The Impact of Larger Basis Sets and Explicitly Correlated Coupled Cluster Theory on the Feller–Peterson–Dixon Composite Method

Potential energy surfaces and dynamic properties via ab initio composite and density functional approaches

Vibrational spectroscopy enables critical insight into the structural and dynamic properties of molecules. Presently, the majority of theoretical approaches to spectroscopy employ wavefunction-based ab initio or density functional methods that rely on the harmonic approximation. This approximation breaks down for large molecules with strongly anharmonic bonds or for molecules with large internuclear separations. An alternative to these methods involves generating molecular anharmonic potential energy surfaces (potentials) and using them to extrapolate the vibrational frequencies. This study examines the efficacy of density functional theory (DFT) and the correlation consistent Composite Approach (ccCA) in generating anharmonic frequencies from potentials of small main group molecules. Vibrational self-consistent field Theory (VSCF) and post-VSCF methods were used to calculate the fundamental frequencies of these molecules from their potentials. Functional choice, basis set selection, and mode-coupling are also examined as factors in influencing accuracy. The absolute deviations for the calculated frequencies using potentials at the ccCA level of theory were lower than the potentials at the DFT level. With DFT resulting in bending modes that are better described than those of ccCA, a multilevel DFT:ccCA approach where DFT potentials are used for single vibrational mode potentials and ccCA is used for vibrational mode-mode couplings can be utilized for larger polyatomic systems. The frequencies obtained with this multilevel approach using VCIPSI-PT2 were closer to experimental frequencies than the scaled harmonic frequencies, indicating the success of utilizing post-VSCF methods to generate more accurate representations of computed infrared spectra.

Approaching the Complete Basis Set Limit for Spin-State Energetics of Mononuclear First-Row Transition Metal Complexes

Convergence to the complete basis set (CBS) limit is analyzed for the problem of spin-state energetics in mononuclear first-row transition metal (TM) complexes by taking under scrutiny a benchmark set of 18 energy differences between spin states for 13 chemically diverse TM complexes. The performance of conventional CCSD(T) and explicitly correlated CCSD(T)-F12a/b calculations in approaching the CCSD(T)/CBS limits is systematically studied. An economic computational protocol is developed based on the CCSD-F12a approximation and (here proposed) modified scaling of the perturbative triples term (T#). This computational protocol recovers the relative spin-state energetics of the benchmark set in excellent agreement with the reference CCSD(T)/CBS limits (mean absolute deviation of 0.4, mean signed deviation of 0.2, and maximum deviation of 0.8 kcal/mol) and enables performing canonical CCSD(T) calculations for mononuclear TM complexes sized up to ca. 50 atoms, which is illustrated by application to heme-related metalloporphyrins. Furthermore, a good transferability of the basis set incompleteness error (BSIE) is demonstrated for spin-state energetics computed using CCSD(T) and other wave function methods (MP2, CASPT2, CASPT2/CC, NEVPT2, and MRCI + Q), which justifies efficient focal-point approximations and simplifies the construction of multimethod benchmark studies.

W4Λ: Leveraging Λ Coupled-Cluster for Accurate Computational Thermochemistry Approaches

High-accuracy composite wave function methods like Weizmann-4 (W4) theory, high-accuracy extrapolated ab initio thermochemistry (HEAT), and the Feller-Peterson-Dixon (FPD) approach enable sub-kJ/mol accuracy in gas-phase thermochemical properties. Their biggest computational bottleneck is the evaluation of the valence post-CCSD(T) correction term. We demonstrate here, for the W4-17 thermochemistry benchmark and subsets thereof, that the Λ coupled-cluster expansion converges more rapidly and smoothly than the regular coupled-cluster series. By means of CCSDT(Q)Λ and CCSDTQ(5)Λ, we can considerably (up to an order of magnitude) accelerate W4- and W4.3-type calculations without loss in accuracy, leading to the W4Λ and W4.3Λ computational thermochemistry protocols.

Supersonically expanded sodium metal-dilute halogen gas interactions. The importance of reaction populated and energy storing reservoir states and population inversion created amplification in Na2

The reactions of Cl, Br, and I with Nan=2,3 produced in a supersonic expansion form Na2* and Na* excited states extending across the visible and ultraviolet regions. Emission in the region extending from 410 to 600 nm indicates selectively formed excited state Na2 emission features. Experimental evidence suggests that this emission is associated with Na3 + X reactions. Broadband (0.5 cm-1) laser measurements demonstrate gain (population inversion) for select features at∼524-528(1%), ∼492(0.3%), and ∼458.7-461(0.8%) nm. Single mode (0.007 cm-1) measurements extending from 528.03 to 527.63 nm demonstrate amplification involving five to six individual rovibronic levels with a maximum gain close to 3% recorded at 527.9 nm. The observed gain is associated with select transitions from levels of the Na2 11Πu state populated, via identified curve crossings, through collision induced transfer from long-lived Na2 21Σg+ and 11Πg reservoir states. Collision induced population buildup in the lowest vibrational levels of these reservoir states and collision induced transfer to the Na2 11Πu state create a population inversion in transitions to the X 1Σg+ state of Na2. The observed amplification is aided by rapid vibrational and rotational relaxation in both the Na2 ground and excited reservoir states producing amplifiers in the visible region like the HF amplifier in the infrared. This study suggests the importance of reaction populated and energy storing long-lived reservoir states in small sodium molecule combustion processes and indicates the potential for providing new short wavelength visible and ultraviolet amplifiers for future laser-based chemical propulsion concepts.

Prediction of Aqueous Reduction Potentials of X•, ChH•, and XO• Radicals with X = Halogen and Ch = Chalcogen

The aqueous electron affinity and aqueous reduction potentials for F•, Cl•, Br•, I•, OH•, SH•, SeH•, TeH•, ClO•, BrO•, and IO• were calculated using electronic structure methods for explicit cluster models coupled with a self-consistent reaction field (SMD) to treat the aqueous solvent. Calculations were conducted using MP2 and correlated molecular orbital theory up to the CCSD(T)-F12b level for water tetramer clusters and MP2 for octamer cluster. Inclusion of explicit waters was found to be important for accurately predicting the redox potentials in a number of cases. The calculated reduction potentials for X• and ChH• were predicted to within ∼0.1 V of the reported literature values. Fluorine is anomalous due to abstraction of a hydrogen from one of the surrounding water molecules to form a hydroxyl radical and hydrogen fluoride, so its redox potential was calculated using only an implicit model. Larger deviations from experiment were predicted for ClO• and BrO•. These deviations are due to the free energy of solvation of the anion being too negative, as found in the pKa calculations, and that for the neutral being too positive with the current approach.

Ab Initio Rovibrational Spectroscopy of the Acetylide Anion

In this work the rovibrational spectrum of the acetylide anion HCC- is investigated using high-level electronic structure methods and variational rovibrational calculations. Using a composite approach the potential energy surface and dipole surface is constructed from explicitly correlated coupled-cluster accounting for corrections due to core-valence correlation, scalar relativistic effects and higher-order excitation effects. Previous approaches for approximating the latter are critically evaluated. Employing the composite potential, accurate spectroscopic parameters determined from variational calculations are presented. In comparison to the few available reference data the present results show excellent agreement with ground state rotational constants within 0.005% of the experimental value. Intensities determined from the variational calculations suggest the bending fundamental transition ν2 around 510 cm-1 to be the best target for detection. The rather weak CD stretching fundamental ν1 in deuterated isotopologues show a second-order resonance with the (0,20,1) state and the consequences are discussed in some detail. The spectroscopic parameters and band intensities provided for a number of vibrational bands in isotopologues of the acetylide anion should facilitate future spectroscopic investigations.

Energetic and Electronic Properties of NpH0/+/- and PuH0/+/

High-level correlated molecular orbital theory calculations have been performed to predict the thermodynamic and electronic properties of diatomic NpH^0/+/- and PuH^0/+/-. The excited states up to ∼10,000 cm^-1 were predicted for these molecules at the multireference SO-CASPT2 level. The inclusion of spin-orbit effects is fundamental to predict the low-lying state ordering. NpH is predicted to have a ⁵Π₀ ground state, and PuH has a ⁶Π_1/2 ground state at the SO-CASPT2 level. The adiabatic electron affinities (AEAs) and ionization energies (IEs) of NpH and PuH were calculated to be 0.389 and 6.156 and 0.396 and 6.296 eV, respectively, using the Feller-Peterson-Dixon approach. The AEA increases going from AcH (0.425 eV) to ThH (0.820 eV) and decreases from ThH to PuH. The IEs of Pa-Np hydrides are close to ∼6.2 eV followed by an increase of 0.14 eV to PuH (6.296 eV). The An-H bond dissociation energy (BDE) decreases from 276.4 (AcH) to 107.1 (PuH) kJ/mol; the BDE(NpH) is ∼80 kJ/mol higher than that of PuH. Natural bond orbital calculations show that the bond character for these molecules is mainly ionic, An⁺H^-. The additional electron in NpH^- and PuH^- populates the 6d orbital, and NpH⁺ and PuH⁺ are formed by the removal of a 7s electron. The current work in conjunction with prior work on the AcH to UH in different charge states provides insights into how these properties change across the actinide series.

MP2-F12 Basis Set Convergence near the Complete Basis Set Limit: Are h Functions Sufficient?

We have investigated the title question for the W4-08 thermochemical benchmark using l-saturated truncations of a large reference (REF) basis set, as well as for standard F12-optimized basis sets. With the REF basis set, the root-mean-square (RMS) contribution of i functions to the MP2-F12 total atomization energies (TAEs) is about 0.01 kcal/mol, the largest individual contributions being 0.04 kcal/mol for P₂ and P₄. However, even for these cases, basis set extrapolation from {g,h} basis sets adequately addresses the problem. Using basis sets insufficiently saturated in the spdfgh angular momenta may lead to exaggerated i function contributions. For extrapolation from spdfg and spdfgh basis sets, basis set convergence appears to be quite close to the theoretical asymptotic ∝ L^–7 behavior. We hence conclude that h functions are sufficient even for highly demanding F12 applications. With one-parameter extrapolation, spdf and spdfg basis sets are adequate, aug-cc-pV{T,Q}Z-F12 yielding a RMSD = 0.03 kcal/mol. A limited exploration of CCSD(F12*) and CCSD-F12b suggests our conclusions are applicable to higher-level F12 methods as well.

Predicting the Mechanism and Products of CO2 Capture by Amines in the Presence of H2O

An extensive correlated molecular orbital theory study of the reactions of CO₂ with a range of substituted amines and H₂O in the gas phase and aqueous solution was performed at the G3(MP2) level with a self-consistent reaction field approach. The G3(MP2) calculations were benchmarked at the CCSD(T)/CBS level for NH₃ reactions. A catalytic NH₃ reduces the energy barrier more than a catalytic H₂O for the formation of H₂NCOOH and H₂CO₃. In aqueous solution, the barriers to form both H₂NCOOH and H₂CO₃ are reduced, with HCO₃^- formation possible with one amine present and H₂NCOO^- formation possible only with two amines. Further reactions of H₂NCOOH to form HNCO and urea via the Bazarov reaction have high barriers and are unlikely in both the gas phase and aqueous solution. Reaction coordinates for CH₃NH₂, CH₃CH₂NH₂, (CH₃)₂NH, CH₃CH₂CH₂NH₂, (CH₃)₃N, and DMAP were also calculated. The barrier for proton transfer correlates with amine basicity for alkylammonium carbamate (ΔG^‡_aq < 15 kcal/mol) and alkylammonium bicarbonate (ΔG^‡_aq < 30 kcal/mol) formation. In aqueous solution, carbamic acids, carbamates, and bicarbonates can all form in small amounts with ammonium carbamates dominating for primary and secondary alkylamines. These results have implications for CO₂ capture by amines in both the gas phase and aqueous solution as well as in the solid state, if enough water is present.

The electron affinity of the uranium atom

The results of a combined experimental and computational study of the uranium atom are presented with the aim of determining its electron affinity. Experimentally, the electron affinity of uranium was measured via negative ion photoelectron spectroscopy of the uranium atomic anion, U^-. Computationally, the electron affinities of both thorium and uranium were calculated by conducting relativistic coupled-cluster and multi-reference configuration interaction calculations. The experimentally determined value of the electron affinity of the uranium atom was determined to be 0.309 ± 0.025 eV. The computationally predicted electron affinity of uranium based on composite coupled cluster calculations and full four-component spin-orbit coupling was found to be 0.232 eV. Predominately due to a better convergence of the coupled cluster sequence for Th and Th^-, the final calculated electron affinity of Th, 0.565 eV, was in much better agreement with the accurate experimental value of 0.608 eV. In both cases, the ground state of the anion corresponds to electron attachment to the 6d orbital.

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.

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.

Canonical and DLPNO-Based G4(MP2)XK-Inspired Composite Wave Function Methods Parametrized against Large and Chemically Diverse Training Sets: Are They More Accurate and/or Robust than Double-Hybrid DFT?

The large and chemically diverse GMTKN55 benchmark was used as a training set for parametrizing composite wave function thermochemistry protocols akin to G4(MP2)XK theory (Chan, B.; Karton, A.; Raghavachari, K. J. Chem. Theory Comput. 2019, 15, 4478–4484). On account of their availability for elements H through Rn, Karlsruhe def2 basis sets were employed. Even after reparametrization, the GMTKN55 WTMAD2 (weighted mean absolute deviation, type 2) for G4(MP2)-XK is actually inferior to that of the best rung-4 DFT functional, ωB97M-V. By increasing the basis set for the MP2 part to def2-QZVPPD, we were able to substantially improve performance at modest cost (if an RI-MP2 approximation is made), with WTMAD2 for this G4(MP2)-XK-D method now comparable to the better rung-5 functionals (albeit at greater cost). A three-tier approach with a scaled MP3/def2-TZVPP intermediate step, however, leads to a G4(MP3)-D method that is markedly superior to even the best double hybrids ωB97M(2) and revDSD-PBEP86-D4. Evaluating the CCSD(T) component with a triple-ζ, rather than split-valence, basis set yields only a modest further improvement that is incommensurate with the drastic increase in computational cost. G4(MP3)-D and G4(MP2)-XK-D have about 40% better WTMAD2, at similar or lower computational cost, than their counterparts G4 and G4(MP2), respectively: detailed comparison reveals that the difference lies in larger molecules due to basis set incompleteness error. An E2/{T,Q} extrapolation and a CCSD(T)/def2-TZVP step provided the G4-T method of high accuracy and with just three fitted parameters. Using KS orbitals in MP2 leads to the G4(MP3|KS)-D method, which entirely eliminates the CCSD(T) step and has no steps costlier than scaled MP3; this shows a path forward to further improvements in double-hybrid density functional methods. None of our final selections require an empirical HLC correction; this cuts the number of empirical parameters in half and avoids discontinuities on potential energy surfaces. G4-T-DLPNO, a variant in which post-MP2 corrections are evaluated at the DLPNO-CCSD(T) level, achieves nearly the accuracy of G4-T but is applicable to much larger systems.

Electronic Structure Predictions of the Energetic Properties of Tellurium Fluorides

The heats of formation, bond dissociation energies (BDEs), fluoride affinities (FA), fluorocation affinities (FCA), electron affinities (EA), and ionization energies (IP) of TeF _n ( n = 1-6) have been predicted using the Feller-Peterson-Dixon (FPD) approach. To benchmark the approach, the bond dissociation energies of Te₂ and TeO, the heats of formation of Te₂, TeH₂, TeO, and TeO₂, and the electron affinity for TeO and TeO₂ were calculated as there are experimental thermodynamic data available for these tellurium compounds, which allow confirmation of the heat of formation of Te gas as Δ H_f,0K(Te) = 50.7 ± 0.6 kcal/mol. Spin-orbit corrections are required for good results and cannot be ignored. A comparison among fluoride affinities, fluorocation affinities, electron affinities, and ionization energies of TeF _n and SeF _n is reported.

Gas Phase Silver Thermochemistry from First Principles

Domain-based local pair natural orbital coupled cluster approach with single, double, and perturbative triple excitations, DLPNO-CCSD(T), has been applied within a framework of a reduced version of the reaction-based Feller-Peterson-Dixon (FPD) scheme to predict gas phase heats of formation and absolute entropies of silver inorganic and organometallic compounds. First, we evaluated all existing experimental data currently limited by thermodynamic functions of 10 silver substances (AgH, AgF, AgBr, AgI, Ag₂, Ag₂S, Ag₂Se, Ag₂Te, AgCN, AgPO₂). The mean average deviation between computed and experimental heats of formation was found to be 1.9 kcal/mol. Notably, all predicted heats of formation turned out to be within the error bounds of their experimental counterparts. Second, we predicted heats of formation and entropies for additional 90 silver species with no experimental data available, substantially enriching silver thermochemistry. Combination of gas phase heats of formation Δ H_f and entropies S° of AgNO₂, AgSCN, Ag₂SO₄, and Ag₂SeO₄ obtained in this work, with respective solid-state information, resulted in accurate sublimation thermochemistry of these compounds. Complementation of predicted Δ H_f with heats of formation of some neutrals and positive ions produced 33 silver bond strengths of high reliability. Obtained thermochemical data are promising for developing the concepts of silver chemistry. In addition, derived heats of formation and bond dissociation enthalpies, due to their high diversity, are found to be relevant for testing and training of computational chemistry methods.

High Accuracy ab Initio Calculations of Rotational-Vibrational Levels of the HCN/HNC System

Highly accurate ab initio calculations of vibrational and rotational-vibrational energy levels of the HCN/HNC (hydrogen cyanide/hydrogen isocyanide) isomerising system are presented for several isotopologues. All-electron multireference configuration interaction (MRCI) electronic structure calculations were performed using basis sets up to aug-cc-pCV6Z on a grid of 1541 geometries. The ab initio energies were used to produce an analytical potential energy surface (PES) describing the two minima simultaneously. An adiabatic Born-Oppenheimer diagonal correction (BODC) correction surface as well as a relativistic correction surface were also calculated. These surfaces were used to compute vibrational and rotational-vibrational energy levels up to 25 000 cm^-1 which reproduce the extensive set of experimentally known HCN/HNC levels with a root-mean-square deviation σ = 1.5 cm^-1. We studied the effect of nonadiabatic effects by introducing opportune radial and angular corrections to the nuclear kinetic energy operator. Empirical determination of two nonadiabatic parameters results in observed energies up to 7000 cm^-1 for four HCN isotopologues (HCN, DCN, H¹³CN, and HC¹⁵N) being reproduced with σ = 0.37 cm^-1. The height of the isomerization barrier, the isomerization energy and the dissociation energy were computed using a number of models; our best results are 16 809.4, 5312.8, and 43 729 cm^-1, respectively.