Toward more accurate adiabatic connection approach for multireference wavefunctions.

A multiconfigurational adiabatic connection (AC) formalism is an attractive approach to compute the dynamic correlation within the complete active space self-consistent field and density matrix renormalization group (DMRG) models. Practical realizations of AC have been based on two approximations: (i) fixing one- and two-electron reduced density matrices (1- and 2-RDMs) at the zero-coupling constant limit and (ii) extended random phase approximation (ERPA). This work investigates the effect of removing the "fixed-RDM" approximation in AC. The analysis is carried out for two electronic Hamiltonian partitionings: the group product function- and the Dyall Hamiltonians. Exact reference AC integrands are generated from the DMRG full configuration interaction solver. Two AC models are investigated, employing either exact 1- and 2-RDMs or their second-order expansions in the coupling constant in the ERPA equations. Calculations for model molecules indicate that lifting the fixed-RDM approximation is a viable way toward improving the accuracy of existing AC approximations.

TREXIO: A file format and library for quantum chemistry.

TREXIO is an open-source file format and library developed for the storage and manipulation of data produced by quantum chemistry calculations. It is designed with the goal of providing a reliable and efficient method of storing and exchanging wave function parameters and matrix elements, making it an important tool for researchers in the field of quantum chemistry. In this work, we present an overview of the TREXIO file format and library. The library consists of a front-end implemented in the C programming language and two different back-ends: a text back-end and a binary back-end utilizing the hierarchical data format version 5 library, which enables fast read and write operations. It is compatible with a variety of platforms and has interfaces for Fortran, Python, and OCaml programming languages. In addition, a suite of tools have been developed to facilitate the use of the TREXIO format and library, including converters for popular quantum chemistry codes and utilities for validating and manipulating data stored in TREXIO files. The simplicity, versatility, and ease of use of TREXIO make it a valuable resource for researchers working with quantum chemistry data.

An efficient implementation of time-dependent linear-response theory for strongly orthogonal geminal wave function models.

We present an implementation of time-dependent linear-response equations for strongly orthogonal geminal wave function models: the time-dependent generalized valence bond (TD-GVB) perfect-pairing theory and the antisymmetrized product of strongly orthogonal geminals. The geminal wave functions are optimized using a restricted-step second-order algorithm suitable for handling many geminals, and the linear-response equations are solved in an efficient way using a direct iterative approach. The wave function optimization algorithm features an original scheme to create initial orbitals for the geminal functions in a black-box fashion. The implementation is employed to examine the accuracy of the geminal linear response for singlet excitation energies of small and medium-sized molecules. In systems dominated by dynamic correlation, geminal models constitute only a minor improvement with respect to time-dependent Hartree-Fock. Compared to the linear-response complete active space self-consistent field, TD-GVB either misses or gives large errors for states dominated by double excitations.

Dataset of noncovalent intermolecular interaction energy curves for 24 small high-spin open-shell dimers.

We introduce a dataset of 24 interaction energy curves of open-shell noncovalent dimers, referred to as the O24 × 5 dataset. The dataset consists of high-spin dimers up to 11 atoms selected to assure diversity with respect to interaction types: dispersion, electrostatics, and induction. The benchmark interaction energies are obtained at the restricted open-shell CCSD(T) level of theory with complete basis set extrapolation (from aug-cc-pVQZ to aug-cc-pV5Z). We have analyzed the performance of selected wave function methods MP2, CCSD, and CCSD(T) as well as the F12a and F12b variants of coupled-cluster theory. In addition, we have tested dispersion-corrected density functional theory methods based on the PBE exchange-correlation model. The O24 × 5 dataset is a challenge to approximate methods due to the wide range of interaction energy strengths it spans. For the dispersion-dominated and mixed-type subsets, any tested method that does not include the triples contribution yields errors on the order of tens of percent. The electrostatic subset is less demanding with errors that are typically an order of magnitude smaller than the mixed and dispersion-dominated subsets.

Molecular multibond dissociation with small complete active space augmented by correlation density functionals.

Molecular multibond dissociation displays a variety of electron correlation effects posing a challenge for theoretical description. We propose a CASΠ(M)DFT approach, which includes these effects in an efficient way by combining the complete active space self-consistent field method with density functional theory (DFT). Within CASΠ(M)DFT, a small complete active space (CAS) accounts for the long-range intrabond and middle-range interbond nondynamic correlation in the stretched bonds. The common short-range dynamic correlation is calculated with the Lee-Yang-Parr (LYP) correlation DFT functional corrected for the suppression of dynamic correlation with nondynamic correlation. The remaining middle-range interbond dynamic correlation is evaluated with the modified LYP functional of the bond densities. As a result, CASΠ(M)DFT potential energy curves (PECs) calculated in the relatively small triple-zeta basis closely reproduce the benchmark complete basis set PECs for the following prototype multibonded molecules: N2, CO, H2O, and C2.

Long-range-corrected multiconfiguration density functional with the on-top pair density.

We propose a multiconfiguration density functional combining a short-range density functional approximation with a novel long-range correction for dynamic correlation effects. The correction is derived from the adiabatic connection formalism so that the resulting functional requires access only to one- and two-electron reduced density matrices of the system. In practice, the functional is formulated for wavefunctions of the complete active space (CAS) type and the short-range density functional part is made dependent on the on-top pair density via auxiliary spin densities. The latter allows for reducing the self-interaction and the static correlation errors without breaking the spin symmetry. We study the properties and the performance of the non-self-consistent variant of the method, termed lrAC0-postCAS. Numerical demonstration on a set of dissociation energy curves and excitation energies shows that lrAC0-postCAS provides accuracy comparable with more computationally expensive ab initio rivals.

The effect of weak intermolecular interactions on the nuclear magnetic resonance shielding constant in N2.

Ab initio calculations are applied to examine the influence of the intermolecular interactions on the shielding constant in gaseous nitrogen. An accurate literature potential energy surface and the nuclear magnetic resonance shielding surface of the N2 -N2 complex calculated in this work provide results in satisfactory agreement with the available experimental estimates of the effect.

How and Why Does Helium Permeate Nonporous Arsenolite Under High Pressure?

Investigations into the helium permeation of arsenolite, the cubic, molecular arsenic(III) oxide polymorph As4 O6 , were carried out to understand how and why arsenolite helium clathrate As4 O6 ⋅2 He is formed. High-pressure synchrotron X-ray diffraction experiments on arsenolite single crystals revealed that the permeation of helium into nonporous arsenolite depends on the time for which the crystal is subjected to high pressure and on the crystal history. The single crystal was totally transformed into As4 O6 ⋅2 He within 45 h under 5 GPa. After release of the pressure, arsenolite was recovered and a repeated increase in pressure up to 3 GPa led to practically instant As4 O6 ⋅2 He formation. However, when a pristine arsenolite single crystal was quickly subjected to a pressure of 13 GPa, no helium permeation was observed at all. No neon permeation was observed in analogous experiments. Quantum mechanical computations indicate that there are no specific attractive interactions between He atoms and As4 O6 molecules at the distances observed in the As4 O6 ⋅2 He crystal structure. Detailed analysis of As4 O6 molecular structure changes has shown that the introduction of He into the arsenolite crystal lattice significantly reduces molecular deformations by decreasing the anisotropy of stress exerted on the As4 O6 molecules. This effect and the pΔV term, rather than any specific As⋅⋅⋅He binding, are the driving forces for the formation As4 O6 ⋅2 He.

The nature of three-body interactions in DFT: Exchange and polarization effects.

We propose a physically motivated decomposition of density functional theory (DFT) 3-body nonadditive interaction energies into the exchange and density-deformation (polarization) components. The exchange component represents the effect of the Pauli exclusion in the wave function of the trimer and is found to be challenging for density functional approximations (DFAs). The remaining density-deformation nonadditivity is less dependent upon the DFAs. Numerical demonstration is carried out for rare gas atom trimers, Ar2-HX (X = F, Cl) complexes, and small hydrogen-bonded and van der Waals molecular systems. None of the tested semilocal, hybrid, and range-separated DFAs properly accounts for the nonadditive exchange in dispersion-bonded trimers. By contrast, for hydrogen-bonded systems, range-separated DFAs achieve a qualitative agreement to within 20% of the reference exchange energy. A reliable performance for all systems is obtained only when the monomers interact through the Hartree-Fock potential in the dispersion-free Pauli blockade scheme. Additionally, we identify the nonadditive second-order exchange-dispersion energy as an important but overlooked contribution in force-field-like dispersion corrections. Our results suggest that range-separated functionals do not include this component, although semilocal and global hybrid DFAs appear to imitate it in the short range.

Experimental and Theoretical Studies of Low-Energy Penning Ionization of NH3 , CH3 F, and CHF3.

We present results from a joint theoretical and experimental study of the low-energy Penning ionization of NH3 , CH3 F, and CHF3 by metastable Ne(3 P2 ) and He(3 S1 ) atoms. We combine the merged neutral beams experiment, covering a range of collision energies between 0.1-150 K, with multichannel quantum defect theory calculations based on interaction potentials from symmetry-adapted perturbation theory. The three symmetric tops provide several distinct properties that make them interesting targets for cold chemistry studies. Of these three, only NH3 has a lone electron pair that leads to a strong binding with rare gas atoms. The CHF3 molecule has much smaller rotational constants than both NH3 and CH3 F, and thus has a considerably higher density of rotational states already at low energies. Their presence opens inelastic collision channels that reduce the observed reactive cross section. We show that this effect dominates the total rate coefficient in heavy molecules already at relatively low collision energies but is much less prominent for lighter molecules.

Interaction of Boron-Nitrogen Doped Benzene Isomers with Water.

The interaction of 1,2-dihydro-1,2-, 1,3-dihydro-1,3- and 1,4-dihydro-1,4-azaborine isomers with one and two water molecules has been studied using a variety of supermolecular (Møller-Plesset = MP, and coupled cluster = CC) as well as perturbational (symmetry-adapted perturbation theory = SAPT) electron-correlation methods in the complete basis-set limit. It has been found that the water molecule binds to azaborine isomers through O-H···π, π-H···O, and dihydrogen bonding linkages. The SAPT interaction energy decomposition shows that these complexes are mostly stabilized by dispersion followed closely by induction contributions. Pauli repulsion hinders water molecule to be polarized by azaborine in the O-H···π type of complexes. According to the interacting-quantum-atoms analysis, the structures with a primary binding of the O-H···π type benefit from an additional stabilization factor resulting from the interaction of the oxygen and the second hydrogen atom of water, i.e., the one which does not point toward the ring, while the interaction of hydrogens from water with azaborines plays a destabilizing role for the π-H···O type. The same method states that the intermolecular bindings between azaborines and the water molecule have a multicenter character with a small bond polarization, and they are classified as closed-shell (noncovalent) by quantum theory of atoms-in-molecules analysis at bond critical points. The complexes of azaborines with two water molecules tend to arrange in a circular fashion with a recognizable water dimer attached to the azaborine molecule. A comparison with the CCSD(T) benchmarks shows that the nonadditive contribution to the interaction energy of the trimers is negative and with a good accuracy can be accounted for by the MP2 method. A good agreement between Hartree-Fock (HF) and MP2 nonadditive energy, as well as the decomposition of HF nonadditive interaction energies divulge the importance of nonadditive induction energy in the trimers. The interaction energies for the azaborine with one water calculated with the SAPT(DFT), MP2, SCS-MP2, and MP2C methods are in satisfactory agreement with each other. Finally, it has been found that the population analysis from the electron localization function offers the most comprehensive explanation of the orientational preferences of the water molecule in the complex.

Communication: Importance of rotationally inelastic processes in low-energy Penning ionization of CHF3.

Low energy reaction dynamics can strongly depend on the internal structure of the reactants. The role of rotationally inelastic processes in cold collisions involving polyatomic molecules has not been explored so far. Here we address this problem by performing a merged-beam study of the He((3)S1)+CHF3 Penning ionization reaction in a range of collision energies E/kB = 0.5-120 K. The experimental cross sections are compared with total reaction cross sections calculated within the framework of quantum defect theory. We find that the broad range of collision energies combined with the relatively small rotational constants of CHF3 makes rotationally inelastic collisions a crucial player in the total reaction dynamics. Quantitative agreement between theory and experiment is only obtained if the energy-dependent probability for rotational excitation is included in the calculations, in stark contrast to previous experiments where classical scaling laws were able to describe the results.

Theoretical study of the buffer-gas cooling and trapping of CrH(X6Σ+) by 3He atoms.

We present a theoretical study of the Zeeman relaxation of the magnetically trappable lowest field seeking state of CrH(X6Σ+) in collisions with 3He. A two dimensional potential energy surface (PES) was calculated with the partially spin-restricted coupled cluster singles, doubles, and non-iterative triples [RCCSD(T)] method. The global minimum was found for the collinear He⋯Cr-H geometry with the well depth of 1143.84 cm-1 at Re = 4.15 a0. Since the RCCSD(T) calculations revealed a multireference character in the region of the global minimum, we performed additional calculations with the internally contracted multireference configuration interaction with the Davidson correction (ic-MRCISD+Q) method. The resulting PES is similar to the RCCSD(T) PES except for the region of the global minimum, where the well depth is 3032 cm-1 at Re = 3.8 a0. An insight into the character of the complex was gained by means of symmetry-adapted perturbation theory based on unrestricted Kohn-Sham description of the monomers. Close coupling calculations of the Zeeman relaxation show that although the ΔMJ=MJ'-MJ = -1 and -2 transitions are the dominant contributions to the collisional Zeeman relaxation, ΔMJ<-2 transitions cannot be neglected due to the large value of CrH spin-spin constant. The calculated elastic to inelastic cross section ratio is 1600 for the RCCSD(T) PES and 500 for the MRCISD+Q PES, while the estimate from the buffer-gas cooling and magnetic trapping experiment is 9000.

Observation of orbiting resonances in He((3)S(1)) + NH3 Penning ionization.

Resonances are among the clearest quantum mechanical signatures of scattering processes. Previously, shape resonances and Feshbach resonances have been observed in inelastic and reactive collisions involving atoms or diatomic molecules. Structure in the integral cross section has been observed in a handful of elastic collisions involving polyatomic molecules. The present paper presents the observation of shape resonances in the reactive scattering of a polyatomic molecule, NH3. A merged-beam study of the gas phase He((3)S1) + NH3 Penning ionization reaction dynamics is described in the collision energy range 3.3 µeV < Ecoll < 10 meV. In this energy range, the reaction rate is governed by long-range attraction. Peaks in the integral cross section are observed at collision energies of 1.8 meV and 7.3 meV and are assigned to ℓ = 15,16 and ℓ = 20,21 partial wave resonances, respectively. The experimental results are well reproduced by theoretical calculations with the short-range reaction probability Psr = 0.035. No clear signature of the orbiting resonances is visible in the branching ratio between NH3 (+) and NH2 (+) formation.

Tuned range-separated hybrid functionals in the symmetry-adapted perturbation theory.

The aim of this study is to present a performance test of optimally tuned long-range corrected (LRC) functionals applied to the symmetry-adapted perturbation theory (SAPT). In the present variant, the second-order energy components are evaluated at the coupled level of theory. We demonstrate that the generalized Kohn-Sham (GKS) description of monomers with optimally tuned LRC functionals may be essential for the quality of SAPT interaction energy components. This is connected to the minimization of a many-electron self-interaction error and exemplified by two model systems: polyacetylenes of increasing length and stretching of He 3 (+). Next we provide a comparison of SAPT approaches based on Kohn-Sham and GKS description of the monomers. We show that LRC leads to results better or comparable with the hitherto prevailing asymptotically corrected functionals. Finally, we discuss the advantages and possible limitations of SAPT based on LRC functionals.

Dynamics of gas phase Ne(*) + NH3 and Ne(*) + ND3 Penning ionisation at low temperatures.

Two isotopic chemical reactions, Ne(*) + NH3, and Ne(*) + ND3, have been studied at low collision energies by means of a merged beams technique. Partial cross sections have been recorded for the two reactive channels, namely, Ne(*) + NH3 → Ne + NH3(+) + e(-), and Ne(*) + NH3 → Ne + NH2(+) + H + e(-), by detecting the NH3(+) and NH2(+) product ions, respectively. The cross sections for both reactions were found to increase with decreasing collision energy, Ecoll, in the range 8 µeV < Ecoll < 20 meV. The measured rate constant exhibits a curvature in a log(k)-log(Ecoll) plot from which it is concluded that the Langevin capture model does not properly describe the Ne(*) + NH3 reaction in the entire range of collision energies covered here. Calculations based on multichannel quantum defect theory were performed to reproduce and interpret the experimental results. Good agreement was obtained by including long range van der Waals interactions combined with a 6-12 Lennard-Jones potential. The branching ratio between the two reactive channels, Γ = [NH2(+)]/[NH2(+)] + [NH3(+)], is relatively constant, Γ ≈ 0.3, in the entire collision energy range studied here. Possible reasons for this observation are discussed and rationalized in terms of relative time scales of the reactant approach and the molecular rotation. Isotopic differences between the Ne(*) + NH3 and Ne(*) + ND3 reactions are small, as suggested by nearly equal branching ratios and cross sections for the two reactions.

Density functional theory approach to gold-ligand interactions: separating true effects from artifacts.

Donor-acceptor interactions are notoriously difficult and unpredictable for conventional density functional theory (DFT) methodologies. This work presents a reliable computational treatment of gold-ligand interactions of the donor-acceptor type within DFT. These interactions require a proper account of the ionization potential of the electron donor and electron affinity of the electron acceptor. This is accomplished in the Generalized Kohn Sham framework that allows one to relate these properties to the frontier orbitals in DFT via the tuning of range-separated functionals. A donor and an acceptor typically require different tuning schemes. This poses a problem when the binding energies are calculated using the supermolecular method. A two-parameter tuning for the monomer properties ensures that a common functional, optimal for both the donor and the acceptor, is found. A reliable DFT approach for these interactions also takes into account the dispersion contribution. The approach is validated using the water dimer and the (HAuPH3)2 aurophilic complex. Binding energies are computed for Au4 interacting with the following ligands: SCN(-), benzenethiol, benzenethiolate anion, pyridine, and trimethylphosphine. The results agree for the right reasons with coupled-cluster reference values.

Theoretical studies of potential energy surface and bound states of the strongly bound He(1S)-BeO (1Σ+) complex.

We perform electronic structure calculations of the potential energy surface of the He···BeO((1)Σ(+)) complex. We use several different methods to characterize this unusual interaction. We apply coupled cluster singles, doubles, and noniterative triples [CCSD(T)] and the multireference configuration interaction [MRCI] levels of theory. The nature of the interaction is studied with symmetry-adapted perturbation theory (SAPT) based on DFT and CCSD description of the intramonomer electron densities. Our best estimate of the well depth is 1876.5 cm(-1) at the CCSD(T) level, while the dissociation energy, corrected for the zero-point energy, is equal to 1446.7 cm(-1). The global minimum is located for the collinear He···Be-O geometry at Re = 4.45a0. The rotational constant of the He-BeO complex in its ground state is 0.863 cm(-1). We also calculate bound states of the He···BeO complex for J = 0 and J = 1 (total angular momentum).

First-principle interaction potentials for metastable He(3S) and Ne(3P) with closed-shell molecules: application to Penning-ionizing systems.

We present new interaction potential curves, calculated from first-principles, for the He((3)S, 1s(1)2s(1))···H2 and He((3)S)···Ar systems, relevant in recent Penning ionization experiments of Henson et al. [Science 338, 234 (2012)]. Two different approaches were applied: supermolecular using coupled cluster (CC) theory and perturbational within symmetry-adapted perturbation theory (SAPT). Both methods gave consistent results, and the potentials were used to study the elastic scattering and determine the positions of shape resonances for low kinetic energy (up to 1 meV). We found a good agreement with the experiment. In addition, we investigated two other dimers composed of metastable Ne ((3)P, 2p(5)3s(1)) and ground state He and Ar atoms. For the Ne((3)P)···He system, a good agreement between CC and SAPT approaches was obtained. The Ne((3)P)···Ar dimer was described only with SAPT, as CC gave divergent results. Ne* systems exhibit extremely small electronic orbital angular momentum anisotropy of the potentials. We attribute this effect to screening of an open 2p shell by a singly occupied 3s shell.

Efficient Calculation of the Dispersion Energy for Multireference Systems with Cholesky Decomposition: Application to Excited-State Interactions.

Accurate and efficient prediction of dispersion interactions in excited-state complexes poses a challenge due to the complex nature of electron correlation effects that need to be simultaneously considered. We propose an algorithm for computing the dispersion energy in nondegenerate ground- or excited-state complexes with arbitrary spin. The algorithm scales with the fifth power of the system size due to employing Cholesky decomposition of Coulomb integrals and a recently developed recursive formula for density response functions of the monomers. As a numerical illustration, we apply the new algorithm in the framework of multiconfigurational symmetry adapted perturbation theory, SAPT(MC), to study interactions in dimers with localized excitons. The SAPT(MC) analysis reveals that the dispersion energy may be the main force stabilizing excited-state dimers.