Single-reference Methods Research Articles

QUEST#4X: An Extension of QUEST#4 for Benchmarking Multireference Wave Function Methods.

Given a number of data sets for evaluating the performance of single reference methods for the low-lying excited states of closed-shell molecules, a comprehensive data set for assessing the performance of multireference methods for the low-lying excited states of open-shell systems is still lacking. For this reason, we propose an extension (QUEST#4X) of the radical subset of QUEST#4 (J. Chem. Theory Comput. 2020, 16, 3720) to cover 110 doublet and 39 quartet excited states. Near-exact results obtained by iterative configuration interaction with selection and second-order perturbation correction (iCIPT2) are taken as benchmark to calibrate static-dynamic-static configuration interaction (SDSCI) and static-dynamic-static second-order perturbation theory (SDSPT2), which are minimal MRCI and CI-like perturbation theory, respectively. It is found that SDSCI is very close in accuracy to internally contracted multireference configuration interaction with singles and doubles (ic-MRCISD), although its computational cost is just that of one iteration of the latter. Unlike most variants of MRPT2, SDSPT2 treats single and multiple states in the same way and performs similarly to multistate n-electron valence second-order perturbation theory (MS-NEVPT2). These findings put SDSCI and SDSPT2 on a firm basis.

Improving Bond Dissociations of Reactive Machine Learning Potentials through Physics-Constrained Data Augmentation.

In the field of computational chemistry, predicting bond dissociation energies (BDEs) presents well-known challenges, particularly due to the multireference character of reactive systems. Many chemical reactions involve configurations where single-reference methods fall short, as the electronic structure can significantly change during bond breaking. As generating training data for partially broken bonds is a challenging task, even state-of-the-art reactive machine learning interatomic potentials (MLIPs) often fail to predict reliable BDEs and smooth dissociation curves. By contrast, simple and inexpensive physics-based models, such as the well-established Morse potential, do not suffer from any such limitations. This work leverages the Morse potential to improve reactive MLIPs by augmenting the training data set with inexpensive Morse data along the dissociation pathways. This physics-constrained data augmentation (PCDA) approach results in MLIPs with smooth bond dissociation curves as well as near coupled-cluster level BDEs, all without requiring any expensive multireference quantum mechanical calculations. A case study for methane combustion demonstrates how the PCDA approach can improve an existing reactive MLIP, namely, ANI-1xnr. Not only are the BDEs and bond dissociation curves for all radicals and molecules significantly improved compared to ANI-1xnr but the PCDA-trained MLIP retains the reliability of ANI-1xnr when performing reactive molecular dynamics simulations.

Solving an industrially relevant quantum chemistry problem on quantum hardware

Abstract Quantum chemical calculations are among the most promising applications for quantum computing. Implementations of dedicated quantum algorithms on available quantum hardware were so far, however, mostly limited to comparatively simple systems without strong correlations. As such, they can also be addressed by classically efficient single-reference methods. Here we calculate the lowest energy eigenvalue of active space Hamiltonians of industrially relevant and strongly correlated metal chelates on trapped ion quantum hardware, and integrate the results into a typical industrial quantum chemical workflow to arrive at chemically meaningful properties. We are able to achieve chemical accuracy by training a variational quantum algorithm on quantum hardware, followed by a classical diagonalization in the subspace of states measured as outputs of the quantum circuit. This approach is particularly measurement-efficient, requiring 600 single-shot measurements per cost function evaluation on a ten qubit system, and allows for efficient post-processing to handle erroneous runs.

Systematic Improvement of Quantum Monte Carlo Calculations in Transition Metal Oxides: sCI-Driven Wavefunction Optimization for Reliable Band Gap Prediction.

Accurate determination of the electronic properties of correlated oxides remains a significant challenge for computational theory. Traditional Hubbard-corrected density functional theory (DFT+U) frequently encounters limitations in precisely capturing electron correlation, particularly in predicting band gaps. We introduce a systematic methodology to enhance the accuracy of diffusion Monte Carlo (DMC) simulations for both ground and excited states, focusing on LiCoO2 as a case study. By employing a selected configuration interaction (sCI) approach, we demonstrate the capability to optimize wavefunctions beyond the constraints of single-reference DFT+U trial wavefunctions. We show that the sCI framework enables accurate prediction of band gaps in LiCoO2, closely aligning with experimental values and substantially improving traditional computational methods. The study uncovers a nuanced mixed state of t2g and eg orbitals at the band edges that is not captured by conventional single-reference methods, further elucidating the limitations of PBE+U in describing d-d excitations. Our findings advocate for the adoption of beyond-DFT methodologies, such as sCI, to capture the essential physics of excited-state wavefunctions in strongly correlated materials. The improved accuracy in band gap predictions and the ability to generate more reliable trial wavefunctions for DMC calculations underscore the potential of this approach for broader applications in the study of correlated oxides. This work not only provides a pathway for more accurate simulations of electronic structures in complex materials but also suggests a framework for future investigations of the excited states of other challenging systems.

Structures, energies and vibrational frequencies of the X and A states of haloacetylene cations, HCCX+ (X = F, Cl, Br, I)

Modeling charge migration resulting from the coherent superposition of cation ground and excited states requires information about the potential energy surfaces of the relevant cation states. Since these states are often of the same electronic symmetry as the ground state of the cation, conventional single reference methods such as coupled cluster cannot be used for the excited states. The EOMCCSD-IP (equation of motion coupled cluster with single and double excitations and ionization) is a convenient and reliable “black-box” method that can be used for the ground and excited states of cations, yielding results of CCSD (coupled cluster with singles and double excitation) quality. Charge migration in haloacetylene cations arises from the superposition of the X and A states of HCCX+ (X = F, Cl, Br and I). The geometries, ionization potentials and vibrational frequencies have been calculated by CCSD/cc-pVTZ for neutral HCCX and the X state of HCCX+ and by EOM CCSD-IP/cc-pVTZ for the X and A states of HCCX+. The results agree very well with each other and with experiment. The very good agreement between CCSD and EOMCCSD-IP for the X states demonstrates that EOMCCSD-IP is a suitable method for calculating the structure and properties of ground and excited states for the HCCX cations.

Theoretical study of the second- and third-H-abstraction reactions of monomethylhydrazine and nitrogen dioxide and its application to hypergolic ignition modeling

The chemical kinetics of the second–H-abstraction and the third-H-abstraction reactions of monomethylhydrazine (MMH) and nitrogen dioxide (NO2) and its application to modeling hypergolic ignition of MMH/NO2 were investigated in this work. Potential energy surfaces (PESs) for the key reactions were obtained by employing the CCSD(T)/CBS//M06-2X/6-311++G(d,p) single-reference method and the MRCI(7e,6o)/CBS//M06-2X/6-311++G(d,p) multi-reference method. The RRKM/Master Equation approach was used to calculate the temperature- and pressure-dependent rate constants. For the second-H-abstraction reactions, the trans-CH3NNH and HNO2/HONO are the major products. For the third-H-abstraction reactions, the bimolecular reaction of cis-CH3NNH+NO2→CH3NN+HNO2 is more favorable. The calculated rate constants and thermodynamics data were fitted and incorporated into two existing mechanisms to investigate their influence on modeling MMH/NO2 hypergolic ignition. The modeling results show that the system reactivity of MMH/NO2 is promoted by the second- and third-H-abstraction reactions, as the ignition delay times decrease by a factor of two at 300–800 K. The production rate and sensitivity analyses further validate the significance of the second-H-abstraction reactions at low temperatures. The sensitivity analyses at 1000 K also indicate the necessity of further investigations on CH2O, N2H2/NO2, and CH3NH/NO2 sub-mechanisms for modeling the MMH/NO2 combustion at high temperatures. This work provides not only new kinetic and thermochemical data but also a better understanding of the hypergolic ignition of MMH/NO2.

Beyond Single-Reference Fixed-Node Approximation in Ab Initio Diffusion Monte Carlo Using Antisymmetrized Geminal Power Applied to Systems with Hundreds of Electrons.

Diffusion Monte Carlo (DMC) is an exact technique to project out the ground state (GS) of a Hamiltonian. Since the GS is always bosonic, in Fermionic systems, the projection needs to be carried out while imposing antisymmetric constraints, which is a nondeterministic polynomial hard problem. In practice, therefore, the application of DMC on electronic structure problems is made by employing the fixed-node (FN) approximation, consisting of performing DMC with the constraint of having a fixed, predefined nodal surface. How do we get the nodal surface? The typical approach, applied in systems having up to hundreds or even thousands of electrons, is to obtain the nodal surface from a preliminary mean-field approach (typically, a density functional theory calculation) used to obtain a single Slater determinant. This is known as single reference. In this paper, we propose a new approach, applicable to systems as large as the C60 fullerene, which improves the nodes by going beyond the single reference. In practice, we employ an implicitly multireference ansatz (antisymmetrized geminal power wave function constraint with molecular orbitals), initialized on the preliminary mean-field approach, which is relaxed by optimizing a few parameters of the wave function determining the nodal surface by minimizing the FN-DMC energy. We highlight the improvements of the proposed approach over the standard single-reference method on several examples and, where feasible, the computational gain over the standard multireference ansatz, which makes the methods applicable to large systems. We also show that physical properties relying on relative energies, such as binding energies, are affordable and reliable within the proposed scheme.

Reference Energies for Valence Ionizations and Satellite Transitions.

Upon ionization of an atom or a molecule, another electron (or more) can be simultaneously excited. These concurrently generated states are called "satellites" (or shakeup transitions) as they appear in ionization spectra as higher-energy peaks with weaker intensity and larger width than the main peaks associated with single-particle ionizations. Satellites, which correspond to electronically excited states of the cationic species, are notoriously challenging to model using conventional single-reference methods due to their high excitation degree compared to the neutral reference state. This work reports 42 satellite transition energies and 58 valence ionization potentials (IPs) of full configuration interaction quality computed in small molecular systems. Following the protocol developed for the quest database [Véril, M.; Scemama, A.; Caffarel, M.; Lipparini, F.; Boggio-Pasqua, M.; Jacquemin, D.; and Loos, P.-F. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517], these reference energies are computed using the configuration interaction using a perturbative selection made iteratively (CIPSI) method. In addition, the accuracy of the well-known coupled-cluster (CC) hierarchy (CC2, CCSD, CC3, CCSDT, CC4, and CCSDTQ) is gauged against these new accurate references. The performances of various approximations based on many-body Green's functions (GW, GF2, and T-matrix) for IPs are also analyzed. Their limitations in correctly modeling satellite transitions are discussed.

BeM(CO)3- (M = Co, Rh, Ir) and BeM(CO)3 (M = Ni, Pd, Pt): Triply bonded terminal beryllium in zero oxidation state.

We perform detailed potential energy surface explorations of BeM(CO)3- (M = Co, Rh, Ir) and BeM(CO)3 (M = Ni, Pd, Pt) using both single-reference and multireference-based methods. The present results at the CASPT2(12,12)/def2-QZVPD//M06-D3/def2-TZVPPD level reveal that the global minimum of BeM(CO)3- (M = Co, Rh, Ir) and BePt(CO)3 is a C3v symmetric structure with an 1A1 electronic state, where Be is located in a terminal position bonded to M along the center axis. For other cases, the C3v symmetric structure is a low-lying local minimum. Although the present complexes are isoelectronic with the recently reported BFe(CO)3- complex having a B-Fe quadruple bond, radial orbital-energy slope (ROS) analysis reveals that the highest occupied molecular orbital (HOMO) in the title complexes is slightly antibonding in nature, which bars a quadruple bonding assignment. Similar weak antibonding nature of HOMO in the previously reported BeM(CO)4 (M = Ru, Os) complexes is also noted in ROS analysis. The bonding analysis through energy decomposition analysis in combination with the natural orbital for chemical valence shows that the bonding between Be and M(CO)3q (q = -1 for M = Co, Rh, Ir and q = 0 for M = Ni, Pd, Pt) can be best described as Be in the ground state (1S) interacting with M(CO)30/- via dative bonds. The Be(spσ) → M(CO)3q σ-donation and the complementary Be(spσ) ← M(CO)3q σ-back donation make the overall σ bond, which is accompanied by two weak Be(pπ) ← M(CO)3q π-bonds. These complexes represent triply bonded terminal beryllium in an unusual zero oxidation state.

Thermal rate constants and kinetic isotope effects of the H + H2O2 reactions: barrier height and reaction energy from single- and multireference methods.

One of the more significant sub-mechanisms of H2/O2 combustion involves the reaction of hydrogen peroxide with hydrogen atoms (H + H2O2), resulting in the production of OH + H2O (R1) and H2 + HO2 (R2) paths. Previous experimental and ab initio calculations reveal some variations in the barrier height for (R1). To improve the energetics of both (R1) and (R2), single reference and multireference ab initio methods are employed, and the rate constants and H/D kinetic isotope effects (KIEs) are calculated as a function of temperature. For (R1), the best results for the barrier height and reaction energies computed with the CASPT2(15,11)/aug-cc-pV6Z are 5.2 and - 70.3kcal.mol-1, respectively. CCSD(T)/aug-cc-pV5Z + CV (core-valence) calculations for (R2) give 9.7 and - 15.6kcal.mol-1 to those parameters. The CVT/SCT rate constants of both paths agree well with the fitted rate constants from uncertainty-weighted statistical analysis of the 14-mechanism of H2/O2. The kinetic isotopic effect (kH/kD) for the reaction D + H2O2 → DH + HO2 was found to be 0.47, which is in excellent agreement with the experimental value of 0.43. The structures of reactants, transition state, and products of (R1) and (R2) are calculated with the aug-cc-pVTZ basis set and M062X DFT, CCSD(T), and CASSCF methods. The barrier heights and reaction energies of (R1) and (R2) are computed using the M06-2X, CCSD(T), MRCI, and CASPT2 methods and various basis sets. The rate constants are calculated with the variational transition state theory including multidimensional tunneling corrections (VTST-MT), with potential energy surfaces built by the M06-2X/aug-cc-pVTZ approach.

DFT Struggles to Predict the Energy Landscape for Iron Pyridine Diimine-Catalyzed [2 + 2] Cycloaddition of Alkenes: Insights into the Problem and Alternative Solutions.

In recent years, noninnocent pyridine diimine (PDI) complexes featuring first-row transition metals have emerged as prominent catalysts, demonstrating efficacy in a diverse range of vital organometallic transformations. However, the inherent complexity of the fundamental reactivity paradigm in these systems arises from the presence of a noninnocent ligand and the multispin feasibility of 3d metals. While density functional theory (DFT) has been widely used to unravel mechanistic insights, its limitations as a single-reference method can potentially misrepresent spin-state energetics, compromising our understanding of these intricate systems. In this study, we employ extensive high-level ab initio state averaged-complete active space self-consistent field/N-electron valence state perturbation theory (SA-CASSCF/NEVPT2) calculations in combination with DFT to investigate an iron-PDI-catalyzed [2 + 2] cycloaddition reaction of alkenes. The transformation proceeds through two major steps: oxidative cyclization and reductive elimination. Contrary to the predictions of DFT calculations, which suggest two-state reactivity in the reaction and identify reductive elimination as the turnover-limiting step, SA-CASSCF/NEVPT2-corrected results unequivocally establish a single-state reactivity scenario with oxidative cyclization as the turnover-limiting step. SA-CASSCF/NEVPT2-based insights into electronic ground states and electron distribution elucidate the intriguing interactions between the PDI ligand and the iron center, revealing the highly multiconfigurational nature of these species and providing a precise depiction of metal-ligand cooperativity throughout the transformation. A comparative assessment of several widely recognized DFT functionals against SA-CASSCF/NEVPT2-corrected data indicates that single-point energy calculations using the modern density functional MN15 on TPSSh geometries offer the most reliable density functional methodology, in scenarios where SA-CASSCF/NEVPT2 computational cost is a consideration.

A theoretical study on toluene oxidization by OH radical

Toluene, a prominent member of volatile organic compounds (VOCs), exerts a substantial adverse influence on both human life and the environment. In the context of advanced oxidation processes, the ·OH radical emerges as a highly efficient oxidant, pivotal in the elimination of VOCs. This study employs computational quantum chemistry methods (G4MP2//B3LYP/6-311++G(d,p)) to systematically investigate the degradation of toluene by ·OH radicals in an implicit solvent model, and validates the rationale of choosing a single-reference method using T1 diagnostics. Our results suggest three possible reaction mechanisms for the oxidation of toluene by ·OH: firstly, the phenyl ring undergoes a hydrogen abstraction reaction followed by direct combination with ·OH to form cresol; secondly, ·OH directly adds to the phenyl ring, leading to ring opening; thirdly, oxidation of sidechain to benzoic acid followed by further addition and ring opening. The last two oxidation pathways involve the ring opening of toluene via the addition of ·OH, significantly facilitating the process. Therefore, both pathways are considered feasible for the degradation of toluene. Subsequently, the UV-H2O2 system was designed to induce the formation of ·OH for toluene degradation and to identify the optimal reaction conditions. It was demonstrated that ·OH and 1O2 are the primary active species for degrading toluene, with their contribution ranking as ·OH > 1O2. The intermediates in the mixture solution after reactions were characterized using GC–MS, demonstrating the validity of theoretical predictions. A comparative study of the toluene consumption rate revealed an experimental comprehensive activation energy of 10.33 kJ/mol, which is consistent with the preliminary activation energies obtained via theoretical analysis of these three mechanisms (0.56 kJ/mol to 13.66 kJ/mol), indicating that this theoretical method can provide a theoretical basis for experimental studies on the oxidation of toluene by ·OH.

A multi-descriptor analysis of substituent effects on the structure and aromaticity of benzene derivatives: π-Conjugation versus charge effects.

This work provides a detailed multi-component analysis of aromaticity in monosubstituted (X = CH3, C , C , NH2, NH-, NH+, OH, O-, and O+) and para-homodisubstituted (X = CH3, CH2, NH2, NH, OH, and O) benzene derivatives. We investigate the effects of substituents using single-reference (B3LYP/DFT) and multireference (CASSCF/MRCI) methods, focusing on structural (HOMA), vibrational (AI(vib)), topological (ELFπ), electronic (MCI), magnetic (NICS), and stability (S0-T1 splitting) properties. The findings reveal that appropriate π-electron-donating and π-electron-accepting substituents with suitable size and symmetry can interact with the π-system of the ring, significantly influencing π-electron delocalization. While the charge factor has a minimal impact on π-electron delocalization, the presence of a pz orbital capable of interacting with the π-electron delocalization is the primary factor leading to a deviation from the typical aromaticity characteristics observed in benzene.

Doubles Connected Moments Expansion: A Tractable Approximate Horn-Weinstein Approach for Quantum Chemistry.

Ab initio methods based on the second-order and higher connected moments, or cumulants, of a reference function have seen limited use in the determination of correlation energies of chemical systems over the years. Moment-based methods have remained unattractive relative to more ubiquitous methods, such as perturbation theory and coupled cluster theory, due in part to the intractable cost of assembling moments of high-order and poor performance of low-order expansions. Many of the traditional quantum chemical methodologies can be recast as a selective summation of perturbative contributions to their energy; using this familiar structure as a guide in selecting terms, we develop a scheme to approximate connected moments limited to double excitations. The tractable Doubles Connected Moments [DCM(N)] approximation is developed and tested against a multitude of common single-reference methods to determine its efficacy in the determination of the correlation energy of model systems and small molecules. The DCM(N) sequence of energies exhibits smooth convergence toward limiting values in the range of N = 11-14, with compute costs that scale as a noniterative O(M6) with molecule size, M. Numerical tests on correlation energy recovery for 55 small molecules comprising the G1 test set in the cc-pVDZ basis show that DCM(N) strongly outperforms MP2 and even CCD with a Hartree-Fock reference. When using an approximate Brueckner reference from orbital-optimized (oo) MP2, the resulting oo:DCM(N) energies converge to values more accurate than CCSD for 49 of 55 molecules. The qualitative success of the method in regions where strong correlation effects begin to dominate, even while maintaining spin purity, suggests this may be a good starting point in the development of methodologies for the description of strongly correlated or spin-contaminated systems while maintaining a tractable single-reference formalism.

When do tripdoublet states fluoresce? A theoretical study of copper(II) porphyrin.

Open-shell molecules rarely fluoresce, due to their typically faster non-radiative relaxation rates compared to closed-shell ones. Even rarer is the fluorescence from states that have two more unpaired electrons than the open-shell ground state, since they involve excitations from closed-shell orbitals to vacant-shell orbitals, which are typically higher in energy compared to excitations from or out of open-shell orbitals. States that are dominated by the former type of excitations are known as tripdoublet states when they can be described as a triplet excitation antiferromagnetically coupled to a doublet state, and their description by unrestricted single-reference methods (e.g., U-TDDFT) is notoriously inaccurate due to large spin contamination. In this work, we applied our spin-adapted TDDFT method, X-TDDFT, and the efficient and accurate static-dynamic-static second order perturbation theory (SDSPT2), to the study of the excited states as well as their relaxation pathways of copper(II) porphyrin; previous experimental works suggested that the photoluminescence of some substituted copper(II) porphyrins originate from a tripdoublet state, formed by a triplet ligand π → π* excitation antiferromagnetically coupled with the unpaired d electron. Our results demonstrated favorable agreement between the X-TDDFT, SDSPT2 and experimental excitation energies, and revealed noticeable improvements of X-TDDFT compared to U-TDDFT, not only for vertical excitation energies but also for adiabatic energy differences. These suggest that X-TDDFT is a reliable tool for the study of tripdoublet state fluorescence. Intriguingly, we showed that the aforementioned tripdoublet state is only slightly above the lowest doublet excited state and lies only slightly higher than the lowest quartet state, which suggests that the tripdoublet of copper(II) porphyrin is long-lived enough to fluoresce due to a lack of efficient non-radiative relaxation pathways; an explanation for this unusual state ordering is given. Indeed, thermal vibration correlation function (TVCF)-based calculations of internal conversion, intersystem crossing, and radiative transition rates confirm that copper(II) porphyrin emits thermally activated delayed fluorescence (TADF) and a small amount of phosphorescence at low temperature (83K), in accordance with experiment. The present contribution is concluded by a few possible approaches of designing new molecules that fluoresce from tripdoublet states.

An indentation method for measuring welding residual stress: Estimation of stress-free indentation curve using BP neural network prediction model

The measurement of welding residual stress (WRS) is necessary to formulate the stress control strategies, in order to ensure the reliability of engineering structures during their service life. The instrumented indentation technique can detect surface residual stress nondestructively with an acceptable accuracy, making it a desirable option for in-situ applications. However, it is difficult to meet the requirement for stress-free samples, particularly in the case of welded joints with non-uniform mechanical properties. In this work, the impact of stress-free indentation curves on determining WRS is furtherly studied based on the previously proposed indentation energy difference method. The WRS in a mismatched welded plate is measured using single reference method and distributed reference method, respectively. The study suggests that using the single reference method can lead to significant errors in determining the sign and magnitude of WRS in the weld zone. A prediction model combining the continuous spherical indentation (CSI) method and Back Propagation (BP) neural network is proposed to obtain the stress-free indentation curves of local positions nondestructively. And the CSI-BP method is verified through reverse finite element analysis and experiments.

The Markovian Multiagent Monte-Carlo method as a differential evolution approach to the SCF problem for restricted and unrestricted Hartree-Fock and Kohn-Sham-DFT.

In this paper we present the Markovian Multiagent Monte-Carlo Second Order Self-Consistent Field Algorithm (M3-SOSCF). This algorithm provides a highly reliable methodology for converging SCF calculations in single-reference methods using a modified differential evolution approach. Additionally, M3 is embarrassingly parallel and modular in regards to Newton-Raphson subroutines. We show that M3 is able to surpass contemporary SOSCFs in reliability, which is illustrated by a benchmark employing poor initial guesses and a second benchmark with SCF calculations which face difficulties using standard SCF algorithms. Furthermore, we analyse inherent properties of M3 and show that in addition to its robustness and efficiency, it is more user-friendly than current SOSCFs.

Core-Excited States and X-ray Absorption Spectra from Multireference Algebraic Diagrammatic Construction Theory.

We report the development and benchmark of multireference algebraic diagrammatic construction theory (MR-ADC) for the simulations of core-excited states and X-ray absorption spectra (XAS). Our work features an implementation that incorporates core-valence separation into the strict and extended second-order MR-ADC approximations (MR-ADC(2) and MR-ADC(2)-X), providing efficient access to high-energy excited states without including inner-shell orbitals in the active space. Benchmark results on a set of small molecules indicate that at equilibrium geometries, the accuracy of MR-ADC is similar to that of single-reference ADC theory when static correlation effects are not important. In this case, MR-ADC(2)-X performs similarly to single- and multireference coupled cluster methods in reproducing the experimental XAS peak spacings. We demonstrate the potential of MR-ADC for chemical systems with multiconfigurational electronic structure by calculating the K-edge XAS spectrum of the ozone molecule with a multireference character in its ground electronic state and the dissociation curve of core-excited molecular nitrogen. For ozone, the MR-ADC results agree well with the data from experimental and previous multireference studies of ozone XAS, in contrast to the results of single-reference methods, which underestimate relative peak energies and intensities. The MR-ADC methods also predict the correct shape of the core-excited nitrogen potential energy curve, and are in good agreement with accurate calculations using driven similarity renormalization group approaches. These findings suggest that MR-ADC(2) and MR-ADC(2)-X are promising methods for the XAS simulations of multireference systems and pave the way for their efficient computer implementation and applications.

Comprehensive Theoretical Study on Four Typical Intramolecular Hydrogen Shift Reactions of Peroxy Radicals: Multireference Character, Recommended Model Chemistry, and Kinetics.

Intramolecular hydrogen shift reactions in peroxy radicals (RO2• → •QOOH) play key roles in the low-temperature combustion and in the atmospheric chemistry. In the present study, we found that a mild-to-moderate multireference character of a potential energy surface (PES) is widely present in four typical hydrogen shift reactions of peroxy radicals (RO2•, R = ethyl, vinyl, formyl methyl, and acetyl) by a systematic assessment based on the T1 diagnostic, %TAE diagnostic, M diagnostic, and contribution of the dominant configuration of the reference CASSCF wavefunction (C02). To assess the effects of these inherent multireference characters on electronic structure calculations, we compared the PESs of the four reactions calculated by the multireference method CASPT2 in the complete basis set (CBS) limit, single-reference method CCSD(T)-F12, and single-reference-based composite method WMS. The results showed that ignoring the multireference character will introduce a mean unsigned deviation (MUD) of 0.46-1.72 kcal/mol from CASPT2/CBS results by using the CCSD(T)-F12 method or a MUD of 0.49-1.37 kcal/mol by WMS for three RO2• reactions (R = vinyl, formyl methyl, and acetyl) with a stronger multireference character. Further tests by single-reference Kohn-Sham (KS) density functional theory methods showed even larger deviations. Therefore, we specifically developed a new hybrid meta-generalized gradient approximation (GGA) functional M06-HS for the four typical H-shift reactions of peroxy radicals based on the WMS results for the ethyl peroxy radical reaction and on the CASPT2/CBS results for the others. The M06-HS method has an averaged MUD of 0.34 kcal/mol over five tested basis sets against the benchmark PESs, performing best in the tested 38 KS functionals. Last, in a temperature range of 200-3000 K, with the new functional, we calculated the high-pressure-limit rate coefficients of these H-shift reactions by the multi-structural variational transition-state theory with the small-curvature tunneling approximation (MS-CVT/SCT) and the thermochemical properties of all of the involved key radicals by the multi-structural torsional (MS-T) anharmonicity approximation method.

Toward an efficient implementation of internally contracted coupled-cluster methods.

A new implementation of the internally contracted multireference coupled-cluster with singles and doubles (icMRCCSD) method is presented. The new code employs an efficient tensor contraction kernel and can also avoid full four-external integral transformations, which significantly extends the scope of the applicability of icMRCCSD. The new implementation is currently restricted to the simple case of two active electrons in two orbitals and also supports the computation of spin-adapted doublet and triplet coupled-cluster wavefunctions. This contribution describes the basic approach for the automated derivation of working equations and benchmarks the current code against efficient implementations of standard methods, such as single-reference coupled-cluster singles and doubles (CCSD) and internally contracted multireference configuration interaction (icMRCI). Run times for linearized variants of icMRCCSD are only twice as long as comparable CCSD runs and similar to those of the icMRCI implementation, while non-linear terms of more complete variants of icMRCCSD lead to an order of magnitude longer computation times. Nevertheless, the new code allows for computations at larger scales than it was possible previously, with less demands on memory and disk-space resources. This is exemplified by numerical structure optimizations and harmonic force field determinations of NC2H5 isomers and the singlet and triplet states of m-benzyne. In addition, the exchange coupling of a dinuclear copper complex is determined. This work also defines a new commutator approximation for icMRCCSD, which includes all terms that are also present in the single-reference CCSD method, thus yielding a consistent pair of single-reference and multireference coupled-cluster methods.