Triple Excitations Research Articles

Full-dimensional quantum scattering calculations on ultracold atom-molecule collisions in magnetic fields: The role of molecular vibrations

Rigorous quantum scattering calculations on ultracold molecular collisions in external fields present an outstanding computational problem due to strongly anisotropic atom-molecule interactions that depend on the relative orientation of the collision partners, as well as on their vibrational degrees of freedom. Here, we present the first numerically exact three-dimensional quantum scattering calculations on strongly anisotropic atom-molecule (Li+CaH) collisions in an external magnetic field based on the parity-adapted total angular momentum representation and a new three-dimensional potential energy surface (PES) for the triplet Li-CaH collision complex using the unrestricted coupled cluster method with single, double and perturbative triple excitations [UCCSD(T)] and a large quadruple-zeta type basis set. We find that while the full three-dimensional treatment is necessary for the accurate description of Li ($M_S=1/2$)+CaH ($v=0,N=0,M_S=1/2$) collisions as a function of magnetic field, the magnetic resonance density and statistical properties of spin-polarized atom-molecule collisions are not strongly affected by vibrational degrees of freedom, justifying the rigid-rotor approximation used in previous calculations. We observe rapid, field-insensitive vibrational quenching in ultracold Li ($M_S=1/2$)+CaH ($v=1,N=0, M_S=1/2$) collisions, leading to efficient collisional cooling of CaH vibrations.

Vibronic coupling in the ground and excited states of the pyridine radical cation.

Vibronic interactions in the pyridine radical cation ground state, 2A1, and its lowest excited states, 2A2 and 2B1, are studied theoretically. These states originate from the ionization out of the highest occupied orbitals of pyridine, 7a1 (nσ), 1a2 (π), and 2b1 (π), respectively, and give rise to the lowest two photoelectron maxima. According to our previous high-level ab initio calculations [Trofimov et al., J. Chem. Phys. 146, 244307 (2017)], the 2A2 (π-1) excited state is very close in energy to the 2A1 (nσ-1) ground state, which suggests that these states could be vibronically coupled. Our present calculations confirm that this is indeed the case. Moreover, the next higher excited state, 2B1 (π-1), is also involved in the vibronic interaction with the 2A1 (nσ-1) and 2A2 (π-1) states. The three-state vibronic coupling problem was treated within the framework of a linear vibronic coupling model employing parameters derived from the ionization energies of pyridine computed using the linear response coupled-cluster method accounting for single, double, and triple excitations (CC3). The potential energy surfaces of the 2A1 and 2A2 states intersect in the vicinity of the adiabatic minimum of the 2A2 state, while the surfaces of the 2A2 and 2B1 states intersect near the 2B1 state minimum. The spectrum computed using the multi-configuration time-dependent Hartree (MCTDH) method accounting for 24 normal modes is in good qualitative agreement with the experimental spectrum of pyridine obtained using high-resolution He I photoelectron spectroscopy and allows for some assignment of the observed features.

A minimum quantum chemistry CCSD(T)/CBS dataset of dimeric interaction energies for small organic functional groups.

We have performed a quantum chemistry study on the bonding patterns and interaction energies for 31 dimers of small organic functional groups (dubbed the SOFG-31 dataset), including the alkane-alkene-alkyne (6 + 4 + 4 = 14, AAA) groups, alcohol-aldehyde-ketone (4 + 4 + 3 = 11, AAK) groups, and carboxylic acid-amide (3 + 3 = 6, CAA) groups. The basis set superposition error corrected super-molecule approach using the second order Møller-Plesset perturbation theory (MP2) with the Dunning's aug-cc-pVXZ (X = D, T, Q) basis sets has been employed in the geometry optimization and energy calculations. To calibrate the MP2 calculated interaction energies for these dimeric complexes, we perform single-point calculations with the coupled cluster with single, double, and perturbative triple excitations method at the complete basis set limit [CCSD(T)/CBS] using the well-tested extrapolation methods. In order to gain more physical insights, we also perform a parallel series of energy decomposition calculations based on the symmetry adapted perturbation theory (SAPT). The collection of these CCSD(T)/CBS interaction energy values can serve as a minimum quantum chemistry dataset for testing or training less accurate but more efficient calculation methods. As an application, we further propose a segmental SAPT model based on chemically recognizable segments in a specific functional group. These model interactions can be used to construct coarse-grained force fields for larger molecular systems.

State-to-state inelastic rate coefficients of phosphine in collision with He at low to moderate temperature

ABSTRACTSeveral phosphorus-bearing molecules, such as the phosphine of interest here, have been detected in astrophysical media. With the aim of satisfying the precision required by the astrophysical community, we report the rate coefficients of PH3 in collision with helium from low to moderate temperature. To this end, we constructed the first three-dimensional potential energy surface (3D-PES) of the PH3–He van der Waals complex, which governs the nuclear motions. The 3D-PES was worked out by means of the standard coupled cluster with single, double and non-iterative triple excitation approach, in conjunction with the aug-cc-pVQZ basis set and complemented by mid-bond functions. This 3D-PES presents a well of 34.92 cm−1 at {R, θ, Φ} = {5.76 a0, 90°, 60°}. Afterwards, we incorporated this 3D-PES into time-independent close-coupling quantum dynamical computations to derive the inelastic cross-sections of rotational excitation of (ortho-) para-PH3 after collision with He up to (1000) 500 cm−1. Subsequently, we evaluated the rate coefficients for temperatures up to (100 K) 50 K populating the (41) 42 low-lying rotational levels of (ortho-) para-PH3. These data were derived by averaging the cross-sections thermally over the Maxwell–Boltzmann velocity distribution. No general propensity rules are found. We also performed a comparison with the rates for NH3–He. Differences are observed that invalidate the use of NH3 rates for deducing accurate abundances of phosphine in cold astrophysical media. Our results should be of great help in determining accurate PH3 abundances and, more generally, constraining the interstellar PH3 chemistry better.

Almost exact energies for the Gaussian-2 set with the semistochastic heat-bath configuration interaction method.

The recently developed semistochastic heat-bath configuration interaction (SHCI) method is a systematically improvable selected configuration interaction plus perturbation theory method capable of giving essentially exact energies for larger systems than is possible with other such methods. We compute SHCI atomization energies for 55 molecules that have been used as a test set in prior studies because their atomization energies are known from experiment. Basis sets from cc-pVDZ to cc-pV5Z are used, totaling up to 500 orbitals and a Hilbert space of 1032 Slater determinants for the largest molecules. For each basis, an extrapolated energy well within chemical accuracy (1 kcal/mol or 1.6 mHa/mol) of the exact energy for that basis is computed using only a tiny fraction of the entire Hilbert space. We also use our almost exact energies to benchmark energies from the coupled cluster method with single, double, and perturbative triple excitations. The energies are extrapolated to the complete basis set limit and compared to the experimental atomization energies. The extrapolations are done both without and with a basis-set correction based on density-functional theory. The mean absolute deviations from experiment for these extrapolations are 0.46 kcal/mol and 0.51 kcal/mol, respectively. Orbital optimization methods used to obtain improved convergence of the SHCI energies are also discussed.

Low-temperature rate constants and radiative transfer for rotational de-excitation of C5S by collision with He

ABSTRACT The C5S molecule is the largest member of the series of sulphur-containing carbon chains CnS observed in space. Given the lack of data concerning this molecule, we computed rate coefficients of C5S(1Σ+) induced by collision with He. These rates are obtained for thermal temperature below 100 K by mean of a new two-dimensional potential energy surface (PES) calculated with the explicit correlated coupled cluster with single, double, and pertubative triple excitation (ccsd(t)-f12) ab initio approach and the aug-cc-pVTZ basis sets. The C5S–He PES presents three minimums of −59.726, −55.355, and −36.506 cm−1 below its dissociation limit. Using this PES, the integral cross-sections are performed in the close-coupling (CC) and coupled-state (CS) quantum time independent formalisms for $E_\mathrm{ c}\le 500 \, \mathrm{ cm}^{-1}$ and J ≤ 13 (for CC) and J ≤ 50 (for CS). By averaging these cross-sections we obtained the downward rate coefficients. The new collisional data are used to simulate the excitation of C5S in the circumstellar gas. We obtain the excitation and brightness temperatures of the four lines observed towards the IRC+10216 which confirms the necessity of using radiative transfer calculations to accurately determine C5S abundance since the local thermodynamic equilibrium conditions are not fulfilled. The new collisional data should help to estimate the abundance of C5S in several interstellar regions.

Assessing the validity of DLPNO-CCSD(T) in the calculation of activation and reaction energies of ubiquitous enzymatic reactions.

The domain-based local pair natural orbital coupled-cluster with single, double, and perturbative triples excitation (DLPNO-CCSD(T)) method was employed to portray the activation and reaction energies of four ubiquitous enzymatic reactions, and its performance was confronted to CCSD(T)/complete basis set (CBS) to assess its accuracy and robustness in this specific field. The DLPNO-CCSD(T) results were also confronted to those of a set of density functionals (DFs) to understand the benefit of implementing this technique in enzymatic quantum mechanics/molecular mechanics (QM/MM) calculations as a second QM component, which is often treated with DF theory (DFT). On average, the DLPNO-CCSD(T)/aug-cc-pVTZ results were 0.51 kcal·mol-1 apart from the canonic CCSD(T)/CBS, without noticeable biases toward any of the reactions under study. All DFs fell short to the DLPNO-CCSD(T), both in terms of accuracy and robustness, which suggests that this method is advantageous to characterize enzymatic reactions and that its use in QM/MM calculations, either alone or in conjugation with DFT, in a two-region QM layer (DLPNO-CCSD(T):DFT), should enhance the quality and faithfulness of the results.

Perspective on Kramers symmetry breaking and restoration in relativistic electronic structure methods for open-shell systems.

Without rigorous symmetry constraints, solutions to approximate electronic structure methods may artificially break symmetry. In the case of the relativistic electronic structure, if time-reversal symmetry is not enforced in calculations of molecules not subject to a magnetic field, it is possible to artificially break Kramers degeneracy in open shell systems. This leads to a description of excited states that may be qualitatively incorrect. Despite this, different electronic structure methods to incorporate correlation and excited states can partially restore Kramers degeneracy from a broken symmetry solution. For single-reference techniques, the inclusion of double and possibly triple excitations in the ground state provides much of the needed correction. Formally, however, this imbalanced treatment of the Kramers-paired spaces is a multi-reference problem, and so methods such as complete-active-space methods perform much better at recovering much of the correct symmetry by state averaging. Using multi-reference configuration interaction, any additional corrections can be obtained as the solution approaches the full configuration interaction limit. A recently proposed "Kramers contamination" value is also used to assess the magnitude of symmetry breaking.

An accurate 5D potential energy surface for H3O+-H2 interaction.

Modeling of the observational spectra of H3O+ allows for a detailed understanding of the interstellar oxygen chemistry. While its spectroscopy was intensively studied earlier, our knowledge about the collision of H3O+ with the abundant colliders in the interstellar medium is rather limited. In order to treat these collisional excitation processes, it is first necessary to calculate the potential energy surface (PES) of the interacting species. We have computed the five-dimensional rigid-rotor PES of the H3O+-H2 system from the explicitly correlated coupled-cluster theory at the level of singles and doubles with perturbative corrections for triple excitations [CCSD(T)-F12] with the moderate-size augmented correlation-consistent valence triple zeta (aug-cc-pVTZ) basis set. The well depth of the PES is found to be rather large, about 1887.2 cm-1. The ab initio potential was fitted over an angular expansion in order to effectively use it in quantum scattering codes. As a first application, we computed dissociation energies for the different nuclear spin isomers of the H3O+-H2 complex.

The ozone-water complex: CCSD(T)/CBS structures and anharmonic vibrational spectroscopy of O3(H2O)n, (n = 1 - 2).

Ozone-water complexes O3(H2O)n (n = 1-2) have been studied using coupled cluster theory with triple excitations CCSD(T) with correlation consistent basis sets aug-cc-pVnZ (n = D, T, Q) and complete basis set (CBS) extrapolation techniques. We identified seven dimer (n = 1) and nine trimer species (n = 2) with open C2v and cyclic D3h ozone. Calculations at the CCSD(T)/CBS level of theory for C2v O3(H2O) on the counterpoise (CP)-corrected potential energy surface yield a dissociation energy of De = 2.31 kcal/mol and an O3 central-oxygen (Oc) H2O oxygen (Ow) distance r[Oc⋯Ow] of 3.097 Å, which is in good agreement with an experimental value of 2.957 Å [J. Z. Gillies et al., J. Mol. Spectrosc. 146, 493 (1991)]. Combining our CCSD(T)/CBS value of De for C2v O3(H2O) with our best estimate anharmonic CCSD(T)/aVTZ ΔZPE yields a Do value of 1.82 kcal/mol; the CCSD(T)/CBS value of De for D3h O3(H2O) is 1.51 kcal/mol and yields an anharmonic CCSD(T)/aVTZ Do = 0.99 kcal/mol. CCSD(T)/aVTZ dissociation energies and structures for C2v O3(H2O)2 are De = 4.15 kcal/mol, (Do = 3.08 kcal/mol) and r[Oc⋯Ow] = 2.973 Å, and De = 2.64 kcal/mol (Do = 1.68 kcal/mol) with r[Oc⋯Ow] = 2.828 Å for D3h O3(H2O)2. The results from ab initio molecular dynamics simulations, which consider dynamic and thermal effects in O3(H2O), show that the O3(H2O) complex remains stable at 50 K and dynamically interconverts between two hydrogen-bonded conformers with short Oc⋯Ow contacts (3.85 Å). Carr-Parrinello molecular dynamic (CPMD) simulations for O3(H2O) and O3(H2O)2 at 100 K demonstrate that O3(H2O)2 remains structurally intact, whereas O3(H2O) dissociates to free ozone and water, a feature consistent with the larger average binding energy in O3(H2O)2 (2.2 kcal/mol) vs that in O3(H2O) (1.8 kcal/mol). Finally, the results from CCSD(T)/CBS and CPMD simulations demonstrate that the large inter-trimer binding energies in O3(H2O)2 would give rise to an elevated trimer/dimer population ratio, making O3(H2O)2 a particularly stable and spectroscopically detectable complex.

DFT, DLPNO-CCSD(T), and NEVPT2 benchmark study of the reaction between ferrocenium and trimethylphosphine.

The reaction between ferrocenium and trimethylphosphine was studied using density functional theory (DFT), domain-based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)), and N-electron valence state perturbation theory (NEVPT2). The accuracy of the DFT functionals decreases compared to the DLPNO-CCSD(T) level in the following order: M06-L > TPSS > M06, BLYP > PBE, PBE0, B3LYP > > PWPB95 > > DSD-BLYP. The roles of thermochemical, continuum solvation (SMD), and counterpoise corrections were evaluated. Grimme's D3 empirical dispersion correction is essential for all functionals studied except M06 and M06-L. The reliability of the frequency calculations performed directly within the SMD was confirmed. The systems showed no significant multireference character according to T1 and T2 diagnostics and the fractional occupation number (FOD) weighted electron density analysis. The multireference NEVPT2 calculations gave qualitatively valid conclusions about the reaction mechanism. However, a multireference approach is generally not recommended because it requires arbitrary chosen active spaces.

Formulation of a Dressed Coupled-Cluster Method with Implicit Triple Excitations and Benchmark Application to Hydrogen-Bonded Systems.

In this paper, we present a coupled-cluster theory based on a double-exponential wave operator ansatz, which is capable of mimicking the effects of connected triple excitations in an iterative manner. The triply excited manifold is spanned via the action of a set of scattering operators on doubly excited determinants, whereas their action annihilates the Hartree-Fock reference determinant. The effect of triple excitations is included at a computational scaling slightly higher than that of conventional coupled-cluster singles and doubles. Furthermore, we demonstrate two approximate schemes, which arise naturally, and argue that both these schemes come equipped with certain renormalization terms capable of handling nonbonding interactions due to robust inclusion of the screened Coulomb interaction. We justify our claims from both a theoretical perspective and a number of numerical applications to prototypical water clusters, in a number of basis functions. Our methods show overall comparable performance to the canonical coupled-cluster theory with singles, doubles, and perturbative triples (CCSD(T)) and allied methods, however, at a lower computational scaling.

Implementation of the iterative triples model CC3 for excitation energies using pair natural orbitals and Laplace transformation techniques.

We present a pair natural orbital (PNO)-based implementation of CC3 excitation energies, which extends our previously published state-specific PNO ansatz for the solution of the excited state eigenvalue problem to methods including connected triple excitations. A thorough analysis of the equations for the excited state triples amplitudes is presented from which we derive a suitable state-specific triple natural orbital basis for the excited state triples amplitudes, which performs equally well for local and non-local excitations. The accuracy of the implementation is evaluated using a large and diverse test set. We find that for states with small contributions from double excitations, a T0 approximation to PNO-CC3 yields accurate results with a mean absolute error (MAE) for TPNO = 10-7 in the range of 0.02 eV. However, for states with larger double excitation contributions, the T0 approximation is found to yield significantly less accurate results, while the Laplace-transformed variant of PNO-CC3 shows a uniform accuracy for singly and doubly excited states (MAE and maximum error of 0.01 eV and 0.07 eV for TPNO = 10-7, respectively). Finally, we apply PNO-CC3 to the calculation of the first excited state of berenil at a S1 minimum geometry, which is shown to be close to a conical intersection. This calculation in the aug-cc-pVTZ basis set (more than 1300 basis functions) is the largest calculation ever performed with CC3 on excitation energies.

Relativistic Fock Space Coupled Cluster Method for Many-Electron Systems: Non-Perturbative Account for Connected Triple Excitations

The Fock space relativistic coupled cluster method (FS-RCC) is one of the most promising tools of electronic structure modeling for atomic and molecular systems containing heavy nuclei. Until recently, capabilities of the FS-RCC method were severely restricted by the fact that only single and double excitations in the exponential parametrization of the wave operator were considered. We report the design and the first computer implementation of FS-RCC schemes with full and simplified non-perturbative account for triple excitations in the cluster operator. Numerical stability of the new computational scheme and thus its applicability to a wide variety of molecular electronic states is ensured using the dynamic shift technique combined with the extrapolation to zero-shift limit. Pilot applications to atomic (Tl, Pb) and molecular (TlH) systems reported in the paper indicate that the breakthrough in accuracy and predictive power of the electronic structure calculations for heavy-element compounds can be achieved. Moreover, the described approach can provide a firm basis for high-precision modeling of heavy molecular systems with several open shells, including actinide compounds.

Potential energy surfaces of charge transfer states

ABSTRACT In this paper the potential energy curves of charge transfer (CT) electronic states and their interaction with local ones have been investigated. Besides the global view of these curves, special attention has been paid to the region of the crossing and the infinite separation limit. It was found that triple excitations are needed to accurately describe potential energy surfaces of CT states. Among the cheaper variants, both STEOM-CCSD and CCSD(T)(a)* methods are promising in this respect. The somewhat larger error of CCSD for CT states can be explained by its size extensivity error and the overestimation of the asymptotic excitation energy. Second order approximations are not advantageous for the error cancellation, in fact CC2 is much worse for CT states than any other method investigated here. The results also show that the location of the (avoided) crossings of local and CT states depend very much on the accurate description of the CT states. Failure to describe this topology might affect dynamics, and a warning, in particular in case of CC2, should be issued if CT states play a role in the physics of the problem.

Descendant of the X-ogen carrier and a ‘mass of 69’: infrared action spectroscopic detection of HC3O+ and HC3S+

ABSTRACT The carbon chain ions HCO and HCS – longer variants of the famous ‘X-ogen’ line carrier HCO – have been observed for the first time using two cryogenic 22-pole ion trap apparatus (FELion, Coltrap) and two different light sources: the Free Electron Laser for Infrared eXperiments (FELIX), which was operated between 460 and 2500 cm, and an optical parametric oscillator operating near 3200 cm; signals from both experiments were detected by infrared predissociation action spectroscopy. The majority of vibrational fundamentals were observed for both ions and their wavenumbers compare very favourably with results from high-level anharmonic force field calculations performed here at the coupled-cluster singles and doubles level augmented by a perturbative treatment of triple excitations, CCSD(T). As the action scheme employed here probes the Ne-tagged weakly bound variants, Ne–HCO and Ne–HCS, corresponding calculations of these systems were also performed. Differences in the structures and molecular force fields between the bare ions and their Ne-tagged complexes are found to be very small.

Interaction of the HCO radical with molecular hydrogen: Ab initio potential energy surface and scattering calculations.

The potential energy surface describing the interaction of the HCO radical with molecular hydrogen has been computed through explicitly correlated coupled cluster calculations including single, double, and (perturbative) triple excitations [RCCSD(T)-F12a], with the assumption of fixed molecular geometries. The computed points were fit to an analytical form suitable for time-independent quantum scattering calculations of rotationally inelastic cross sections and rate coefficients. Since the spin-rotation splittings in HCO are small, cross sections for fine-structure resolved transitions are computed with electron-spin free T matrix elements through the recoupling technique usually employed to determine hyperfine-resolved cross sections. Both spin-free and fine-structure resolved state-to-state cross sections for rotationally inelastic transitions are presented and discussed.

A New Benchmark Set for Excitation Energy of Charge Transfer States: Systematic Investigation of Coupled Cluster Type Methods.

The numerous existing publications on benchmarking quantum chemistry methods for excited states rarely include Charge Transfer (CT) states, although many interesting phenomena in, e.g., biochemistry and material physics involve the transfer of electrons between fragments of the system. Therefore, it is timely to test the accuracy of quantum chemical methods for CT states, as well. In this study we first propose a new benchmark set consisting of dimers having low-energy CT states. On this set, the vertical excitation energy has been calculated with Coupled Cluster methods including triple excitations (CC3, CCSDT-3, CCSD(T)(a)*), as well as with methods including full or approximate doubles (CCSD, STEOM-CCSD, CC2, ADC(2), EOM-CCSD(2)). The results show that the popular CC2 and ADC(2) methods are much less accurate for CT states than for valence states. On the other hand, EOM-CCSD seems to have similar systematic overestimation of the excitation energies for both types of states. Among the triples methods the novel EOM-CCSD(T)(a)* method including noniterative triple excitations is found to stand out with its consistently good performance for all types of states, delivering essentially EOM-CCSDT quality results.

Rotational relaxation of H2S by collision with He

Context. The H2S molecule has been detected in several regions of the interstellar medium (ISM). The use of non-LTE models requires knowledge of accurate collisional rate coefficients of the molecules detected with the most common collider in the ISM. Aims. The main goal of this work is to study the collision of H2S with He. Methods. A grid of ab initio energies was computed at the coupled cluster level of theory including single, double, and perturbative triple excitations (CCSD(T)) and using the augmented correlation consistent polarized quadruple zeta (aug-cc-pVQZ) basis set supplemented by a set of mid-bond functions. These energies were fitted to an analytical function, which was employed to study the dynamics of the system. Close coupling calculations were performed to study the collision of H2S with He. Results. The rate coefficients determined from the close coupling calculation were compared with those of the collision with H2O+He, and large differences were found. Finally, the rate coefficients for the lower rotational de-excitation of H2S by collision with He are reported.

Theoretical analysis of an anion-πcomplex: I−·C6F6

Recently, Anstöter and co-workers [J. Am. Chem. Soc. 141, 6132 (2019)] have provided the first photoelectron spectroscopic determination of the anion-π bond strength (De) using iodide-hexafluorobenzene (I−·C6F6) as the archetypical system. In combination with an equation-of-motion coupled cluster theory, namely EOM-IP-CCSD(dT), using Dunning’s aug-cc-pVDZ (aVDZ) basis set, De in I−·C6F6 was found to be −0.53 eV with an uncertainty less than 0.03 eV. The interaction was claimed to arise for a large part from correlation forces (41%) with only a 23% contribution from electrostatic forces. In the present work, we performed the coupled-cluster with single and double and perturbative triple excitations, CCSD(T), calculations. We found that CCSD(T)/aVDZ can have an uncertainty up to 0.113 eV due to the basis set incompleteness. Our calculations disclosed that the previous calculations on the electrostatic contribution are concealed by the contributions from the exchange and Pauli repulsion. The electrostatic contribution is actually determinant, being more than double of the correlation contribution in the I−·C6F6 complex at the equilibrium binding distance.