The MRCC program system: Accurate quantum chemistry from water to proteins

Three-Component Reaction of 3-Formyl-6-Methylchromone, Primary Amines, and Secondary Phosphine Oxides: A Synthetic and Mechanistic Study

A fast, mild, and efficient catalyst-free approach has been developed for the synthesis of chromonyl-substituted α-aminophosphine oxides by the three-component reaction of 3-formyl-6-methylchromone, primary amines, and secondary phosphine oxides at ambient temperature. Carrying out the reaction with aliphatic amines or aminoalcohols at a higher temperature (80 °C), phosphinoyl-functionalized 3-aminomethylene chromanones were formed instead of the corresponding chromonyl-substituted α-aminophosphine oxides. No reaction occurred when 3-formyl-6-methylchromone and secondary phosphine oxides were reacted with aromatic amines in the absence of any catalyst. Applying a basic catalyst, the formation of the phosphinoyl-functionalized 3-aminomethylene chromanones was observed; however, the reaction was not complete. Detailed experimental and quantum chemical studies were performed to study the transformation. Moreover, the in vitro cytotoxicity of phosphinoyl-functionalized 3-aminomethylene chromanones was also investigated in three different cell lines, such as human lung adenocarcinoma (A549), mouse fibroblast (NIH/3T3), and human promyelocytic leukemia (HL60) cells. Several derivatives showed modest activity against the human promyelocytic leukemia (HL60) cell line.

Ground- and Excited-State Dipole Moments and Oscillator Strengths of Full Configuration Interaction Quality

We report ground- and excited-state dipole moments and oscillator strengths (computed in different "gauges" or representations) of full configuration interaction (FCI) quality using the selected configuration interaction method known as Configuration Interaction using a Perturbative Selection made Iteratively (CIPSI). Thanks to a set encompassing 35 ground- and excited-state properties computed in 11 small molecules, the present near-FCI estimates allow us to assess the accuracy of high-order coupled-cluster (CC) calculations including up to quadruple excitations. In particular, we show that incrementing the excitation degree of the CC expansion (from CC with singles and doubles (CCSD) to CC with singles, doubles, and triples (CCSDT) or from CCSDT to CC with singles, doubles, triples, and quadruples (CCSDTQ)) reduces the average error with respect to the near-FCI reference values by approximately 1 order of magnitude.

Toward Large-Scale Restricted Active Space Calculations Inspired by the Schmidt Decomposition

We present an alternative, memory-efficient, Schmidt decomposition-based description of the inherently bipartite restricted active space (RAS) scheme, which can be implemented effortlessly within the density matrix renormalization group (DMRG) method via the dynamically extended active space procedure. Benchmark calculations are compared against state-of-the-art results of C₂ and Cr₂, which are notorious for their multireference character. Our results for ground and excited states together with spectroscopic constants demonstrate that the proposed novel approach, dubbed as DMRG-RAS, which is variational and free of uncontrolled method errors, has the potential to outperfom conventional methods for strongly correlated molecules.

Benchmark Ab Initio Determination of the Conformers, Proton Affinities, and Gas-Phase Basicities of Cysteine

A systematic conformational mapping combined with literature data leads to 85 stable neutral cysteine conformers. The implementation of the same mapping process for the protonated counterparts reveals 21 N-(amino-), 64 O-(carbonyl-), and 37 S-(thiol-)protonated cysteine conformers. Their relative energies and harmonic vibrational frequencies are given at the MP2/aug-cc-pVDZ level of theory. Further benchmark ab initio computations are performed for the 10 lowest-lying neutral and protonated amino acid conformers (for each type) such as CCSD(T)-F12a/cc-pVDZ-F12 geometry optimizations (and frequency computations for cysteine) as well as auxiliary correction computations of the basis set effects up to CCSD(T)-F12b/cc-pVQZ-F12, electron correlation effects up to CCSDT(Q), core correlation effects, second-order Douglass-Kroll relativistic effects, and zero-point energy contributions. Boltzmann-averaged 0 (298.15) K proton affinity and [298.15 K gas-phase basicity] values of cysteine are predicted to be 214.96 (216.39) [208.21], 201.83 (203.55) [194.16], and 193.31 (194.74) [186.40] kcal/mol for N-, O-, and S-protonation, respectively, also considering the previously described auxiliary corrections.

Basis Set Limit CCSD(T) Energies for Extended Molecules via a Reduced-Cost Explicitly Correlated Approach

Several approximations are introduced and tested to reduce the computational expenses of the explicitly correlated coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method for both closed and open-shell species. First, the well-established frozen natural orbital (FNO) technique is adapted to explicitly correlated CC approaches. Second, our natural auxiliary function (NAF) scheme is employed to reduce the size of the auxiliary basis required for the density fitting approximation regularly used in explicitly correlated calculations. Third, a new approach, termed the natural auxiliary basis (NAB) approximation, is proposed to decrease the size of the auxiliary basis needed for the expansion of the explicitly correlated geminals. The performance of the above approximations and that of the combined FNO-NAF-NAB approach are tested for atomization and reaction energies. Our results show that overall speedups of 7-, 5-, and 3-times can be achieved with double-, triple-, and quadruple-ζ basis sets, respectively, without any loss in accuracy. The new method can provide, e.g., reaction energies and barrier heights well within chemical accuracy for molecules with more than 40 atoms within a few days using a few dozen processor cores, and calculations with 50+ atoms are still feasible. These routinely affordable computations considerably extend the reach of explicitly correlated CCSD(T).

Performance of Localized-Orbital Coupled-Cluster Approaches for the Conformational Energies of Longer n-Alkane Chains

We report an update and enhancement of the ACONFL (conformer energies of large alkanes [J. Phys. Chem. A2022,126, 3521-3535]) dataset. For the ACONF12 (n-dodecane) subset, we report basis set limit canonical coupled-cluster with singles, doubles, and perturbative triples [i.e., CCSD(T)] reference data obtained from the MP2-F12/cc-pV{T,Q}Z-F12 extrapolation, [CCSD(F12*)-MP2-F12]/aug-cc-pVTZ-F12, and a (T) correction from conventional CCSD(T)/aug-cc-pV{D,T}Z calculations. Then, we explored the performance of a variety of single and composite localized-orbital CCSD(T) approximations, ultimately finding an affordable localized natural orbital CCSD(T) [LNO-CCSD(T)]-based post-MP2 correction that agrees to 0.006 kcal/mol mean absolute deviation with the revised canonical reference data. In tandem with canonical MP2-F12 complete basis set extrapolation, this was then used to re-evaluate the ACONF16 and ACONF20 subsets for n-hexadecane and n-icosane, respectively. Combining those with the revised canonical reference data for the dodecane conformers (i.e., ACONF12 subset), a revised ACONFL set was obtained. It was then used to assess the performance of different localized-orbital coupled-cluster approaches, such as pair natural orbital localized CCSD(T) [PNO-LCCSD(T)] as implemented in MOLPRO, DLPNO-CCSD(T0) and DLPNO-CCSD(T1) as implemented in ORCA, and LNO-CCSD(T) as implemented in MRCC, at their respective "Normal", "Tight", "vTight", and "vvTight" accuracy settings. For a given accuracy threshold and basis set, DLPNO-CCSD(T1) and DLPNO-CCSD(T0) perform comparably. With "VeryTightPNO" cutoffs, explicitly correlated DLPNO-CCSD(T1)-F12/VDZ-F12 is the best pick among all the DLPNO-based methods tested. To isolate basis set incompleteness from localized-orbital-related truncation errors (domain, LNOs), we have also compared the localized coupled-cluster approaches with canonical DF-CCSD(T)/aug-cc-pVTZ for the ACONF12 set. We found that gradually tightening the cutoffs improves the performance of LNO-CCSD(T), and using a composite scheme such as vTight + 0.50[vTight - Tight] improves things further. For DLPNO-CCSD(T1), "TightPNO" and "VeryTightPNO" offer a statistically similar accuracy, which gets slightly better when TCutPNO is extrapolated to the complete PNO space limit. Similar to Brauer et al.'s [Phys. Chem. Chem. Phys.2016,18 (31), 20905-20925] previous report for the S66x8 noncovalent interactions, the dispersion-corrected direct random phase approximation (dRPA)-based double hybrids perform remarkably well for the ACONFL set. While the revised reference data do not affect any conclusions on the less accurate methods, they may upend orderings for more accurate methods with error statistics on the same order as the difference between reference datasets.

New Local Explorations of the Unitary Coupled Cluster Energy Landscape

The recent quantum information boom has effected a resurgence of interest in the unitary coupled cluster (UCC) theory. Our group's interest in local energy landscapes of unitary ansätze prompted us to investigate the classical approach of truncating the Taylor series expansion (instead of a perturbative expansion) of the UCC with singles and doubles (UCCSD) energy at the second order. This amounts to an approach where the electron correlation energy is estimated by taking a single Newton-Raphson step from Hartree-Fock toward UCCSD. Such an approach has been explored previously, but the accuracy was not extensively studied. In this paper, we investigate the performance and observe similar pathologies to the linearized coupled cluster with singles and doubles. We introduce the use of derivatives of order three or greater to help partially recover the variational lower bound of true UCCSD, restricting these derivatives to those of the "unmixed" category in order to simplify the model. By testing the approach on several potential energy surfaces and reaction energies, we find this "diagonal" approximation to higher order terms to be effective at reducing sensitivity near singularities for strongly correlated regimes, while not significantly diminishing the accuracy of weakly correlated systems.

Theoretical and Experimental Study of the Spectroscopy and Thermochemistry of UC+/0/

A combination of high-level ab initio calculations and anion photoelectron detachment (PD) measurements is reported for the UC, UC^-, and UC⁺ molecules. To better compare the theoretical values with the experimental photoelectron spectrum (PES), a value of 1.493 eV for the adiabatic electron affinity (AEA) of UC was calculated at the Feller-Peterson-Dixon (FPD) level. The lowest vertical detachment energy (VDE) is predicted to be 1.500 eV compared to the experimental value of 1.487 ± 0.035 eV. A shoulder to lower energy in the experimental PD spectrum with the 355 nm laser can be assigned to a combination of low-lying excited states of UC^- and excited vibrational states. The VDEs calculated for the low-lying excited electronic states of UC at the SO-CASPT2 level are consistent with the observed additional electron binding energies at 1.990, 2.112, 2.316, and 3.760 eV. Potential energy curves for the Ω states and the associated spectroscopic properties are also reported. Compared to UN and UN⁺, the bond dissociation energy (BDE) of UC (411.3 kJ/mol) is predicted to be considerably lower. The natural bond orbitals (NBO) calculations show that the UC^0/+/- molecules have a bond order of 2.5 with their ground-state configuration arising from changes in the oxidation state of the U atom in terms of the 7s orbital occupation: UC (5f²7s¹), UC^- (5f²7s²), and UC⁺ (5f²7s⁰). The behavior of the UN and UC sequence of molecules and anions differs from the corresponding sequences for UO and UF.

Accurate Prediction of Vertical Ionization Potentials and Electron Affinities from Spin-Component Scaled CC2 and ADC(2) Models

The CC2 and ADC(2) wave function models and their spin-component scaled modifications are adopted for predicting vertical ionization potentials (VIPs) and electron affinities (VEAs). The ionic solutions are obtained as electronic excitations in the continuum orbital formalism, making possible the use of existing, widespread quantum chemistry codes with minimal modifications, in full consistency with the treatment of charge transfer excitations. The performance of different variants is evaluated via benchmark calculations on various sets from previous works, containing small- and medium-sized systems, including the nucleobases. It is shown that with the spin-scaled approximate methods, in particular the scaled opposite-spin variant of the ADC(2) method, the accuracy of EOM-CCSD is achievable at a fraction of the computational cost, also outperforming many common electron propagator approaches.

Electronic Properties of UN and UN- from Photoelectron Spectroscopy and Correlated Molecular Orbital Theory

The results of calculations of the properties of the anion UN^- including electron detachment are described, which further expand our knowledge of this diatomic molecule. High-level electronic structure calculations were conducted for the UN and UN^- diatomic molecules and compared to photoelectron spectroscopy measurements. The low-lying Ω states were obtained using multireference CASPT2 including spin-orbit effects up to ∼20,000 cm^-1. At the Feller-Peterson-Dixon (FPD) level, the adiabatic electron affinity (AEA) of UN is estimated to be 1.402 eV and the vertical detachment energy (VDE) is 1.423 eV. The assignment of the UN excited states shows good agreement with the experimental results with a VDE of 1.424 eV. An Ω = 4 ground state was obtained for UN^- which is mainly associated with the ³H ΛS state. Thermochemical calculations estimate a bond dissociation energy (BDE) for UN^- (U^- + N) of 665.9 kJ/mol, ∼15% larger than that of UN and UN⁺. The NBO analysis reveals U-N triple bonds for the UN, UN^-, and UN⁺ species.

Quantitative Kinetics of HO2 Reactions with Aldehydes in the Atmosphere: High-Order Dynamic Correlation, Anharmonicity, and Falloff Effects Are All Important

Kinetics provides the fundamental parameters for elucidating sources and sinks of key atmospheric species and for atmospheric modeling more generally. Obtaining quantitative kinetics in the laboratory for the full range of atmospheric temperatures and pressures is quite difficult. Here, we use computational chemistry to obtain quantitative rate constants for the reactions of HO₂ with HCHO, CH₃CHO, and CF₃CHO. First, we calculate the high-pressure-limit rate constants by using a dual-level strategy that combines conventional transition state theory using a high level of electronic structure wave function theory with canonical variational transition state theory including small-curvature tunneling using density functional theory. The wave-function level is beyond-CCSD(T) for HCHO and CCSD(T)-F12a (Level-A) for XCHO (X = CH₃, CF₃), and the density functional (Level-B) is specifically validated for these reactions. Then, we calculate the pressure-dependent rate constants by using system-specific quantum RRK theory (SS-QRRK) and also by an energy-grained master equation. The two treatments of the pressure dependence agree well. We find that the Level-A//Level-B method gives good agreement with CCSDTQ(P)/CBS. We also find that anharmonicity is an important factor that increases the rate constants of all three reactions. We find that the HO₂ + HCHO reaction has a significant dependence on pressure, but the HO₂ + CF₃CHO reaction is almost independent of pressure. Our findings show that the HO₂ + HCHO reaction makes important contribution to the sink for HCHO, and the HO₂ + CF₃CHO reaction is the dominant sink for CF₃CHO in the atmosphere.

Sensitivity of coupled cluster electronic properties on the reference determinant: Can Kohn-Sham orbitals be more beneficial than Hartree-Fock orbitals?

Coupled cluster calculations are traditionally performed over Hartree-Fock reference orbitals (HF-CC methodology). However, in the literature it has been repeatedly raised whether the use of a Kohn-Sham reference (KS-CC methodology) might result in improved performance relative to HF-CC. In the present study, we re-examine the relation of HF-CC and KS-CC methods by comparing the results of widely applied truncated CC calculations (CCSD, CCSD(T), CCSDT) to the limit of full configuration interaction (FCI), which serves as an undebatable reference point of accuracy. Based on a series of CC calculations on diatoms and transition metal complexes, we demonstrate that no systematic improvement of coupled cluster electronic energies, densities and chemical reaction energies is expected when changing from HF to a KS reference. Nevertheless, fortuitous error cancellations might occasionally result in illusory improvement compared to HF-CC. Altogether, the application of KS-CC is not advantageous over HF-CC, but it is also not unreasonable as the choice of reference has negligible influence on the results at sufficiently high CC levels. In addition, KS-CC can be a particularly useful alternative if difficulties are encountered in HF or HF-CC convergence. It is also notable that KS-CC results are found to be practically independent of the chosen density functional, which implies that almost any KS-CC method can be used in place of HF-CC.

Theoretical dissociation, ionization, and spin–orbit energetics of the diatomic platinum hydrides PtH, PtH+, and PtH–

Spin–orbit configuration interaction (SO-CI) and coupled-cluster [CCSDT(Q)] theoretical methods are combined to evaluate zero-temperature thermochemical properties of PtH, PtH+, and PtH−. We obtain vibrational zero-point energies and spin–orbit stabilization energies, which lead to predictions for observable quantities: ionization energy IE(PtH) = (9.44 ± 0.07) eV; electron affinity EA(PtH) = (1.65 ± 0.04) eV; and dissociation energies D0(Pt–H) = (329.6 ± 3.9) kJ mol−1, D0(Pt+–H) = (279.3 ± 5.7) kJ mol−1, and D0(Pt−–H) = (285.0 ± 2.4) kJ mol−1 (uncertainty coverage factor = 2). Compared with available experiments, our value of D0(Pt+–H) is higher by (8 ± 8) kJ mol−1, EA(PtH) is higher by 0.15 eV, and D0(Pt–H) is lower than the upper bound by (2 ± 4) kJ mol−1.

New Theoretical Infrared Line List for the Methyl Radical with Accurate Vibrational Band Origins from High-Level Ab Initio Calculations

In the present work, high-level ab initio calculations were carried out for the ground electronic state of the methyl radical (CH₃). Dunning's augmented correlation-consistent orbital basis sets were employed up to the quintuple-ζ valence quality with the core-valence electron correlation [aug-cc-pCV5Z] combined with the single- and double-excitation unrestricted coupled-cluster approach with a perturbative treatment of triple excitations [RHF-UCCSD(T)]. The explicitly correlated version of the coupled-cluster approach [RHF-UCCSD(T)-F12x{x = a, b}] was additionally applied with the core-valence cc-pCVQZ-F12 basis set in order to study convergence with respect to the basis set size. The contributions beyond the coupled-cluster level of the theory like Douglas-Kroll-Hess scalar relativistic Hamiltonian, diabatic Born-Oppenheimer corrections, and high-order electronic correlations have been included into the ab initio potential energy surfaces (PESs). It is shown that the theoretical band origins of CH₃ converge gradually to the experimental values when applying the ab initio PESs using the aug-cc-pCVXZ [X = T, Q, and 5] basis sets. For the first time, all available experimental band origins of the gaseous CH₃ are reproduced within an accuracy of 0.2 cm^-1 using a newly developed PES extrapolated to the complete basis set limit [CBS(TQ5Z)]. The reached accuracy is one order of magnitude better than that of the best available calculations. A new theoretical infrared line list was generated for astrophysical applications using an ab initio dipole moment surface computed at the RHF-UCCSD(T)/aug-cc-pCVQZ level of the theory. The manifestation of a large-amplitude motion in CH₃ is also discussed.

Protactinium and Actinium Monohydrides: A Theoretical Study on Their Spectroscopic and Thermodynamic Properties

Spectroscopic and thermodynamics properties including bond dissociation energies (BDEs), adiabatic electron affinities (AEAs), and ionization energies (IEs) have been predicted for AcH and PaH using the Feller-Peterson-Dixon composite approach. Comparisons with previous studies on ThH and UH were performed to identify possible trends in the actinide series. Multireference CASPT2 calculations were used to predict the spin-orbit effects and obtain potential energy curves for the low-lying Ω states around the equilibrium distance as well as the vertical detachment energies (VDEs) from AcH^- and PaH^- to excited states of the neutral species. The calculated AEA for AnH (An = Ac, Th, Pa, U) showed that the AEA increases from AcH (0.425 eV) to ThH (0.820 eV) and decreases to PaH (0.781 eV) and to UH (0.457 eV), whereas the IE values are 5.887 eV (AcH), 6.181 eV (ThH), 6.204 eV (PaH), and 6.182 eV (UH). The ground state of AcH, AcH^-, PaH, and PaH^- are predicted to be¹Σ⁺₀,²Π_3/2, ³H₄, and ⁴I_9/2, respectively. The BDEs for AcH and PaH are 276.4 and 237.2 kJ/mol, and those for AcH^- and PaH^- are 242.8 and 239.8 kJ/mol, respectively. The natural bond analysis shows a significant ionic character, An⁺H^-, in the bonding of the neutral hydrides.

Benchmark ab initio potential energy surface mapping of the F + CH3NH2 reaction

This electronic structure study reveals four exothermic and two endothermic reaction pathways of the F + CH₃NH₂ system: the barrierless hydrogen abstraction from the methyl/amino group (HF + CH₂NH₂/CH₃NH), amino/methyl substitution (NH₂ + CH₃F and CH₃ + NH₂F) and hydrogen substitution from the two functional groups (H + CH₂FNH₂/CH₃NHF). The benchmark classical and adiabatic energies are obtained using a high-accuracy composite ab initio approach, where the gold-standard explicitly-correlated coupled cluster method (CCSD(T)-F12b) is applied with the correlation-consistent polarized valence quintuple-zeta F12 basis set (cc-pV5Z-F12) and further additive energy contributions. Considering indispensable post-(T) correlation, core correlation, scalar relativistic, spin-orbit and harmonic zero-point energy corrections, the obtained global minimum of the potential energy surface is the post-reaction CH₂NH₂⋯HF complex in the product channel. Although each substitution pathway has a high barrier, the energies of amino-substitution and methyl-hydrogen-substitution products are below the energy of the reactants, as well as the submerged-barrier hydrogen-abstraction pathways.

Perturbative Expansion of Nonorthogonal Product Approach for Charge Transfer States

Modeling of the excited states of multichromophoric systems is crucial for the understanding of photosynthesis functioning. The excitonic Hamiltonian method is widely used for such calculations. Excited states of the combined system are constructed from the wave functions of individual chromophores while their interactions are described by excitonic couplings. In the current study, we enhance a previously proposed nonorthogonal product approach to incorporate dynamic correlation effects accounted for by the multireference perturbation theory. We discuss the problems of constructing the excitonic Hamiltonian including charge transfer states for the molecular systems where the overlap contribution to the excitonic couplings is non-negligible. The benchmark calculations were performed for a model system. It was shown that the overlap component of the excitonic coupling is of great importance. The enhanced method provides an accurate description of the excited state energies and other properties.

Pericyclic reaction benchmarks: hierarchical computations targeting CCSDT(Q)/CBS and analysis of DFT performance

Hierarchical, convergent ab initio benchmark computations were performed followed by a systematic analysis of DFT performance for five pericyclic reactions comprising Diels-Alder, 1,3-dipolar cycloaddition, electrocyclic rearrangement, sigmatropic rearrangement, and double group transfer prototypes. Focal point analyses (FPA) extrapolating to the ab initio limit were executed via explicit quantum chemical computations with electron correlation treatments through CCSDT(Q) and correlation-consistent Gaussian basis sets up to aug'-cc-pV5Z. Optimized geometric structures and vibrational frequencies of all stationary points were obtained at the CCSD(T)/cc-pVTZ level of theory. The FPA reaction barriers and energies exhibit convergence to within a few tenths of a kcal mol-1. The FPA benchmarks were used to evaluate the performance of 60 density functionals (eight dispersion-corrected), covering the local-density approximation (LDA), generalized gradient approximations (GGAs), meta-GGAs, hybrids, meta-hybrids, double-hybrids, and range-separated hybrids. The meta-hybrid M06-2X functional provided the best overall performance [mean absolute error (MAE) of 1.1 kcal mol-1] followed closely by the double-hybrids B2K-PLYP, mPW2K-PLYP, and revDSD-PBEP86 [MAE of 1.4-1.5 kcal mol-1]. The regularly used GGA functional BP86 gave a higher MAE of 5.8 kcal mol-1, but it qualitatively described the trends in reaction barriers and energies. Importantly, we established that accurate yet efficient meta-hybrid or double-hybrid DFT potential energy surfaces can be acquired based on geometries from the computationally efficient and robust BP86/DZP level.

Photoelectron spectroscopy of cryogenically cooled NiO2-via slow photoelectron velocity-map imaging

High-resolution anion photoelectron spectra of cryogenically cooled NiO₂^- anions, obtained using slow photoelectron velocity-map imaging (cryo-SEVI), are presented in tandem with coupled cluster electronic structure calculations including relativistic effects. The experimental spectra encompass the X̃¹Σ_g⁺ ← X̃²Π_g, ã³Π_g ← X̃²Π_g, and ùΠ_g ← X̃²Π_g photodetachment transitions of linear ONiO^0/-, revealing previously unobserved vibrational structure in all three electronic bands. The high-resolution afforded by cryo-SEVI allows for the extraction of vibrational frequencies for each state, consistent with those previously measured in the ground state and in good agreement with scalar-relativistic coupled-cluster calculations. Previously unobserved vibrational structure is observed in the ã³Π_g and ùΠ_g states and is tentatively assigned. Further, a refined electron affinity of 3.0464(7) eV for NiO₂ is obtained as well as precise term energies for the ã and à states of NiO₂ of 0.3982(7) and 0.7422(10) eV, respectively. Numerous Franck-Condon forbidden transitions involving the doubly degenerate ν₂ bending mode are observed and ascribed to Herzberg-Teller coupling to an excited electronic state.

Experimental and Computational Description of the Interaction of H and H- with U

The results of ab initio correlated molecular orbital theory electronic structure calculations for low-lying electronic states are presented for UH and UH^- and compared to photoelectron spectroscopy measurements. The calculations were performed at the CCSD(T)/CBS and multireference CASPT2 including spin-orbit effects by the state interacting approach levels. The ground states of UH and UH^- are predicted to be ⁴Ι_9/2 and ⁵Λ₆, respectively. The spectroscopic parameters T_e, r_e, ω_e, ω_ex_e, and B_e were obtained, and potential energy curves were calculated for the low energy Ω states of UH. The calculated adiabatic electron affinity is 0.468 eV in excellent agreement with an experimental value of 0.462 ± 0.013 eV. The lowest vertical detachment energy was predicted to be 0.506 eV for the ground state, and the adiabatic ionization energy (IE) is predicted to be 6.116 eV. The bond dissociation energy (BDE) and heat of formation values of UH were obtained using the IE calculated at the Feller-Peterson-Dixon level. For UH, UH^-, and UH⁺, the BDEs were predicted to be 225.5, 197.9, and 235.5 kJ/mol, respectively. The BDE for UH is predicted to be ∼20% lower in energy than that for ThH. The analysis of the natural bond orbitals shows a significant U⁺H^- ionic component in the bond of UH.

Reference Energies for Cyclobutadiene: Automerization and Excited States

Cyclobutadiene is a well-known playground for theoretical chemists and is particularly suitable to test ground- and excited-state methods. Indeed, due to its high spatial symmetry, especially at the D_4h square geometry but also in the D_2h rectangular arrangement, the ground and excited states of cyclobutadiene exhibit multiconfigurational characters and single-reference methods, such as standard adiabatic time-dependent density-functional theory (TD-DFT) or standard equation-of-motion coupled cluster (EOM-CC), are notoriously known to struggle in such situations. In this work, using a large panel of methods and basis sets, we provide an extensive computational study of the automerization barrier (defined as the difference between the square and rectangular ground-state energies) and the vertical excitation energies at D_2h and D_4h equilibrium structures. In particular, selected configuration interaction (SCI), multireference perturbation theory (CASSCF, CASPT2, and NEVPT2), and coupled-cluster (CCSD, CC3, CCSDT, CC4, and CCSDTQ) calculations are performed. The spin-flip formalism, which is known to provide a qualitatively correct description of these diradical states, is also tested within TD-DFT (combined with numerous exchange-correlation functionals) and the algebraic diagrammatic construction [ADC(2)-s, ADC(2)-x, and ADC(3)]. A theoretical best estimate is defined for the automerization barrier and for each vertical transition energy.

Efficient implementation of molecular CCSD gradients with Cholesky-decomposed electron repulsion integrals

We present an efficient implementation of ground and excited state coupled cluster singles and doubles (CCSD) gradients based on Cholesky-decomposed electron repulsion integrals. Cholesky decomposition and density fitting are both inner projection methods, and, thus, similar implementation schemes can be applied for both methods. One well-known advantage of inner projection methods, which we exploit in our implementation, is that one can avoid storing large V3 O and V4 arrays by instead considering three-index intermediates. Furthermore, our implementation does not require the formation and storage of Cholesky vector derivatives. The new implementation is shown to perform well, with less than 10% of the time spent calculating the gradients in geometry optimizations. Furthermore, the computational time per optimization cycle is significantly lower compared to other implementations based on an inner projection method. We showcase the capabilities of the implementation by optimizing the geometry of the retinal molecule (C20H28O) at the CCSD/aug-cc-pVDZ level of theory.

Atomic Mean-Field Approach within Exact Two-Component Theory Based on the Dirac-Coulomb-Breit Hamiltonian

An extension of the exact two-component theory with atomic mean-field integrals (the X2CAMF scheme) to the treatment of the Breit term together with efficient implementation using an atomic Dirac-Coulomb-Breit Hartree-Fock program is reported. The accuracy of the X2CAMF scheme for treating the contributions from the Breit term to the molecular properties is demonstrated using benchmark calculations of equilibrium bond lengths, harmonic frequencies, and dipole moments for molecules containing elements across the periodic table. Calculations of the properties for molecules containing period four elements aiming at high accuracy as well as for Th- and U-containing molecules are also presented and compared with experimental results to demonstrate the usefulness of the X2CAMF scheme in combination with accurate treatments of electron correlation by the coupled-cluster (CC) methods. The combination of CC methods and the X2CAMF scheme shows potential to extend the accuracy of CC calculations to heavy elements, e.g., to computational heavy-element thermochemistry.

A Mountaineering Strategy to Excited States: Revising Reference Values with EOM-CC4

In the framework of the computational determination of highly accurate vertical excitation energies in small organic compounds, we explore the possibilities offered by the equation-of-motion formalism relying on the approximate fourth-order coupled-cluster (CC) method, CC4. We demonstrate, using an extended set of more than 200 reference values based on CC including up to quadruples excitations (CCSDTQ), that CC4 is an excellent approximation to CCSDTQ for excited states with a dominant contribution from single excitations with an average deviation as small as 0.003 eV. We next assess the accuracy of several additive basis set correction schemes, in which vertical excitation energies obtained with a compact basis set and a high-order CC method are corrected with lower-order CC calculations performed in a larger basis set. Such strategies are found to be overall very beneficial, though their accuracy depends significantly on the actual scheme. Finally, CC4 is employed to improve several theoretical best estimates of the QUEST database for molecules containing between four and six (nonhydrogen) atoms, for which previous estimates were computed at the CCSDT level.

Non-covalent interactions atlas benchmark data sets 4: σ-hole interactions

The SH250×10 dataset presented here extends the Non-Covalent Interactions Atlas database (https://www.nciatlas.org) to complexes bound by σ-hole interactions - halogen, chalcogen and pnictogen bonds. It comprises 250 complexes where Cl, Br, I, S, Se, P and As interact with diverse electron donors. An accurate CCSD(T)/CBS benchmark is provided for ten points along a dissociation curve of each complex. The SH250×10 set is used in testing a wide variety of DFT functionals and semiempirical quantum-mechanical methods. In DFT calculations, the new data set exposes large errors of some functionals related to exaggerated charge transfer. The size and diversity of the data set have also been exploited in the reparametrization of a halogen-bond correction for the PM6 semiempirical method.

Comparison of approximate intermolecular potentials for ab initio fragment calculations on medium sized N-heterocycles

The ground state intermolecular potential of bimolecular complexes of N-heterocycles is analyzed for the impact of individual terms in the interaction energy as provided by various, conceptually different theories. Novel combinations with several formulations of the electrostatic, Pauli repulsion, and dispersion contributions are tested at both short- and long-distance sides of the potential energy surface, for various alignments of the pyrrole dimer as well as the cytosine-uracil complex. The integration of a DFT/CCSD density embedding scheme, with dispersion terms from the effective fragment potential (EFP) method is found to provide good agreement with a reference CCSD(T) potential overall; simultaneously, a quantum mechanics/molecular mechanics approach using CHELPG atomic point charges for the electrostatic interaction, augmented by EFP dispersion and Pauli repulsion, comes also close to the reference result. Both schemes have the advantage of not relying on predefined force fields; rather, the interaction parameters can be determined for the system under study, thus being excellent candidates for ab initio modeling.

ATOMIC-2 Protocol for Thermochemistry

ATOMIC is a midlevel thermochemistry protocol that uses Pople's concept of bond separation reactions (BSRs) as a theoretical framework to reduce computational demands in the evaluation of atomization energies and enthalpies of formation. Various composite models are available that approximate bond separation energies at the complete-basis-set limit of all-electron CCSD(T), each balancing computational cost with achievable accuracy. Evaluated energies are then combined with very high-level, precomputed atomization energies of all auxiliary molecules appearing in the BSR to obtain the atomization energy of the molecule under study. ATOMIC-2 is a new version of the protocol that retains the overall concept and all previously defined composite models but improves on ATOMIC-1 in various other ways: Geometry optimization and zero-point-energy evaluation are performed at the density functional level (PBE0-D3/6-311G(d)), which shows significant computational savings and better accuracy than the previously employed RI-MP2/cc-pVTZ. The BSR framework is improved, using more accurate complete-basis-set (CBS) extrapolations toward the Full CI limit for the atomization energies of all auxiliary molecules. Finally, and most importantly, an error and uncertainty model termed ATOMIC-2_um is added that estimates average bias and uncertainty for each of the atomization energy contributions that arise from the simplified treatment of some contributions to bond separation energies (CCSD(T)) and the neglect of others (such as higher order, scalar relativistic, or diagonal Born-Oppenheimer corrections) or from residual error in the energies of auxiliary molecules. Large and diverse benchmarks including up to 1179 molecules are used to evaluate necessary reference data and to correlate the observed error for each of the contributions with appropriate proxies that are available without additional quantum-chemical calculations for a particular molecule and represent its size and type. The implementation of ATOMIC-2 considers neutral, closed-shell molecules containing H, C, N, O, and F atoms; compared to ATOMIC-1, the framework has been extended to cover a few challenging but rare bond topologies. In comparison to highly accurate reference data for 184 molecules taken from the ATcT database (V. 1.122r), regular ATOMIC-2 shows noticeable underbinding, but the bias-corrected protocol ATOMIC-2_um is found to be more accurate than either ATOMIC-1 or standard Gaussian-4 theory, and the uncertainty model is consistent with statistics of actually observed errors. Problems arising from ambiguous or challenging Lewis-valence structures defining BSRs are discussed, and computational efficiency is demonstrated. Computer code is made available to perform ATOMIC-2_um analyses.

Temperature-dependent kinetics of the atmospheric reaction between CH2OO and acetone

Criegee intermediates are important oxidants produced in the ozonolysis of alkenes in the atmosphere. Quantitative kinetics of the reactions of Criegee intermediates are required for atmospheric modeling. However, the experimental studies do not cover the full relevant range of temperature and pressure. Here we report the quantitative kinetics of CH₂OO + CH₃C(O)CH₃ by using our recently developed dual strategy that combines coupled cluster theory with high excitation levels for conventional transition state theory and well validated levels of density functional theory for direct dynamics calculations using canonical variational transition theory including tunneling. We find that the W3X-L//DF-CCSD(T)-F12b/jun-cc-pVDZ electronic structure method can be used to obtain quantitative kinetics of the CH₂OO + CH₃C(O)CH₃ reaction. Whereas previous investigations considered a one-step mechanistic pathway, we find that the CH₂OO + CH₃C(O)CH₃ reaction occurs in a stepwise manner. This has implications for the modeling of Criegee-intermediate reactions with other ketones and with aldehydes. In the kinetics calculations, we show that recrossing effects of the conventional transition state are negligible for determining the rate constant of CH₂OO + CH₃C(O)CH₃. The present findings reveal that the rate ratio between CH₂OO + CH₃C(O)CH₃ and OH + CH₃C(O)CH₃ has a significant negative dependence on temperature such that the CH₂OO + CH₃C(O)CH₃ reaction can contribute as a significant sink for atmospheric CH₃C(O)CH₃ at low temperature. The present findings should have broad implications in understanding the reactions of Criegee intermediates with carbonyl compounds and ketones in the atmosphere.

Structure, energetics, and spectroscopy of the chromophores of HHe+n, H2He+n, and He+n clusters and their deuterated isotopologues

The linear molecular ions H₂He⁺, HHe+2, and He+3 are the central units (chromophores) of certain He-solvated complexes of the H₂He+n, HHe+n, and He+n families, respectively. These are complexes which do exist, according to mass-spectrometry studies, up to very high n values. Apparently, for some of the H₂He+n and He+n complexes, the linear symmetric tetratomic H₂He+2 and the diatomic He+2 cations, respectively, may also be the central units. In this study, definitive structures, relative energies, zero-point vibrational energies, and (an)harmonic vibrational fundamentals, and, in some cases, overtones and combination bands, are established mostly for the triatomic chromophores. The study is also extended to the deuterated isotopologues D₂He⁺, DHe+2, and D₂He+2. To facilitate and improve the electronic-structure computations performed, new atom-centered, fixed-exponent, Gaussian-type basis sets called MAX, with X = T(3), Q(4), P(5), and H(6), are designed for the H and He atoms. The focal-point-analysis (FPA) technique is employed to determine definitive relative energies with tight uncertainties for reactions involving the molecular ions. The FPA results determined include the 0 K proton and deuteron affinities of the ⁴He atom, 14 875(9) cm^-1 [177.95(11) kJ mol^-1] and 15 229(8) cm^-1 [182.18(10) kJ mol^-1], respectively, the dissociation energies of the He+2 → He⁺ + He, HHe+2 → HHe⁺ + He, and He+3 → He+2 + He reactions, 19 099(13) cm^-1 [228.48(16) kJ mol^-1], 3948(7) cm^-1 [47.23(8) kJ mol^-1], and 1401(12) cm^-1 [16.76(14) kJ mol^-1], respectively, the dissociation energy of the DHe+2 → DHe⁺ + He reaction, 4033(6) cm^-1 [48.25(7) kJ mol^-1], the isomerization energy between the two linear isomers of the [H, He, He]⁺ system, 3828(40) cm^-1 [45.79(48) kJ mol^-1], and the dissociation energies of the H₂He⁺ → H+2 + He and the H₂He+2 → H₂He⁺ + He reactions, 1789(4) cm^-1 [21.40(5) kJ mol^-1] and 435(6) cm^-1 [5.20(7) kJ mol^-1], respectively. The FPA estimates of the first dissociation energy of D₂He⁺ and D₂He+2 are 1986(4) cm^-1 [23.76(5) kJ mol^-1] and 474(5) cm^-1 [5.67(6) kJ mol^-1], respectively. Determining the vibrational fundamentals of the triatomic chromophores with second-order vibrational perturbation theory (VPT2) and vibrational configuration interaction (VCI) techniques, both built around the Eckart-Watson Hamiltonian, proved unusually challenging. For the species studied, VPT2 has difficulties yielding dependable results, in some cases even for the fundamentals of the H-containing molecular cations, while carefully executed VCI computations yield considerably improved spectroscopic results. In a few cases unusually large anharmonic corrections to the fundamentals, on the order of 15% of the harmonic value, have been observed.

Benchmark Ab Initio Characterization of the Abstraction and Substitution Pathways of the Cl + CH3CN Reaction

We investigate the reaction pathways of the Cl + CH₃CN system: hydrogen abstraction, methyl substitution, hydrogen substitution, and cyanide substitution, leading to HCl + CH₂CN, ClCN/CNCl + CH₃, ClCH₂CN + H, and CH₃Cl + CN, respectively. Hydrogen abstraction is exothermic and has a low barrier, whereas the other channels are endothermic with high barriers. The latter two can proceed via a Walden inversion or front-side attack mechanism, and the front-side attack barriers are always higher. The C-side methyl substitution has a lower barrier and also a lower endothermicity than the N-side reaction. The computations utilize an accurate composite ab initio approach and the explicitly correlated CCSD(T)-F12b method. The benchmark classical and vibrationally adiabatic energies of the stationary points are determined with the most accurate CCSD(T)-F12b/aug-cc-pVQZ energies adding further contributions of the post-(T) and core correlation, scalar relativistic effects, spin–orbit coupling, and zero-point energy corrections. These contributions are found to be non-negligible to reach subchemical accuracy.

Understanding the Mechanism of Diels-Alder Reactions with Anionic Dienophiles: A Systematic Comparison of [ECX]- (E = P, As; X = O, S, Se) Anions

While Diels–Alder (DA) reactions involving neutral or cationic dienophiles are well-known, the characteristics of the analogous reactions with anionic dienophiles are practically unexplored. Herein we present the first comparative computational investigations on the characteristics of DA cycloadditions with anionic dienophiles on the basis of the reactions of [ECX]⁻ anions (E = P, As; X = O, S, Se) with 2H-pyran-2-one. All of these reactions were found to be both kinetically and thermodynamically feasible, enabling synthetic access toward 2-phosphaphenolate and arsaphenolate derivatives in the future. This study also reveals that the [ECO]⁻ anions show clear regioselectivity, while for [ECS]⁻ and [ECSe]⁻ anions, the two possible reaction channels have very similar energetics. Additionally, the activation barriers for the [ECO]⁻ anions are lower than those of the heavier analogues. The observed differences can be traced back to the starkly differing nucleophilic character of the pnictogen center in the anions, leading to a barrier-lowering effect in the case of the [ECO]⁻ anions. Furthermore, analysis of the geometries and electron distributions of the corresponding transition states revealed structure–property relationships, and thus a direct comparison of the cycloaddition reactivity of these anions was achieved. Along one of the two pathways, a good correlation was found between the activation barriers and suitable nucleophilicity descriptors (nucleophilic Parr function and global nucleophilicity). Additionally, the tendency of the reaction energies can be explained by the changing aromaticity of the products.

In contrast to the phosphaethynolate [PCO]⁻ anion, the cycloaddition reactivity of the heavier congeners ([ECX]⁻, where E = P, As and X = O, S, Se) is unexplored. In this computational study, the Diels−Alder reaction between the known [ECX]⁻ anions and 2-pyrone was employed to compare the reactivity patterns. The first activation barrier of these reactions correlates with the nucleophilicity of the anions, indicating a barrier-lowering effect. The feasibility of the studied reactions, leading to P and As heterocycles, was also explored.

Highly accurate HF dimer ab initio potential energy surface

A highly accurate, (HF)₂ potential energy surface (PES) is constructed based on ab initio calculations performed at the coupled-cluster single double triple level of theory with an aug-cc-pVQZ-F12 basis set at about 152 000 points. A higher correlation correction is computed at coupled-cluster single double triple quadruple level for 2000 points and is considered alongside other more minor corrections due to relativity, core-valence correlation, and Born-Oppenheimer failure. The analytical surface constructed uses 500 constants to reproduce the ab initio points with a standard deviation of 0.3 cm^-1. Vibration-rotation-inversion energy levels of the HF dimer are computed for this PES by variational solution of the nuclear-motion Schrödinger equation using the program WAVR4. Calculations over an extended range of rotationally excited states show very good agreement with the experimental data. In particular, the known empirical rotational constants B for the ground vibrational states are predicted to better than about 2 MHz. B constants for excited vibrational states are reproduced several times more accurately than by previous calculations. This level of accuracy is shown to extend to higher excited inter-molecular vibrational states v and higher excited rotational quantum numbers (J, K_a).

Implementation and Optimization of the Embedded Cluster Reference Interaction Site Model with Atomic Charges

In this work, we implemented the embedded cluster reference interaction site model (EC-RISM) originally developed by Kloss, Heil, and Kast (J. Phys. Chem. B2008, 112, 4337–4343). This method combines quantum mechanical calculations with the 3D reference interaction site model (3D-RISM). Numerous options, such as buffer, grid space, basis set, charge model, water model, closure relation, and so forth, were investigated to find the best settings. Additionally, the small point charges, which are derived from the solvent distribution from the 3D-RISM solution to represent the solvent in the QM calculation, were neglected to reduce the overhead without the loss of accuracy. On the MNSOL[a], MNSOL, and FreeSolv databases, our implemented and optimized method provides solvation free energies in water with 5.70, 6.32, and 6.44 kJ/mol root-mean-square deviations, respectively, but with different settings, 5.22, 6.08, and 6.63 kJ/mol can also be achieved. Only solvent models containing fitting parameters, like COSMO-RS and EC-RISM with universal correction and directly used electrostatic potential, perform better than our EC-RISM implementation with atomic charges.

The He–H3+ complex. I. Vibration-rotation-tunneling states and transition probabilities

With a He–[Formula: see text] interaction potential obtained from advanced electronic structure calculations, we computed the vibration-rotation-tunneling (VRT) states of this complex for total angular momenta J from 0 to 9, both for the vibrational ground state and for the twofold degenerate v2 = 1 excited state of [Formula: see text]. The potential has three equivalent global minima with depth D e = 455.3 cm−1 for He in the plane of [Formula: see text], three equatorial saddle points that separate these minima with barriers of 159.5 cm−1, and two axial saddle points with energies of 243.1 cm−1 above the minima. The dissociation energies calculated for the complexes of He with ortho-[Formula: see text] (o[Formula: see text]) and para-[Formula: see text] (p[Formula: see text]) are D0 = 234.5 and 236.3 cm−1, respectively. Wave function plots of the VRT states show that they may be characterized as weakly hindered internal rotor states, delocalized over the three minima in the potential and with considerable amplitude at the barriers. Most of them are dominated by the j k = 10 and 11 rotational ground states of o[Formula: see text] and p[Formula: see text], with the intermolecular stretching mode excited up to v = 4 inclusive. However, we also found excited internal rotor states: 33 in He–o[Formula: see text], and 22 and 21 in He–p[Formula: see text]. The VRT levels and wave functions were used to calculate the frequencies and line strengths of all allowed v2 = 0 → 1 rovibrational transitions in the complex. Theoretical spectra generated with these results are compared with the experimental spectra in Paper II [Salomon et al., J. Chem. Phys. 156, 144308 (2022)] and are extremely helpful in assigning these spectra. This comparison shows that the theoretical energy levels and spectra agree very well with the measured ones, which confirms the high accuracy of our ab initio He–[Formula: see text] interaction potential and of the ensuing calculations of the VRT states.