Ab Initio Potentials for the Ground S0 and the First Electronically Excited Singlet S1 States of Benzene-Helium with Application to Tunneling Intermolecular Vibrational States.

We present new ab initio intermolecular potential energy surfaces for the benzene-helium complex in its ground (S0) and first excited (S1) states. The coupled-cluster level of theory with single, double, and perturbative triple excitations, CCSD(T), was used to calculate the ground state potential. The excited state potential was obtained by adding the excitation energies S0 → S1 of the complex, calculated using the equation of motion approach EOM-CCSD, to the ground state potential interaction energies. Analytical potentials are constructed and applied to study the structural and vibrational dynamics of benzene-helium. The binding energies and equilibrium distances of the ground and excited states were found to be 89 cm-1, 3.14 Å and 77 cm-1, 3.20 Å, respectively. The calculated vibrational energy levels exhibit tunneling of He through the benzene plane and are in reasonable agreement with recently reported experimental values for both the ground and excited states [Hayashi, M.; Ohshima, Y. J. Phys. Chem. Lett. 2020, 11, 9745]. Prospects for the theoretical study of complexes with large aromatic molecules and He are also discussed.

Long-range interactions of aromatic molecules with alkali-metal and alkaline-earth-metal atoms.

The isotropic and anisotropic coefficients Cn l,m of the long-range spherical expansion ∼1/Rn (R-the intermolecular distance) of the dispersion and induction intermolecular energies are calculated using the first principles for the complexes containing an aromatic molecule (benzene, pyridine, furan, and pyrrole) and alkali-metal (Li, Na, K, Rb, and Cs) or alkaline-earth-metal (Be, Mg, Ca, Sr, and Ba) atoms in their electronic ground states. The values of the first- and second-order properties of the aromatic molecules are calculated using the response theory with the asymptotically corrected LPBE0 functional. The second-order properties of the closed-shell alkaline-earth-metal atoms are obtained using the expectation-value coupled cluster theory and of the open-shell alkali-metal atoms using analytical wavefunctions. These properties are used for the calculation of the dispersion Cn,disp l,m and induction Cn,ind l,m coefficients (Cn l,m=Cn,disp l,m+Cn,ind l,m) with n up to 12 using the available implemented analytical formulas. It is shown that the inclusion of the coefficients with n > 6 is important for reproducing the interaction energy in the van der Waals region at R ≈ 6 Å. The reported long-range potentials should be useful for constructing the analytical potentials valid for the whole intermolecular interaction range, which are needed for spectroscopic and scattering studies.

Character of intermolecular vibrations in the benzene-neon complex based on CCSD(T) and SAPT potential energy surfaces.

The intermolecular potential energy surface of the benzene-neon complex is constructed using highly accurate electronic structure methods for the ground electronic state. The interaction energies have been calculated with the CCSD(T) (coupled cluster level including single and double excitations supplemented by triple excitation) method and symmetry-adapted perturbation theory based on the density functional and CCSD descriptions of monomer properties (DFT-SAPT and CCSD-SAPT) with augmented triple Dunning's basis set (aug-cc-pVTZ) supplemented by the midbond functions. The analytical PESs have been constructed using an analytical long-range part based on spherical multipole expansion and a short-range part based on many-body expansion. The potential is characterized by two symmetrically equivalent global minima located at the benzene C6 axis of symmetry and by local minima lying in the benzene plane on the axes connecting the benzene center of mass and the middle of CC bonds. The values of the equilibrium geometry parameters, the dissociation energy and vibrational energy have been extracted from these potentials and compared to their empirical counterparts derived previously from the microwave spectra. The complex is characterized by large-amplitude motion of the Ne atom which, however, can be studied with a theoretical approach with neglected tunneling motion through the monomer plane, when the lowest vibrational energy levels are considered.

Ab initio relativistic potential energy surfaces of benzene-Xe complex with application to intermolecular vibrations.

The benzene-Xe (BXe) complex in its electronic ground state is studied using ab initio methods. Since this complex contains the heavy Xe atom, the relativistic effects cannot be neglected. We test two different approaches that describe the scalar relativistic effects in the framework of the coupled-cluster level of theory with single, double, and perturbative triple excitations, used for the interaction energy calculations. The first one is based on the small core pseudopotential (PP), and the second one is based on the explicit treatment of scalar relativistic effects using the Douglas-Kroll-Hess (DKH) Hamiltonian. A few basis sets are tested with the PP and DKH, and for each one, the analytical potential energy surface (PES) is constructed. It is shown that the difference between PESs determined with PP and DKH methods is small, if the orbitals of the 4d subshell in Xe are correlated. We select the most appropriate approach for the calculation of the potential energy surface of BXe, with respect to accuracy and computational cost. The optimal level of theory includes a small Dunning's basis set for the benzene monomer and a larger PP basis set for Xe supplemented by midbond functions. The PES obtained using such an approach provides a reasonable accuracy when compared to the empirical one derived from the microwave spectra of BXe. The empirical and the theoretical values of intermolecular vibrational energies agree within 0.5 cm-1 up to second overtones. The vibrational energy level pattern of BXe is characterized by a distinct polyad structure.

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.

Theoretical study of the complexes of dichlorobenzene isomers with argon. I. Global potential energy surface for all the isomers with application to intermolecular vibrations.

The complexes of para- (p-), meta- (m-), and ortho- (o-)dichlorobenzene (DCB) isomers with argon are studied using an ab initio method. The interaction energy in the ground electronic state of the complexes has been calculated using the CCSD(T) method (coupled cluster method including single and double excitations with perturbative triple excitations) and Dunning's double-ζ (aug-cc-pVDZ) basis set supplemented by midbond functions. Local interaction parameters have been defined and interesting relations fulfilled by them, independent of the DCB isomer, have been revealed. This finding has allowed us to construct the accurate global analytical intermolecular potential energy surface for all the DCB-Ar complexes with the same set of parameters, except for the monomer geometries. Each complex is characterized by two symmetrically equivalent global minima, one located above and the other located below the monomer plane at distances equal to 3.497 Å, 3.494 Å, and 3.485 Å for p-, m-, and o-isomers of DCB bound to Ar, respectively. Additionally, the Ar atom is shifted from the geometrical center of the DCB monomer towards the chlorine atoms by the value xe of 0.182 Å for m-isomer and 0.458 Å for o-isomer. The calculated binding energy De of 460 cm-1, 465 cm-1, and 478 cm-1 for p-, m-, and o-complex, respectively, are related to xe by simple relations. The intermolecular bending fundamentals calculated from PES depend strongly on the isomer structure. The calculated dissociation energies fit in the intervals estimated by the experiment of Gaber et al. for the S0 state [Phys. Chem. Chem. Phys. 11, 1628 (2009)].

Theoretical study of the complexes of dichlorobenzene isomers with argon. II. SAPT analysis of the intermolecular interaction.

The interaction of argon with dichlorobenzene isomers (DCB-Ar) has been analyzed with the help of the symmetry-adapted perturbation theory based on the density functional description of monomer properties (DFT-SAPT). The global potential energy surface (PES) of these complexes determined from the DFT-SAPT interaction energy (Eint) values has been compared to the CCSD(T) (coupled cluster method including single and double excitations with perturbative triple excitations) PES reported in the companion Paper I [J. Makarewicz and L. Shirkov, J. Chem. Phys. 150, 074301 (2019)]. The equilibrium structures and the binding energies found using DFT-SAPT and CCSD(T) methods combined with adequate basis sets are in good agreement. Besides DCB-Ar, we confirmed that DFT-SAPT gives accurate values of these quantities for other complexes containing an aromatic molecule and Ar. However, DFT-SAPT PES of DCB-Ar is flatter than the corresponding CCSD(T) one. As a result, the intermolecular vibrational energies are systematically underestimated. The analytical form of the important interrelations between SAPT components of Eint, established previously by us [J. Makarewicz and L. Shirkov, J. Chem. Phys. 144, 204115 (2016)], has been approved for the DCB-Ar complexes. Simplified SAPT models based on these relations have been employed to explain physical reasons for differences in the structures and the binding energies of DCB-Ar isomers. It is shown that the equilibrium distance of Ar to DCB plane and the binding energy are determined mainly by dispersion energy. The shift of Ar toward Cl is caused by both exchange and dispersion terms.

Benchmark CCSD-SAPT study of rare gas dimers with comparison to MP-SAPT and DFT-SAPT.

Symmetry-adapted perturbation theory (SAPT) based on coupled cluster approach with single and double excitations (CCSD) treatment of intramonomer electron correlation effects was applied to study rare gas homodimers from He2 to Kr2. The obtained benchmark CCSD-SAPT energies, including cumulant contributions to first order exchange and second-order exchange-induction terms, were then compared to their counterparts found using other methods-Møller-Plesset-SAPT based on many-body Møller-Plesset perturbation theory and DFT-SAPT based on density functional theory. The SAPT terms up to the second-order were calculated with the basis sets close to the complete basis set at the large range of interatomic distances R. It was shown that overestimation of the binding energies De found with DFT-SAPT reported in the work of Shirkov and Makarewicz [J. Chem. Phys. 142, 064102 (2015)] for Ar2 and Kr2 is mostly due to underestimation of the exchange energy Eexch(1) when comparing to the CCSD-SAPT benchmark. The CCSD-SAPT potentials were found to give the following values of the dissociation energies D0: 0.0006 cm-1 for He2, 16.71 cm-1 for Ne2, 85.03 cm-1 for Ar2, and 129.81 cm-1 for Kr2, which agree well with the values found from previously reported highly accurate ab initio supermolecular potentials and experimental data. The long-range dispersion coefficients C2n up to n = 6 that give the dispersion energy asymptotically equivalent to its SAPT counterpart were calculated from dynamic multipole polarizabilities at different levels of theory.

Character of intermolecular interaction in pyridine-argon complex: Ab initio potential energy surface, internal dynamics, and interrelations between SAPT energy components.

The pyridine-Ar (PAr) van der Waals (vdW) complex is studied using a high level ab initio method. Its structure, binding energy, and intermolecular vibrational states are determined from the analytical potential energy surface constructed from interaction energy (IE) values computed at the coupled cluster level of theory with single, double, and perturbatively included triple excitations with the augmented correlation consistent polarized valence double-ζ (aug-cc-pVDZ) basis set complemented by midbond functions. The structure of the complex at its global minimum with Ar at a distance of 3.509 Šfrom the pyridine plane and shifted by 0.218 Šfrom the center of mass towards nitrogen agrees well with the corresponding equilibrium structure derived previously from the rotational spectrum of PAr. The PAr binding energy De of 392 cm(-1) is close to that of 387 cm(-1) calculated earlier at the same ab initio level for the prototypical benzene-Ar (BAr) complex. However, under an extension of the basis set, De for PAr becomes slightly lower than De for BAr. The ab initio vdW vibrational energy levels allow us to estimate the reliability of the methods for the determination of the vdW fundamentals from the rotational spectra. To disclose the character of the intermolecular interaction in PAr, the symmetry-adapted perturbation theory (SAPT) is employed for the analysis of different physical contributions to IE. It is found that SAPT components of IE can be approximately expressed in the binding region by only two of them: the exchange repulsion and dispersion energy. The total induction effect is negligible. The interrelations between various SAPT components found for PAr are fulfilled for a few other complexes involving aromatic molecules and Ar or Ne, which indicates that they are valid for all rare gas (Rg) atoms and aromatics.

The study of basis sets for the calculation of the structure and dynamics of the benzene-Kr complex.

An ab initio intermolecular potential energy surface (PES) has been constructed for the benzene-krypton (BKr) van der Waals (vdW) complex. The interaction energy has been calculated at the coupled cluster level of theory with single, double, and perturbatively included triple excitations using different basis sets. As a result, a few analytical PESs of the complex have been determined. They allowed a prediction of the complex structure and its vibrational vdW states. The vibrational energy level pattern exhibits a distinct polyad structure. Comparison of the equilibrium structure, the dipole moment, and vibrational levels of BKr with their experimental counterparts has allowed us to design an optimal basis set composed of a small Dunning's basis set for the benzene monomer, a larger effective core potential adapted basis set for Kr and additional midbond functions. Such a basis set yields vibrational energy levels that agree very well with the experimental ones as well as with those calculated from the available empirical PES derived from the microwave spectra of the BKr complex. The basis proposed can be applied to larger complexes including Kr because of a reasonable computational cost and accurate results.

Does DFT-SAPT method provide spectroscopic accuracy?

Ground state potential energy curves for homonuclear and heteronuclear dimers consisting of noble gas atoms from He to Kr were calculated within the symmetry adapted perturbation theory based on the density functional theory (DFT-SAPT). These potentials together with spectroscopic data derived from them were compared to previous high-precision coupled cluster with singles and doubles including the connected triples theory calculations (or better if available) as well as to experimental data used as the benchmark. The impact of midbond functions on DFT-SAPT results was tested to study the convergence of the interaction energies. It was shown that, for most of the complexes, DFT-SAPT potential calculated at the complete basis set (CBS) limit is lower than the corresponding benchmark potential in the region near its minimum and hence, spectroscopic accuracy cannot be achieved. The influence of the residual term δ(HF) on the interaction energy was also studied. As a result, we have found that this term improves the agreement with the benchmark in the repulsive region for the dimers considered, but leads to even larger overestimation of potential depth De. Although the standard hybrid exchange-correlation (xc) functionals with asymptotic correction within the second order DFT-SAPT do not provide the spectroscopic accuracy at the CBS limit, it is possible to adjust empirically basis sets yielding highly accurate results.