atom being closer to the N-side. Using analytical representation of the potentials, we have estimated zero-point energy corrected dissociation energies from anharmonic calculations with BOUND program and also from the harmonic approximation. The binding energies increase with the polarization of the Rg atom in series from He to Xe and are 196 cm(-1), 360 cm(-1), 1024 cm(-1), 1434 cm(-1), and 2141 cm(-1), respectively. Their corresponding dissociation energies are 132 cm(-1), 300 cm(-1), 927 cm(-1), 1320 cm(-1), and 1994 cm(-1) for the complexes with He to Xe, respectively. We find good agreement with previous theoretical and experimental results. The harmonic vibrational frequencies were calculated for the bending and stretching modes of the Rg-NO(+) complexes.