Local explicitly correlated second-order perturbation theory for the accurate treatment of large molecules

Local Wave Function Embedding: Correlation Regions in PNO-LCCSD(T)-F12 Calculations

Many chemical reactions affect only a rather small number of bonds, leaving the largest part of the chemical and geometrical structure of the molecules nearly unchanged. In this work we extended the previously proposed region method [J. Chem. Phys. 128, 144106 (2008)] to PNO-LCCSD(T)-F12. Using this method, we investigate whether accurate reaction energies for larger systems can be obtained by correlating only the electrons in a region of localized molecular orbitals close to the reaction center at high-level (PNO-LCCSD(T)-F12). The remainder is either treated at lower level (PNO-LMP2-F12) or left uncorrelated (Hartree-Fock frozen core). It is demonstrated that indeed the computed reaction energies converge rather quickly with the size of the correlation regions toward the results of the full calculations. Typically, 2-3 bonds from the reacting atoms need to be included to reproduce the results of the full calculations to within ±0.2 kcal/mol. We also computed spin-state energy differences in a large transition metal complex, where a factor of 15 in computation time could be saved, still yielding a result that is within ±0.1 kcal/mol of the one obtained in a full PNO-LCCSD(T)-F12 calculation.

Analytic Gradients for Density Fitting MP2 Using Natural Auxiliary Functions

The natural auxiliary function (NAF) approach is an approximation to decrease the size of the auxiliary basis set required for quantum chemical calculations utilizing the density fitting technique. It has been proven efficient to speed up various correlation models, such as second-order Møller-Plesset (MP2) theory and coupled-cluster methods. Here, for the first time, we discuss the theory of analytic derivatives for correlation methods employing the NAF approximation on the example of MP2. A detailed algorithm for the gradient calculation with the NAF approximation is proposed in the framework of the method of Lagrange multipliers. To assess the effect of the NAF approximation on gradients and optimized geometric parameters, a series of benchmark calculations on small and medium-sized systems was performed. Our results demonstrate that, for MP2, sufficiently accurate gradients and geometries can be achieved with a moderate time reduction of 15-20% for both small and medium-sized molecules.

Isotopic effects on the rotational (de-)excitation rate coefficients of ortho-CH3Cl colliding with He

Chloromethane, CH3Cl, is the first organohalogen molecule to be detected in the interstellar medium. Using the recently generated accurate three-dimensional potential energy surface (3D-PES) for the weakly bound CH335Cl-He complex, we deduced that of CH337Cl-He. Both 3D-PESs were incorporated later into dynamical computations code for nuclear motions treatments of each isotopologue colliding with He. We determined the state-to-state (de-)excitation cross sections for transitions among the 105 lowest rotational levels of both ortho-CH335Cl and ortho-CH337Cl (up to jkɛ = 206±). For total energies up to 100 cm-1, we used the quantum close-coupling methodology, and we adopted the coupled state approach for higher energies (up to 2500 cm-1). Rate coefficients for temperatures ranging from 5 to 150 K are then deduced after averaging these cross sections over a Maxwell-Boltzmann velocity distribution. Computations show that isotopic effects are weak, validating the use of collision rates of ortho-CH335Cl for ortho-CH337Cl and vice-versa. However, we expect that our results will be helpful to accurately determine the abundances of these isotopologues in the interstellar medium and, more generally, for understanding the complex and still not fully elucidated chemistry of chlorine containing molecular species there.

Accurate Enthalpies of Formation for PFAS from First-Principles: Combining Different Levels of Theory in a Generalized Thermochemical Hierarchy

The enthalpies of formation are computed for a large number of per- and poly fluoroalkyl substances (PFAS) using a connectivity-based hierarchy (CBH) approach. A combination of different electronic structure methods are used to provide the reference data in a hierarchical manner. The ANL0 method, in conjunction with the active thermochemical tables, provides enthalpies of formation for smaller species with subchemical accuracy. Coupled-cluster theory with explicit correlations are used to compute enthalpies of formation for intermediate species, based upon the ANL0 results. For the largest PFAS, including perfluorooctanoic acid (PFOA) and heptafluoropropylene oxide dimer acid (GenX), coupled-cluster theory with local correlations is used. The sequence of homodesmotic reactions proposed by the CBH are determined automatically by a new open-source code, AutoCBH. The results are the first reported enthalpies of formation for the majority of the species. A convergence analysis and global uncertainty quantification confirm that the enthalpies of formation at 0 K should be accurate to within ±5 kJ/mol. This new approach is not limited to PFAS, but can be applied to many chemical systems.

Accurate Calculation of Isomerization and Conformational Energies of Larger Molecules Using Explicitly Correlated Local Coupled Cluster Methods in Molpro and ORCA

An overview of the approximations in the explicitly correlated local coupled cluster methods PNO-LCCSD(T)-F12 in Molpro and DLPNO-CCSD(T)F12 in ORCA is given. Options to select the domains of projected atomic orbitals (PAOs), pair natural orbitals (PNOs), and triples natural orbitals (TNOs) in both programs are described and compared in detail. The two programs are applied to compute isomerization and conformational energies of the ISOL24 and ACONFL test sets, where the former is part of the GMTKN55 benchmark suite. Thorough studies of basis set effects are presented for selected systems. These revealed large intramolecular basis set superposition effects that make it practically impossible to reliably determine the complete basis set (CBS) limits without including explicitly correlated terms. The latter strongly reduce the basis set dependence and at the same time also errors caused by the local domain approximations. On the basis of these studies, the PNO-LCCSD(T)-F12 method is applied to determine new reference energies for the above-mentioned benchmark sets. We are confident that our results should agree within a few tenths of a kcal mol-1 with the (unknown) CCSD(T)/CBS values, which therefore allowed us to define computational settings for accurate explicitly correlated local coupled cluster methods with moderate computational effort. With these protocols, especially PNO-LCCSD(T)-F12b/AVTZ', reliable reference values for comprehensive benchmark sets can be generated efficiently. This can significantly advance the development and evaluation of the performance of approximate electronic structure methods, especially improved density functional approximations or machine learning approaches.

Corrigendum: Coupled cluster theory on modern heterogeneous supercomputers

[This corrects the article DOI: 10.3389/fchem.2023.1154526.].

Coupled cluster theory on modern heterogeneous supercomputers

This study examines the computational challenges in elucidating intricate chemical systems, particularly through ab-initio methodologies. This work highlights the Divide-Expand-Consolidate (DEC) approach for coupled cluster (CC) theory-a linear-scaling, massively parallel framework-as a viable solution. Detailed scrutiny of the DEC framework reveals its extensive applicability for large chemical systems, yet it also acknowledges inherent limitations. To mitigate these constraints, the cluster perturbation theory is presented as an effective remedy. Attention is then directed towards the CPS (D-3) model, explicitly derived from a CC singles parent and a doubles auxiliary excitation space, for computing excitation energies. The reviewed new algorithms for the CPS (D-3) method efficiently capitalize on multiple nodes and graphical processing units, expediting heavy tensor contractions. As a result, CPS (D-3) emerges as a scalable, rapid, and precise solution for computing molecular properties in large molecular systems, marking it an efficient contender to conventional CC models.

Valence-shell ionization of acetyl cyanide: simulation of the photoelectron and infra-red spectra

The vibrational envelopes of the first and second lines of the acetyl cyanide valence photoelectron spectrum [Katsumata et al., J. Electron Spectrosc. Relat. Phenom., 2000, 49, 113] in the gas phase have been simulated considering the Taylor expansion of the dipole moment from zero up to the second order as well as the changes of geometries/frequencies/normal modes between the initial neutral electronic ground state and the final (15a'^(-1), 3a''^(-1)) cationic states. It is shown that the vibrational profile of the first band (A') extending over 3500 cm^-1 with a vibrational spacing of 500 cm^-1 is not due solely to the overtones (v = 0 → v' = 1, 2, 3,…) of the C-CO bending mode as previously suggested but results from a collection of (v = 0 → v' = 1) transitions with frequencies multiple of 500 cm^-1 associated with the CO stretching at 1550 cm^-1, C-C stretching at 1045 cm^-1 and C-CO, C-CN bending modes at 370/500 cm^-1 completed by combination bands. Our calculations also reveal that the structureless and asymmetric shape of the second band (A'') is due to the activation of the torsion mode at low-frequency (ω ≈ 150 cm^-1) induced by the rotation (60 degrees) of the methyl group blurring the main vibrational progression (ω ≈ 1115 cm^-1) corresponding to the cooperative motions of the methyl CH bending and C-CO bending/CO stretching. Infra-red spectra of the fundamental and both the 15a'^(-1) and 3a''^(-1) cationic states were finally simulated. In contrast to the photoemission spectra, the infrared intensity of the CO stretching motion is very weak. The spectra are mainly dominated by the v = 0 → v = 1 transition of the CN stretching and the CH symmetric bending/stretching modes, providing complementary information between photoemission and infra-red spectroscopies to capture the nature of the cationic states in acetyl-cyanide.

Product Identification in the Low-Temperature Oxidation of Cyclohexane Using a Jet-Stirred Reactor in Combination with SVUV-PEPICO Analysis and Theoretical Quantum Calculations

Cyclohexane oxidation chemistry was investigated using a near-atmospheric pressure jet-stirred reactor at T = 570 K and equivalence ratio ϕ = 0.8. Numerous intermediates including hydroperoxides and highly oxygenated molecules were detected using synchrotron vacuum ultraviolet photoelectron photoion coincidence spectroscopy. Supported by high-level quantum calculations, the analysis of photoelectron spectra allowed the firm identification of molecular species formed during the oxidation of cyclohexane. Besides, this work validates recently published gas chromatography and synchrotron vacuum ultraviolet photoionization mass spectrometry data. Unambiguous detection of characteristic hydroperoxides (e.g., γ-ketohydroperoxides) and their respective decomposition products provides support for the conventional O₂ addition channels up to the third addition and their relative contribution to the cyclohexane oxidation. The results were also compared with the predictions of a recently proposed new detailed kinetic model of cyclohexane oxidation. Most of the predictions are in line with the current experimental findings, highlighting the robustness of the kinetic model. However, the analysis of the recorded slow photoelectron spectra indicating the possible presence of C₅ species in the kinetic model provides hints that the substituted cyclopentyl radicals from cyclohexyl ring opening might play a minor role in cyclohexane oxidation. Potentially important missing reactions are also discussed.

Probing the dynamics of the photo-induced decarboxylation of neutral and ionic pyruvic acid

The dynamics of the electronically excited pyruvic acid (PA) and of its unimolecular decomposition upon single photon ionization are investigated by means of a table top fs laser and VUV...

Diastereomers and Low-Temperature Oxidation

Diastereomers have historically been ignored when building kinetic mechanisms for combustion. Low-temperature oxidation kinetics, which continues to gain interest in both combustion and atmospheric communities, may be affected by the inclusion of diastereomers in radical chain-branching pathways. In this work, key intermediates and transition states lacking stereochemical specification in an existing diethyl ether low-temperature oxidation mechanism were replaced with their diastereomeric counterparts. Rate coefficients for reactions involving diastereomers were computed with ab initio transition state theory master equation calculations. The presence of diastereomers increased rate coefficients by factors of 1.2-1.6 across various temperatures and pressures. Ignition delay simulations incorporating these revised rate coefficients indicate that the diastereomers enhanced the overall reactivity of the mechanism by almost 15% and increased the peak ketohydroperoxide concentration by 30% in the negative temperature coefficient region at combustion-relevant pressures. These results provide an illustrative indication of the important role of stereomeric effects in oxidation kinetics.

Explicitly correlated potential energy surface of the CH3Cl-He van der Waals complex and applications

A new 3D-potential energy surface (3D-PES) for the weakly bound CH₃Cl-He complex is mapped in Jacobi coordinates. Electronic structure calculations are performed using the explicitly correlated coupled clusters with single, double, and perturbative triple excitations approach in conjunction with the aug-cc-pVTZ basis set. Then, an analytical expansion of this 3D-PES is derived. This PES shows three minimal structures for collinear C-Cl-He arrangements and for He located in between two H atoms, in the plane parallel to the three H atoms, which is near the center of mass of CH₃Cl. The latter form corresponds to the global minimum. Two maxima are also found, which connect the minimal structures. We then evaluated the pressure broadening coefficients of the spectral lines of CH₃Cl in a helium bath based on our ab initio potential. Satisfactory agreement with experiments was observed, confirming the good accuracy of our 3D-PES. We also derived the bound rovibronic levels for ortho- and para-CH₃Cl-He dimers after quantum treatment of the nuclear motions. For both clusters, computations show that although the ground vibrational state is located well above the intramolecular isomerization barriers, the rovibronic levels may be associated with a specific minimal structure. This can be explained by vibrational localization and vibrational memory effects.

Scalable Electron Correlation Methods. 8. Explicitly Correlated Open-Shell Coupled-Cluster with Pair Natural Orbitals PNO-RCCSD(T)-F12 and PNO-UCCSD(T)-F12

We present explicitly correlated open-shell pair natural orbital local coupled-cluster methods, PNO-RCCSD(T)-F12 and PNO-UCCSD(T)-F12. The methods are extensions of our previously reported PNO-R/UCCSD methods (J. Chem. Theory Comput., 2020, 16, 3135-3151, https://pubs.acs.org/doi/10.1021/acs.jctc.0c00192) with additions of explicit correlation and perturbative triples corrections. The explicit correlation treatment follows the spin-orbital CCSD-F12b theory using Ansatz 3*A, which is found to yield comparable or better basis set convergence than the more rigorous Ansatz 3C in computed ionization potentials and reaction energies using double- to quaduple-ζ basis sets. The perturbative triples correction is adapted from the spin-orbital (T) theory to use triples natural orbitals (TNOs). To address the coupling due to off-diagonal Fock matrix elements, the local triples amplitudes are iteratively solved using small domains of TNOs, and a semicanonical (T0) domain correction with larger domains is applied to reduce the domain errors. The performance of the methods is demonstrated through benchmark calculations on ionization potentials, radical stabilization energies, reaction energies of fragmentations and rearrangements in radical cations, and spin-state energy differences of iron complexes. For a few test sets where canonical calculations are feasible, PNO-RCCSD(T)-F12 results agree with the canonical ones to within 0.4 kcal mol^-1, and this maximum error is reduced to below 0.2 kcal mol^-1 when large local domains are used. For larger systems, results using different thresholds for the local approximations are compared to demonstrate that 1 kcal mol^-1 level of accuracy can be achieved using our default settings. For a couple of difficult cases, it is demonstrated that the errors from individual approximations are only a fraction of 1 kcal mol^-1, and the overall accuracy of the method does not rely on error compensations. In contrast to canonical calculations, the use of spin-orbitals does not lead to a significant increase of computational time and memory usage in the most expensive steps of PNO-R/UCCSD(T)-F12 calculations. The only exception is the iterative solution of the (T) amplitudes, which can be avoided without significant errors by using a perturbative treatment of the off-diagonal coupling, known as (T1) approximation. For most systems, even the semicanonical approximation (T0) leads only to small errors in relative energies. Our program is well parallelized and capable of computing accurate correlation energies for molecules with 100-200 atoms using augmented triple-ζ basis sets in less than a day of elapsed time on a small computer cluster.

Introductory lecture: when the density of the noninteracting reference system is not the density of the physical system in density functional theory

A major challenge in density functional theory (DFT) is the development of density functional approximations (DFAs) to overcome errors in existing DFAs, leading to more complex functionals. For such functionals, we consider roles of the noninteracting reference systems. The electron density of the Kohn-Sham (KS) reference with a local potential has been traditionally defined as being equal to the electron density of the physical system. This key idea has been applied in two ways: the inverse calculation of such a local KS potential for the reference from a given density and the direct calculation of density and energy based on given DFAs. By construction, the inverse calculation can yield a KS reference with the density equal to the input density of the physical system. In application of DFT, however, it is the direct calculation of density and energy from a DFA that plays a central role. For direct calculations, we find that the self-consistent density of the KS reference defined by the optimized effective potential (OEP), is not the density of the physical system, when the DFA is dependent on the external potential. This inequality holds also for the density of generalized KS (GKS) or generalized OEP reference, which allows a nonlocal potential, when the DFA is dependent on the external potential. Instead, the density of the physical system, consistent with a given DFA, is given by the linear response of the total energy with respect to the variation of the external potential. This is a paradigm shift in DFT on the use of noninteracting references: the noninteracting KS or GKS references represent the explicit computational variables for energy minimization, but not the density of the physical system for external potential-dependent DFAs. We develop the expressions for the electron density so defined through the linear response for general DFAs, demonstrate the results for orbital functionals and for many-body perturbation theory within the second-order and the random-phase approximation, and explore the connections to developments in DFT.

Unimolecular decomposition of methyl ketene and its dimer in the gas phase: theory and experiment

We present a combined theoretical and experimental investigation on the single photoionization and dissociative photoionization of gas-phase methyl ketene (MKE) and its neutral dimer (MKE2). The performed experiments entail the recording of photoelectron photoion coincidence (PEPICO) spectra and slow photoelectron spectra (SPES) in the energy regime 8.7-15.5 eV using linearly polarized synchrotron radiation. We observe both dimerization and trimerization of the monomer which brings about significantly complex and abstruse dissociative ionization patterns. These require the implementation of theoretical calculations to explore the potential energy surfaces of the monomer and dimer's neutral and ionized geometries. To this end, explicitly correlated quantum chemical methodologies involving the coupled cluster with single, double and perturbative triple excitations (R)CCSD(T)-F12 method, are utilized. An improvement in the adiabatic ionization energy of MKE is presented (AIE = 8.937 ± 0.020 eV) as well as appearance energies for multiple fragments formed through dissociative ionization of either the MKE monomer or dimer. In this regard, the synergy of experiment and theory is crucial to interpreting the obtained results. We discuss the potential astrochemical implications of this work in the context of recent advances in the field of astrochemistry and speculate on the potential presence and eventual fate of interstellar MKE molecules.

The Molpro quantum chemistry package

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

Isomer-sensitive characterization of low temperature oxidation reaction products by coupling a jet-stirred reactor to an electron/ion coincidence spectrometer: case of n-pentane

Using a tunable vacuum ultraviolet synchrotron beam line and first principle computations, a jet-stirred reactor was coupled for the first time to a photoionization mass spectrometer using electron/ion coincidence imaging.

Comprehensive Benchmark Results for the Domain Based Local Pair Natural Orbital Coupled Cluster Method (DLPNO-CCSD(T)) for Closed- and Open-Shell Systems

In this study we examine the accuracy of domain-based local pair natural orbital coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD(T)) on a large benchmark data set. To this end, we use the recently published GMTKN55 superset of molecules that contains 1505 relative energies and 2462 single-point calculations. To our knowledge this is the most comprehensive benchmark evaluation of any highly correlated wave function based ab initio method to date. In the first part of the study, canonical CCSD(T) reference calculations were carried out on the entire test set in order to guarantee that the reference data are of uniform quality. Second, DLPNO-CCSD(T) calculations were carried out under identical conditions. The main finding is that with the exception of two data sets, all data sets have a MAD of 0.4 kcal/mol or less and the majority of sets have a MAD of less than 0.2 kcal/mol. For open shells, the accuracy of the DLPNO calculations was significantly improved through an iterative version of the triples correction.

Shock Tube Laser Schlieren Study of the Pyrolysis of Isopropyl Nitrate

The decomposition of isopropyl nitrate was measured behind incident shock waves using laser schlieren densitometry in a diaphragmless shock tube. Experiments were conducted over the temperature range of 700-1000 K and at pressures of 71, 126, and 240 Torr. Electronic structure theory and RRKM Master Equation methods were used to predict the decomposition kinetics. RRKM/ME parameters were optimized against the experimental data to provide an accurate prediction over a broader range of conditions. The initial decomposition i-C₃H₇ONO₂ ⇌ i-C₃H₇O + NO₂ has a high-pressure limit rate coefficient of 5.70 × 10²²T^-1.80 exp[-21287.5/T] s^-1. A new chemical kinetic mechanism was developed to model the chemistry after the initial dissociation. A new shock tube module was developed for Cantera, which allows for arbitrarily large mechanisms in the simulation of laser schlieren experiments. The present work is in good agreement with previous experimental studies.

Explicitly correlated potential energy surface of the CO2-CO van der Waals dimer and applications

The four-dimensional-potential energy surface (4D-PES) of the CO2-CO van der Waals complex is generated using the explicitly correlated coupled cluster with single, double, and perturbative triple excitation (CCSD(T)-F12) method in conjunction with the augmented correlation-consistent triple zeta (aug-cc-pVTZ) basis set. This 4D-PES is developed over the set of inter-molecular coordinates and where the CO2 and CO monomers are treated as rigid rotors. Afterwards, analytic fits of this 4D-PES are carried out. In addition to the already known C-bound and O-bound stable structures of CO2-CO, we characterise a new isomer: it has a T-shaped structure where the O atom of the CO2 moiety points into the centre of mass of CO. We also find the saddle points connecting these minimal structures. This new isomer may play a role during the intramolecular isomerization processes at low energies. Then, the 4D-PES expansion is incorporated into bound vibrational state computations of C-bound and O-bound complexes. We also computed the temperature dependence of the second virial coefficient for CO2-CO. A good agreement with experiments is found.

Energetics and ionization dynamics of two diarylketone molecules: benzophenone and fluorenone

Single photon ionization and subsequent unimolecular ion decomposition were studied on jet-cooled benzophenone and fluorenone separately, using VUV synchrotron radiation in a photoion/photoelectron coincidence setup. Slow PhotoElectron Spectra (SPES) were recorded in coincidence with either the parent or the fragment ions for hν < 12.5 eV. Dissociative ionization is observed for benzophenone only. The full interpretation of the measurements, including the identification of the neutral and ionic species when dissociative ionization is at play, benefits from high level ab initio computations for determining the equilibrium structures and the energetics of the neutral and ionized molecules and of their fragments. Electronically excited states of the parent molecular ions were calculated also. From this analysis, an accurate experimental determination of the energetics of the benzophenone and fluorenone ions and of their fragmentation channels is available: adiabatic ionization energies of benzophenone at 8.923 ± 0.005 eV and of fluorenone at 8.356 ± 0.007 eV; and appearance energies of benzophenone fragment ions at 11.04 ± 0.02 eV (loss of C₆H₅), 11.28 ± 0.02 eV (loss of H) and 11.45 ± 0.02 eV (loss of CO). The corresponding fragmentation mechanisms are explored, showing likely concerted bonds rearrangement. Possible pre-ionizing fragmentation is discussed in light of the spectra presented. The structural rigidity of fluorenone diarylketone seems to be the origin of the inhibition of the fragmentation of its cation.

Photoionization and dissociative photoionization of propynal in the gas phase: theory and experiment

Propynal (HCCCHO) is a complex organic compound (COM) of astrochemical and astrobiological interest. We present a combined theoretical and experimental investigation on the single photon ionization of gas-phase propynal, in the 10 to 15.75 eV energy range. Fragmentation pathways of the resulting cation were investigated both theoretically and experimentally. The adiabatic ionization energy (AIE) has been measured to be AIEexp = 10.715 ± 0.005 eV using tunable VUV synchrotron radiation coupled with a double imaging photoelectron photoion coincidence (i2PEPICO) spectrometer. In the energy range under study, three fragments formed by dissociative photoionization were identified experimentally: HC3O+, HCO+ and C2H2+, and their respective appearance energies (AE) were found to be AE = 11.26 ± 0.03, 13.4 ± 0.3 and 11.15 ± 0.03 eV, respectively. Using explicitly correlated coupled cluster calculations and after inclusion of the zero point vibrational energy, core-valence and scalar relativistic effects, the AIE is calculated to be AIEcalc = 10.717 eV, in excellent agreement with the experimental finding. The appearance energies of the fragments were calculated using a similar methodological approach. To further interpret the observed vibrational structure, anharmonic frequencies were calculated for the fundamental electronic state of the propynal cation. Moreover, MRCI calculations were carried out to understand the population of excited states of the cationic species. This combined experimental and theoretical study will help to understand the presence and chemical evolution of propynal in the external parts of interstellar clouds where it has been observed.

Understanding non-covalent interactions in larger molecular complexes from first principles

Non-covalent interactions pervade all matter and play a fundamental role in layered materials, biological systems, and large molecular complexes. Despite this, our accumulated understanding of non-covalent interactions to date has been mainly developed in the tens-of-atoms molecular regime. This falls considerably short of the scales at which we would like to understand energy trends, structural properties, and temperature dependencies in materials where non-covalent interactions have an appreciable role. However, as more reference information is obtained beyond moderately sized molecular systems, our understanding is improving and we stand to gain pertinent insights by tackling more complex systems, such as supramolecular complexes, molecular crystals, and other soft materials. In addition, accurate reference information is needed to provide the drive for extending the predictive power of more efficient workhorse methods, such as density functional approximations that also approximate van der Waals dispersion interactions. In this perspective, we discuss the first-principles approaches that have been used to obtain reference interaction energies for beyond modestly sized molecular complexes. The methods include quantum Monte Carlo, symmetry-adapted perturbation theory, non-canonical coupled cluster theory, and approaches based on the random-phase approximation. By considering the approximations that underpin each method, the most accurate theoretical references for supramolecular complexes and molecular crystals to date are ascertained. With these, we also assess a handful of widely used exchange-correlation functionals in density functional theory. The discussion culminates in a framework for putting into perspective the accuracy of high-level wavefunction-based methods and identifying future challenges.

Rotational (de-)excitation of isocyanogen by collision with helium at low energies

Isocyanogen, CNCN, was discovered very recently in the interstellar medium (ISM). At present, the rate coefficients for the rotational (de-)excitation of CNCN by collisions with He are determined. First, we mapped the interaction potential between CNCN and He in Jacobi coordinates using highly correlated ab initio methodology. Then, an analytical expansion of the CNCN-He potential energy surface is derived. Later on, quantum dynamical treatments of nuclear motions are performed using the close coupling technique. We obtained the cross sections for the rotational (de-)excitation of CNCN after a collision by He up to 2000 cm^-1 total energies. These cross sections are used to deduce the collision rates in the 10-300 K range. These data are needed for modeling the CNCN abundances in the ISM. This work should help for determining the abundance of such non-symmetrical dicyanopolyynes in astrophysical media and indirectly the symmetric one [Cyanogen (NCCN)].

Crystal Field Splittings in Lanthanide Complexes: Inclusion of Correlation Effects beyond Second Order Perturbation Theory

State-averaged complete active space self-consistent field (CASSCF) calculations and a subsequent spin-orbit calculation mixing the CASSCF wave functions (CASSCF/state-interaction with spin-orbit coupling) is the conventional approach used for ab initio calculations of crystal-field splittings and magnetic properties of lanthanide complexes. However, this approach neglects dynamical correlation. Complete active space second-order perturbation theory (CASPT2) can be used to account for dynamical correlation but suffers from the well-known problems of multireference perturbation theory, e.g., intruder state problems. Variational multireference configuration interaction (MRCI) calculations do not show these problems but are usually not feasible due to the large size of real lanthanide complexes. Here, we present a quasi-local projected internally contracted MRCI approach which makes MRCI calculations of lanthanide complexes feasible and allows assessing the influence of dynamical correlation beyond second-order perturbation theory. We apply the method to two well-studied molecules, namely, [Er{N(SiMe₃)₂}₃] and {C(NH₂)₃}₅[Er(CO₃)₄]·11H₂O.

A new near-linear scaling, efficient and accurate, open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory

The Coupled-Cluster expansion, truncated after single and double excitations (CCSD), provides accurate and reliable molecular electronic wave functions and energies for many molecular systems around their equilibrium geometries. However, the high computational cost, which is well-known to scale as O(N⁶) with system size N, has limited its practical application to small systems consisting of not more than approximately 20-30 atoms. To overcome these limitations, low-order scaling approximations to CCSD have been intensively investigated over the past few years. In our previous work, we have shown that by combining the pair natural orbital (PNO) approach and the concept of orbital domains it is possible to achieve fully linear scaling CC implementations (DLPNO-CCSD and DLPNO-CCSD(T)) that recover around 99.9% of the total correlation energy [C. Riplinger et al., J. Chem. Phys. 144, 024109 (2016)]. The production level implementations of the DLPNO-CCSD and DLPNO-CCSD(T) methods were shown to be applicable to realistic systems composed of a few hundred atoms in a routine, black-box fashion on relatively modest hardware. In 2011, a reduced-scaling CCSD approach for high-spin open-shell unrestricted Hartree-Fock reference wave functions was proposed (UHF-LPNO-CCSD) [A. Hansen et al., J. Chem. Phys. 135, 214102 (2011)]. After a few years of experience with this method, a few shortcomings of UHF-LPNO-CCSD were noticed that required a redesign of the method, which is the subject of this paper. To this end, we employ the high-spin open-shell variant of the N-electron valence perturbation theory formalism to define the initial guess wave function, and consequently also the open-shell PNOs. The new PNO ansatz properly converges to the closed-shell limit since all truncations and approximations have been made in strict analogy to the closed-shell case. Furthermore, given the fact that the formalism uses a single set of orbitals, only a single PNO integral transformation is necessary, which offers large computational savings. We show that, with the default PNO truncation parameters, approximately 99.9% of the total CCSD correlation energy is recovered for open-shell species, which is comparable to the performance of the method for closed-shells. UHF-DLPNO-CCSD shows a linear scaling behavior for closed-shell systems, while linear to quadratic scaling is obtained for open-shell systems. The largest systems we have considered contain more than 500 atoms and feature more than 10 000 basis functions with a triple-ζ quality basis set.

Insights on the interaction of Zn2+ cation with triazoles: Structures, bonding, electronic excitation and applications

At present, we investigate the structures, the stability, the bonding and the spectroscopy of the Zn²⁺-triazole complexes (Zn²⁺-Tz), which are subunits of triazolate based porous materials and Zn-enzymes. This theoretical work is performed using ab initio methods and density functional theory (DFT) where dispersion correction is included. Through these benchmarks, we establish the ability and reliability of M05-2X+D3 and PBE0+D3 functionals for the correct description of Zn²⁺-Tz bond since these DFTs lead to close agreement with post Hartree-Fock methods. Therefore, M05-2X+D3 and PBE0+D3 functionals are recommended for the characterization of larger organometallic complexes formed by Zn and N-rich linkers. For Zn²⁺-Tz, we found two stable σ-type complexes: (i) a planar structure where Zn²⁺ links to unprotonated nitrogen and (ii) an out-of-plane cluster where carbon interacts with Zn²⁺. The most stable isomers consist on a coordinated covalent bond between the lone pair of unprotonated nitrogen and the vacant 4s orbital of Zn²⁺. The roles of covalent interactions within these complexes are discussed after vibrational, NBO, NPA charges and orbital analyses. The bonding is dominated by charge transfer from Zn²⁺ to Tz and intramolecular charge transfer, which plays a vital role for the catalytic activity of these complexes. These findings are important to understand, at the microscopic level, the structure and the bonding within triazolate based macromolecular porous materials and Zn-enzymes.

An ab initio study of the ground and excited electronic states of the methyl radical

The ground and some excited electronic states of the methyl radical have been characterized by means of highly correlated ab intio techniques. The specific excited states investigated are those involved in the dissociation of the radical, namely the 3s and 3p_z Rydberg states, and the A₁ and B₁ valence states crossing them, respectively. The C-H dissociative coordinate and the HCH bending angle were considered in order to generate the first two-dimensional ab initio representation of the potential surfaces of the above electronic states of CH₃, along with the nonadiabatic couplings between them. Spectroscopic constants and frequencies calculated for the ground and bound excited states agree well with most of the available experimental data. Implications of the shape of the excited potential surfaces and couplings for the dissociation pathways of CH₃ are discussed in the light of recent experimental results for dissociation from low-lying vibrational states of CH₃. Based on the ab initio data some predictions are made regarding methyl photodissociation from higher initial vibrational states.

Optimization of the linear-scaling local natural orbital CCSD(T) method: Redundancy-free triples correction using Laplace transform

An improved algorithm is presented for the evaluation of the (T) correction as a part of our local natural orbital (LNO) coupled-cluster singles and doubles with perturbative triples [LNO-CCSD(T)] scheme [Z. Rolik et al., J. Chem. Phys. 139, 094105 (2013)]. The new algorithm is an order of magnitude faster than our previous one and removes the bottleneck related to the calculation of the (T) contribution. First, a numerical Laplace transformed expression for the (T) fragment energy is introduced, which requires on average 3 to 4 times fewer floating point operations with negligible compromise in accuracy eliminating the redundancy among the evaluated triples amplitudes. Second, an additional speedup factor of 3 is achieved by the optimization of our canonical (T) algorithm, which is also executed in the local case. These developments can also be integrated into canonical as well as alternative fragmentation-based local CCSD(T) approaches with minor modifications. As it is demonstrated by our benchmark calculations, the evaluation of the new Laplace transformed (T) correction can always be performed if the preceding CCSD iterations are feasible, and the new scheme enables the computation of LNO-CCSD(T) correlation energies with at least triple-zeta quality basis sets for realistic three-dimensional molecules with more than 600 atoms and 12 000 basis functions in a matter of days on a single processor.

Computational Kinetics by Variational Transition-State Theory with Semiclassical Multidimensional Tunneling: Direct Dynamics Rate Constants for the Abstraction of H from CH3OH by Triplet Oxygen Atoms

Rate constants and the product branching ratio for hydrogen abstraction from CH3OH by O(3P) were computed with multistructural variational transition-state theory including microcanonically optimized multidimensional tunneling. Benchmark calculations of the forward and reverse classical barrier heights and the reaction energetics have been carried out by using coupled cluster theory and multireference calculations to select the most reliable density functional method for direct dynamics computations of the rate constants. The dynamics calculations included the anharmonicity of the zero-point energies and partition functions, with specific-reaction-parameter scaling factors for reactants and transition states, and multistructural torsional anharmonicity was included for the torsion around the C-O bond in methanol and in the transition states. The resulting rate constants are presented over a wider range than they are available from experiment, but in the temperature range where experiments are available, they agree well with experimental values, which is encouraging for their reliability over the wider temperature range and for future computations of oxygen atom reaction rates. In contrast to a previous computational prediction, the branching ratio predicted by the present work shows that the formation of CH2OH + OH is the dominant channel over the whole range of temperature from 250 to 2000 K.

SparseMaps--A systematic infrastructure for reduced-scaling electronic structure methods. IV. Linear-scaling second-order explicitly correlated energy with pair natural orbitals

We present a formulation of the explicitly correlated second-order Møller-Plesset (MP2-F12) energy in which all nontrivial post-mean-field steps are formulated with linear computational complexity in system size. The two key ideas are the use of pair-natural orbitals for compact representation of wave function amplitudes and the use of domain approximation to impose the block sparsity. This development utilizes the concepts for sparse representation of tensors described in the context of the domain based local pair-natural orbital-MP2 (DLPNO-MP2) method by us recently [Pinski et al., J. Chem. Phys. 143, 034108 (2015)]. Novel developments reported here include the use of domains not only for the projected atomic orbitals, but also for the complementary auxiliary basis set (CABS) used to approximate the three- and four-electron integrals of the F12 theory, and a simplification of the standard B intermediate of the F12 theory that avoids computation of four-index two-electron integrals that involve two CABS indices. For quasi-1-dimensional systems (n-alkanes), the ON DLPNO-MP2-F12 method becomes less expensive than the conventional ON(5) MP2-F12 for n between 10 and 15, for double- and triple-zeta basis sets; for the largest alkane, C200H402, in def2-TZVP basis, the observed computational complexity is N(∼1.6), largely due to the cubic cost of computing the mean-field operators. The method reproduces the canonical MP2-F12 energy with high precision: 99.9% of the canonical correlation energy is recovered with the default truncation parameters. Although its cost is significantly higher than that of DLPNO-MP2 method, the cost increase is compensated by the great reduction of the basis set error due to explicit correlation.