Second quantization-based symmetry-adapted perturbation theory: Generalizing exchange beyond single electron pair approximation.

This paper presents a general second-quantized form of a permutation operator interchanging n pairs of electrons between interacting subsystems in the framework of the symmetry-adapted perturbation theory (SAPT). We detail the procedure for constructing this operator through the consecutive multiplication of single-pair permutation operators. This generalized form of the permutation operator has enabled the derivation of universal formulas for S2n approximations of the exchange energies in the first and second order of the interaction operator. We present expressions for corrections of S4 approximations and assess its efficacy on a selection of systems anticipated to exhibit a slowly converging overlap expansion. Additionally, we outline a method to sum the overlap expansion series to infinity in second-quantization, up to the second order in V. This new approach offers an alternative to the existing formalism based on density-matrix formulations. When combined with a symbolic algebra program for automated derivations, it paves the way for advancements in SAPT theory, particularly for intricate wavefunction theories.

Towards the generation of potential energy surfaces of weakly bound medium-sized molecular systems: the case of benzonitrile-He complex.

Currently, the explicitly correlated coupled cluster method is used routinely to generate the multi-dimensional potential energy surfaces (mD-PESs) of van der Waals complexes of small molecular systems relevant for atmospheric, astrophysical and industrial applications. Although very accurate, this method is computationally prohibitive for medium and large molecules containing clusters. For instance, the recent detections of complex organic molecules (COMs) in the interstellar medium, such as benzonitrile, revealed the need to establish an accurate enough electronic structure approach to map the mD-PESs of these species interacting with the surrounding gases. As a benchmark, we have treated the case of the polar molecule benzonitrile interacting with helium, where we use post-Hartree-Fock and symmetry-adapted perturbation theory (SAPT) techniques. Accordingly, we show that MP2 and distinguishable-cluster approximation (DCSD) cannot be used for this purpose, whereas accurate enough PESs may be obtained using the corresponding explicitly correlated versions (MP2-F12 or DCSD-F12) with a reduction in computational costs. Alternatively, computations revealed that SAPT(DFT) is as performant as CCSD(T)-F12/aug-cc-pVTZ, making it the method of choice for mapping the mD-PESs of COMs containing clusters. Therefore, we have used this approach to generate the 3D-PES of the benzonitrile-He complex along the intermonomer Jacobi coordinates. As an application, we have incorporated the analytic form of this PES into quantum dynamical computations to determine the cross sections of the rotational (de-)excitation of benzonitrile colliding with helium at a collision energy of 10 cm-1.

H2O-HCN complex: A new potential energy surface and intermolecular rovibrational states from rigorous quantum calculations.

In this work the H2O-HCN complex is quantitatively characterized in two ways. First, we report a new rigid-monomer 5D intermolecular potential energy surface (PES) for this complex, calculated using the symmetry-adapted perturbation theory based on density functional theory method. The PES is based on 2833 ab initio points computed employing the aug-cc-pVQZ basis set, utilizing the autoPES code, which provides a site-site analytical fit with the long-range region given by perturbation theory. Next, we present the results of the quantum 5D calculations of the fully coupled intermolecular rovibrational states of the H2O-HCN complex for the total angular momentum J values of 0, 1, and 2, performed on the new PES. These calculations rely on the quantum bound-state methodology developed by us recently and applied to a variety of noncovalently bound binary molecular complexes. The vibrationally averaged ground-state geometry of H2O-HCN determined from the quantum 5D calculations agrees very well with that from the microwave spectroscopic measurements. In addition, the computed ground-state rotational transition frequencies, as well as the B and C rotational constants calculated for the ground state of the complex, are in excellent agreement with the experimental values. The assignment of the calculated intermolecular vibrational states of the H2O-HCN complex is surprisingly challenging. It turns out that only the excitations of the intermolecular stretch mode can be assigned with confidence. The coupling among the angular degrees of freedom (DOFs) of the complex is unusually strong, and as a result most of the excited intermolecular states are unassigned. On the other hand, the coupling of the radial, intermolecular stretch mode and the angular DOFs is weak, allowing straightforward assignment of the excitation of the former.

Theoretical study of the CO2-O2 van der Waals complex: potential energy surface and applications.

A four-dimensional-potential energy surface (4D-PES) of the atmospherically relevant carbon dioxide-oxygen molecule (CO2-O2) van der Waals complex is mapped using the ab initio explicitly correlated coupled cluster method with single, double, and perturbative triple excitations (UCCSD(T)-F12b), and extrapolation to the complete basis set (CBS) limit using the cc-pVTZ-F12/cc-pVQZ-F12 bases and the l-3 formula. An analytic representation of the 4D-PES was fitted using the method of interpolating moving least squares (IMLS). These calculations predict that the most stable configuration of CO2-O2 complex corresponds to a planar slipped-parallel structure with a binding energy of V ∼ -243 cm-1. Another isomer is found on the PES, corresponding to a non-planar cross-shaped structure, with V ∼ -218 cm-1. The transition structure connecting the two minima is found at V ∼ -211 cm-1. We also performed comparisons with some CO2-X van der Waals complexes. Moreover, we provide a SAPT analysis of this molecular system. Then, we discuss the complexation induced shifts of CO2 and O2. Afterwards, this new 4D-PES is employed to compute the second virial coefficient including temperature dependence. A comparison between quantities obtained in our calculations and those from experiments found close agreement attesting to the high quality of the PES and to the importance of considering a full description of the anisotropic potential for the derivation of thermophysical properties of CO2-O2 mixtures.

Electronic Structure and Spectroscopy of the AuO+ Cation.

The electronic structure and spectroscopy of the 29 lowest electronic states of the AuO+ cation were studied using ab initio multiconfigurational methods. These states correlate to the Au+(1S) + O(3P) and Au+(3D) + O(3P) dissociation limits. Their potentials were calculated along the Au-O internuclear distance. There are 23 of these electronic states with potential wells deep enough to allow for long lifetimes of the AuO+ cation in the corresponding states. These bound electronic states were characterized spectroscopically by solving the radial Schrödinger equation for the nuclear motion, to deduce full sets of spectroscopic parameters. The effects of the spin-orbit coupling on the lowest electronic states have been studied by determining the potentials and spectroscopic constants of the seven lowest spin-orbit Ω components. We also carried out precise calculations to determine the adiabatic ionization energy of the AuO molecule, where several corrections of the electronic energies obtained with the standard coupled cluster approach were taken into account. Our results will facilitate the correct assignment of the IR, vis, and UV spectra of the AuO+ cation and the photoelectron spectrum of the neutral AuO diatomic.

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.

Absolute frequency and isotope shift measurements of mercury 1S0-3P1 transition.

We report the measurement of the absolute frequencies of the 6s2 1S0-6s6p 3P1 transition (253.7 nm) and the relevant isotope shifts in five mercury isotopes  198Hg,  199Hg,  200Hg,  202Hg, and  204Hg. The Doppler-free saturated absorption measurements were performed in an atomic vapour cell at room temperature with a four-harmonic generated (FHG) continuous-wave (cw) laser digitally locked to the atomic transition. It was referenced with a femtosecond optical frequency comb synchronized to the frequency of local representation of the International Atomic Time to provide traceability to the SI second by the 330 km-long stabilized fibre optical link. The transition frequencies and isotope shifts have been determined with an accuracy of a few hundred kHz, at least one order of magnitude better than any previous measurement. By making a King plot with the isotope shifts of 6s6p 3P2-6s7s 3S1 transition (546 nm) we determined the accurate value of the ratio of the electronic field-shift parameters E546/E254 and estimated the electronic field-shift term E254.

First-order symmetry-adapted perturbation theory for multiplet splittings.

We present a symmetry-adapted perturbation theory (SAPT) for the interaction of two high-spin open-shell molecules (described by their restricted open-shell Hartree-Fock determinants) resulting in low-spin states of the complex. The previously available SAPT formalisms, except for some system-specific studies for few-electron complexes, were restricted to the high-spin state of the interacting system. Thus, the new approach provides, for the first time, a SAPT-based estimate of the splittings between different spin states of the complex. We have derived and implemented the lowest-order SAPT term responsible for these splittings, that is, the first-order exchange energy. We show that within the so-called S2 approximation commonly used in SAPT (neglecting effects that vanish as fourth or higher powers of intermolecular overlap integrals), the first-order exchange energies for all multiplets are linear combinations of two matrix elements: a diagonal exchange term that determines the spin-averaged effect and a spin-flip term responsible for the splittings between the states. The numerical factors in this linear combination are determined solely by the Clebsch-Gordan coefficients: accordingly, the S2 approximation implies a Heisenberg Hamiltonian picture with a single coupling strength parameter determining all the splittings. The new approach is cast into both molecular-orbital and atomic-orbital expressions: the latter enable an efficient density-fitted implementation. We test the newly developed formalism on several open-shell complexes ranging from diatomic systems (Li⋯H, Mn⋯Mn, …) to the phenalenyl dimer.

Dual Hg-Rb magneto-optical trap.

We present a two-species laser cooling apparatus capable of simultaneously collecting Rb and Hg atomic gases into a magneto-optical trap (MOT). The atomic sources, laser system, and vacuum set-up are described. While there is a loss of Rb atoms in the MOT due to photoionization by the Hg cooling laser, we show that it does not prevent simultaneous trapping of Rb and Hg. We also demonstrate interspecies collision-induced losses in the 87Rb-202Hg system.

Ab Initio Study of Chemical Reactions of Cold SrF and CaF Molecules with Alkali-Metal and Alkaline-Earth-Metal Atoms: The Implications for Sympathetic Cooling.

We investigate the energetics of the atom exchange reaction in the SrF + alkali-metal atom and CaF + alkali-metal atom systems. Such reactions are possible only for collisions of SrF and CaF with the lithium atoms, while they are energetically forbidden for other alkali-metal atoms. Specifically, we focus on SrF interacting with Li, Rb, and Sr atoms and use ab initio methods to demonstrate that the SrF + Li and SrF + Sr reactions are barrierless. We present potential energy surfaces for the interaction of the SrF molecule with the Li, Rb, and Sr atoms in their energetically lowest-lying electronic spin states. The obtained potential energy surfaces are deep and exhibit profound interaction anisotropies. We predict that the collisions of SrF molecules in the rotational or Zeeman excited states most likely have a strong inelastic character. We discuss the prospects for the sympathetic cooling of SrF and CaF molecules using ultracold alkali-metal atoms.

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.

Dispersion Energy from the Time-Independent Coupled-Cluster Polarization Propagator.

We present a new method of calculation of the dispersion energy in the second-order symmetry-adapted perturbation theory. Using the Longuet-Higgins integral and time-independent coupled-cluster response theory, one shows that the general expression for the dispersion energy can be written in terms of cluster amplitudes and the excitation operators σ, which can be obtained by solving a linear equation. We introduced an approximate scheme dubbed CCPP2(T) for the dispersion energy accurate to the second order of intramonomer correlation, which includes certain classes to be summed to infinity. Assessment of the accuracy of the CCPP2(T) dispersion energy against the FCI dispersion for He2 demonstrates its high accuracy. For more complex systems, CCPP2(T) matches the accuracy of the best methods introduced for calculations of dispersion so far. The method can be extended to higher-order levels of excitations, providing a systematically improvable theory of dispersion interaction.

Structures and optical properties of zinc oxide nanoclusters: a combined experimental and theoretical approach.

CONTEXT: In this study, theoretical and experimental analysis of the electrical, optical, and structural properties of a wurtzite-like zinc oxide (ZnO) nanostructure has been done. To investigate how quantum confinement affects the optical characteristics, two distinct ZnO clusters in nanowire structures have been investigated. The [(ZnO)55(H2O)4] system's HOMO-LUMO band gap (BG) was calculated to be 2.99 eV, which is quite close to the experimental measurement. It was found that the BG decreases with the increase in the number of atoms in the cluster in connection with the quantum confinement in nanoclusters. In addition, the lowest excitation energy in TD-DFT calculations of the identical system is in fairly good agreement with the experimental value with a difference of 0.1 eV. We conclude that the CAM-B3LYP functional has highly successful in reproducing the experimental data reported in the present study and previously reported experimental data. METHODS: The geometrical optimization of two different sizes of ZnO clusters ([(ZnO)25(H2O)4] and [ZnO)55(H2O)4]) was performed using the CAM-B3LYP functional with no symmetry constraints applied in the gas phase. LANL2DZ basis sets were used for the Zinc (Zn) atom and 6-31G* basis sets for the O and H atoms. To determine their optical and electronic properties, excited state calculations of the pre-optimized structures were performed using the Time-Dependent DFT (TD-DFT) method. Multiwfn, Gaussum 3.0, and GaussView 5.0 programs were used to visualize the results.

Symmetry-adapted perturbation theory based on unrestricted Kohn-Sham orbitals for high-spin open-shell van der Waals complexes.

Two open-shell formulations of the symmetry-adapted perturbation theory are presented. They are based on the spin-unrestricted Kohn-Sham (SAPT(UKS)) and unrestricted Hartree-Fock (SAPT(UHF)) descriptions of the monomers, respectively. The key reason behind development of SAPT(UKS) is that it is more compatible with density functional theory (DFT) compared to the previous formulation of open-shell SAPT based on spin-restricted Kohn-Sham method of Zuchowski et al. [J. Chem. Phys. 129, 084101 (2008)]. The performance of SAPT(UKS) and SAPT(UHF) is tested for the following open-shell van der Waals complexes: He···NH, H(2)O···HO(2), He···OH, Ar···OH, Ar···NO. The results show an excellent agreement between SAPT(UKS) and SAPT(ROKS). Furthermore, for the first time SAPT based on DFT is shown to be suitable for the treatment of interactions involving Π-state radicals (He···OH, Ar···OH, Ar···NO). In the interactions of transition metal dimers ((3)Σ(u)(+))Au(2) and ((13)Σ(g)(+))Cr(2) we show that SAPT is incompatible with the use of effective core potentials. The interaction energies of both systems expressed instead as supermolecular UHF interaction plus dispersion from SAPT(UKS) result in reasonably accurate potential curves.

Cold collisions of N (4S) atoms and NH (3Σ) molecules in magnetic fields.

We calculate the interaction potential between N atoms and NH molecules and use it to investigate cold and ultracold collisions important for sympathetic cooling. The ratio of elastic to inelastic cross sections is large over a wide range of collision energy and magnetic field for most isotopic combinations, so that sympathetic cooling of NH molecules by N atoms is a good prospect. However, there are important effects due to a p-wave shape resonance that may inhibit cooling in some cases. We show that scaling the reduced mass used in the collision is approximately equivalent to scaling the interaction potential. We then explore the dependence of the scattering properties on the reduced mass and explain the resonant effects observed using angular-momentum-insensitive quantum defect theory.

Interaction between LiH molecule and Li atom from state-of-the-art electronic structure calculations.

State-of-the-art ab initio techniques have been applied to compute the potential energy surface for the lithium atom interacting with the lithium hydride molecule in the Born-Oppenheimer approximation. The interaction potential was obtained using a combination of the explicitly correlated unrestricted coupled-cluster method with single, double, and noniterative triple excitations [UCCSD(T)-F12] for the core-core and core-valence correlation and full configuration interaction for the valence-valence correlation. The potential energy surface has a global minimum 8743 cm(-1) deep if the Li-H bond length is held fixed at the monomer equilibrium distance or 8825 cm(-1) deep if it is allowed to vary. In order to evaluate the performance of the conventional CCSD(T) approach, calculations were carried out using correlation-consistent polarized valence X-tuple-zeta basis sets, with X ranging from 2 to 5, and a very large set of bond functions. Using simple two-point extrapolations based on the single-power laws X(-2) and X(-3) for the orbital basis sets, we were able to reproduce the CCSD(T)-F12 results for the characteristic points of the potential with an error of 0.49% at worst. The contribution beyond the CCSD(T)-F12 model, obtained from full configuration interaction calculations for the valence-valence correlation, was shown to be very small, and the error bars on the potential were estimated. At linear LiH-Li geometries, the ground-state potential shows an avoided crossing with an ion-pair potential. The energy difference between the ground-state and excited-state potentials at the avoided crossing is only 94 cm(-1). Using both adiabatic and diabatic pictures, we analyze the interaction between the two potential energy surfaces and its possible impact on the collisional dynamics. When the Li-H bond is allowed to vary, a seam of conical intersections appears at C(2v) geometries. At the linear LiH-Li geometry, the conical intersection is at a Li-H distance which is only slightly larger than the monomer equilibrium distance, but for nonlinear geometries it quickly shifts to Li-H distances that are well outside the classical turning points of the ground-state potential of LiH. This suggests that the conical intersection will have little impact on the dynamics of Li-LiH collisions at ultralow temperatures. Finally, the reaction channels for the exchange and insertion reactions are also analyzed and found to be unimportant for the dynamics.

Cold and ultracold NH-NH collisions: the field-free case.

We present elastic and inelastic spin-changing cross sections for cold and ultracold NH(X (3)Σ(-)) + NH(X (3)Σ(-)) collisions, obtained from full quantum scattering calculations on an accurate ab initio quintet potential-energy surface. Although we consider only collisions in zero field, we focus on the cross sections relevant for magnetic trapping experiments. It is shown that evaporative cooling of both fermionic (14)NH and bosonic (15)NH is likely to be successful for hyperfine states that allow s-wave collisions. The calculated cross sections are very sensitive to the details of the interaction potential, due to the presence of (quasi)bound state resonances. The remaining inaccuracy of the ab initio potential-energy surface therefore gives rise to an uncertainty in the numerical cross-section values. However, based on a sampling of the uncertainty range of the ab initio calculations, we conclude that the exact potential is likely to be such that the elastic-to-inelastic cross-section ratio is sufficiently large to achieve efficient evaporative cooling. This likelihood is only weakly dependent on the size of the channel basis set used in the scattering calculations.

Kinetic Isotope Effect in Low-Energy Collisions between Hydrogen Isotopologues and Metastable Helium Atoms: Theoretical Calculations Including the Vibrational Excitation of the Molecule.

We present very accurate theoretical results of Penning ionization rate coefficients of the excited metastable helium atoms (4He(23S) and 3He(23S)) colliding with the hydrogen isotopologues (H2, HD, D2) in the ground and first excited rotational and vibrational states at subkelvin regime. The calculations are performed using the current best ab initio interaction energy surface, which takes into account the nonrigidity effects of the molecule. The results confirm a recently observed substantial quantum kinetic isotope effect (Nat. Chem. 2014, 6, 332-335) and reveal that the change of the rotational or vibrational state of the molecule can strongly enhance or suppress the reaction. Moreover, we demonstrate the mechanism of the appearance and disappearance of resonances in Penning ionization. The additional model computations, with the morphed interaction energy surface and mass, give better insight into the behavior of the resonances and thereby the reaction dynamics under study. Our theoretical findings are compared with all available measurements, and comprehensive data for prospective experiments are provided.

Supramolecular Approach to Tuning the Photophysical Properties of Quadrupolar Squaraines.

In the present study, the influence of the hydrogen bonding for the one- and two-photon absorption of the prototypical squaraine dye is investigated with quantum chemistry tools. The central squaraine unit is bound by strong hydrogen bonds with 4-substituted N,N'-diphenylurea and, alternatively, N,N'-diphenylthiourea molecules, which affects to a high extend the properties of the squaraine electron accepting moiety, thus shifting its maximum absorption wavelength and enhancing the TPA cross section. The replacement of oxygen by sulfur atoms in the squaraine central ring, known to affect its photophysical behavior, is considered here as the way of modifying the strength and nature of the intermolecular contacts. Additionally, the influence of the oxygen-by-sulfur replacement is also considered in the N,N'-diphenylurea moiety, as the factor affecting the acidity of the N-H protons. The introduction of the sequence of the substituents of varying electron-donating or electron-withdrawing characters in the position 4 of N,N'-diphenyl(thio)urea subsystems allows to finely tune the hydrogen bonding with the central squaraine unit by further modification of the N-H bond characteristics. All of these structural modifications lead to the controlled adjustment of the electron density distribution, and thus, the properties affected such as transition moments and absorption intensity. Ab initio calculations provide strong support for this way of tailoring of one- or two-photon absorption due to the obtained strong hypsochromic shift of the maximum one-photon absorption wavelength observed particularly for thiosquaraine complexes and an increase in the TPA wavelength together with the increase in the TPA cross section. Moreover, the source of the strong modification of the thiosquaraine OPA in contrast to the pristine oxosquaraine upon N,N'-diphenyl(thio)urea substitution is determined. Furthermore, for the first time, the linear dependence of the non-additivity in the interaction energy on the Hammett substituent constant is reported. The stronger the electron-donating character of the substituent, the larger the three-body non-additive components and the larger their percentage to the total interaction energy.

Ultracold RbSr molecules can be formed by magnetoassociation.

We investigate the interactions between ultracold alkali-metal atoms and closed-shell atoms using electronic structure calculations on the prototype system Rb+Sr. There are molecular bound states that can be tuned across atomic thresholds with a magnetic field and previously neglected terms in the collision Hamiltonian that can produce zero-energy Feshbach resonances with significant widths. The largest effect comes from the interaction-induced variation of the Rb hyperfine coupling. The resonances may be used to form paramagnetic polar molecules if the magnetic field can be controlled precisely enough.