A joint theoretical and experimental study of state-to-state rotationally inelastic polarization dependent differential cross sections (PDDCSs) for CO (v = 0, j = 0, 1, 2) molecules colliding with helium is reported for collision energies of 513 and 840 cm–1. In a crossed molecular beam experiment, velocity map imaging (VMI) with state-selective detection by (2 + 1) and (1 + 1′) resonance enhanced multiphoton ionization (REMPI) is used to probe rotational excitation of CO due to scattering. By taking account of the known fractions of the j = 0, 1, and 2 states of CO in the rotationally cold molecular beam (Trot ≈ 3 K), close-coupling theory based on high-quality ab initio potential energy surfaces for the CO–He interaction is used to simulate the differential cross sections for the mixed initial states. With polarization-sensitive 1 + 1′ REMPI detection and a direct analysis procedure described by Suits et al. ( J. Phys, Chem. A 2015, 119, 5925), alignment moments are extracted from the images and the latter are compared with images simulated by theory using the calculated DCS and alignment moments. In general, good agreement of theory with the experimental results is found, indicating the reliability of the experiment in reproducing state-to-state differential and polarization-dependent differential cross sections.

We report a combined theoretical and microwave spectroscopy study of the internal dynamics of the benzene dimer, a benchmark system for dispersion forces. Although the extensive ab initio calculations and experimental work on the equilibrium geometry of this dimer have converged to a tilted T-shaped structure, the rich internal dynamics due to low barriers for internal rotation have remained largely unexplored. We present new microwave spectroscopy data for both the normal (C6H6)2 and partially deuterated (C6D6)(C6H6) dimers. The splitting patterns obtained for both species are unraveled and understood using a reduced-dimensionality theoretical approach. The hindered sixfold rotation of the stem can explain the observed characteristic 1:2:1 tunneling splitting pattern, but only the concerted stem rotation and tilt tunneling motion, accompanied by overall rotation of the dimer, yield the correct magnitude of the splittings and their strong dependence on the dimer angular momentum J that is essential to explain the experimental data. Also the surprising observation that the splittings are reduced by 30% for the mixed (C6D6)C(C6H6)S dimer in which only the cap (C) in the T-shaped structure is deuterated, while the rotating stem (S) monomer is the same as in the homodimer, is understood using this approach. Stark shift measurements allowed us to determine the dipole moment of the benzene dimer, μ = 0.58 ± 0.051 D. The assumption that this dipole moment is the vector sum of the dipole moments induced in the monomers by the electric field of the quadrupole on the other monomer yields a calculated value of μ = 0.63 D. Furthermore, the observed Stark behavior is typical for a symmetric top, another confirmation of our analysis.

An improved intermolecular potential surface for the benzene dimer is constructed from interaction energies computed by symmetry-adapted perturbation theory, SAPT(DFT), with the inclusion of third-order contributions. Twelve characteristic points on the surface have been investigated also using the coupled-cluster method with single, double, and perturbative triple excitations, CCSD(T), and triple-zeta quality basis sets with midbond functions. The SAPT and CCSD(T) results are in close agreement and provide the best representation of these points to date. The potential was used in calculations of vibration–rotation-tunneling (VRT) levels of the dimer by a method appropriate for large amplitude intermolecular motions and tunneling between multiple equivalent minima in the potential. The resulting VRT levels were analyzed with the use of the permutation-inversion full cluster tunneling (FCT) group G576 and a chain of subgroups that starts from the molecular symmetry group Cs(M) of the rigid dimer at its equilibrium Cs geometry and leads to G576 if all possible intermolecular tunneling mechanisms are feasible. Further information was extracted from the calculated wave functions. It was found, in agreement with the experimental data, that for all of the 54 G576 symmetry species (with different nuclear spin statistical weights) the lower VRT states have a tilted T-shape (TT) structure; states with the parallel-displaced structure are higher in energy than the ground state of A+1 symmetry by at least 30 cm−1. The dissociation energy D0 equals 870 cm−1, while the depth De of the TT minimum in the potential is 975 cm−1. Hindered rotation of the cap in the TT structure and tilt tunneling lead to level splittings on the order of 1 cm−1. Also intermolecular vibrations with excitation energies starting at a few cm−1 were identified. A further small, but probably significant, level splitting was assigned to cap turnover, although in scans of the potential surface we could not find a plausible ‘reaction path’ for this process. Rotational constants were extracted from energy levels calculated for total angular momentum J = 0 and 1, and from expectation values of the inertia tensor. Although the end-over-end rotational constant B + C agrees well with the measured microwave spectra, there is disagreement with the measurements concerning the (a)symmetric rotor character of the benzene dimer. It is concluded from calculations for the 54 nuclear spin species that the microwave spectrum should show overlapping contributions from many different species. Another interesting conclusion regards the role of the quantum number K, for a prolate near-symmetric rotor the projection of the total angular momentum on the prolate axis. For the benzene dimer, K has a substantial effect on the energy levels associated with the intermolecular motions of the complex.

The ab initiowater dimer interaction energies obtained from coupled cluster calculations and used in the CC-pol water pair potential (Bukowski et al., Science, 2007, 315, 1249) have been refitted to a site–site form containing eight symmetry-independent sites in each monomer and denoted as CC-pol-8s. Initially, the site–site functions were assumed in a B-spline form, which allowed a precise optimization of the positions of the sites. Next, these functions were assumed in the standard exponential plus inverse powers form. The root mean square error of the CC-pol-8s fit with respect to the 2510 ab initio points is 0.10 kcal mol−1, compared to 0.42 kcal mol−1 of the CC-pol fit (0.010 kcal mol−1 compared to 0.089 kcal mol−1 for points with negative interaction energies). The energies of the stationary points in the CC-pol-8s potential are considerably more accurate than in the case of CC-pol. The water dimer vibration–rotation–tunneling spectrum predicted by the CC-pol-8s potential agrees substantially and systematically better with experiment than the already very accurate spectrum predicted by CC-pol, while specific features that could not be accurately predicted previously now agree very well with experiment. This shows that the uncertainties of the fit were the largest source of error in the previous predictions and that the present potential sets a new standard of accuracy in investigations of the water dimer.

We report a combined theoretical and microwave spectroscopy study of the internal dynamics of the benzene dimer, a benchmark system for dispersion forces. Although the extensive ab initio calculations and experimental work on the equilibrium geometry of this dimer have converged to a tilted T-shaped structure, the rich internal dynamics due to low barriers for internal rotation have remained largely unexplored. We present new microwave spectroscopy data for both the normal (C6H6)2 and partially deuterated (C6D6)(C6H6) dimers. The splitting patterns obtained for both species are unraveled and understood using a reduced-dimensionality theoretical approach. The hindered sixfold rotation of the stem can explain the observed characteristic 1:2:1 tunneling splitting pattern, but only the concerted stem rotation and tilt tunneling motion, accompanied by overall rotation of the dimer, yield the correct magnitude of the splittings and their strong dependence on the dimer angular momentum J that is essential to explain the experimental data. Also the surprising observation that the splittings are reduced by 30% for the mixed (C6D6)C(C6H6)S dimer in which only the cap (C) in the T-shaped structure is deuterated, while the rotating stem (S) monomer is the same as in the homodimer, is understood using this approach. Stark shift measurements allowed us to determine the dipole moment of the benzene dimer, μ = 0.58 ± 0.051 D. The assumption that this dipole moment is the vector sum of the dipole moments induced in the monomers by the electric field of the quadrupole on the other monomer yields a calculated value of μ = 0.63 D. Furthermore, the observed Stark behavior is typical for a symmetric top, another confirmation of our analysis.

The ab initiowater dimer interaction energies obtained from coupled cluster calculations and used in the CC-pol water pair potential (Bukowski et al., Science, 2007, 315, 1249) have been refitted to a site–site form containing eight symmetry-independent sites in each monomer and denoted as CC-pol-8s. Initially, the site–site functions were assumed in a B-spline form, which allowed a precise optimization of the positions of the sites. Next, these functions were assumed in the standard exponential plus inverse powers form. The root mean square error of the CC-pol-8s fit with respect to the 2510 ab initio points is 0.10 kcal mol−1, compared to 0.42 kcal mol−1 of the CC-pol fit (0.010 kcal mol−1 compared to 0.089 kcal mol−1 for points with negative interaction energies). The energies of the stationary points in the CC-pol-8s potential are considerably more accurate than in the case of CC-pol. The water dimer vibration–rotation–tunneling spectrum predicted by the CC-pol-8s potential agrees substantially and systematically better with experiment than the already very accurate spectrum predicted by CC-pol, while specific features that could not be accurately predicted previously now agree very well with experiment. This shows that the uncertainties of the fit were the largest source of error in the previous predictions and that the present potential sets a new standard of accuracy in investigations of the water dimer.

An improved intermolecular potential surface for the benzene dimer is constructed from interaction energies computed by symmetry-adapted perturbation theory, SAPT(DFT), with the inclusion of third-order contributions. Twelve characteristic points on the surface have been investigated also using the coupled-cluster method with single, double, and perturbative triple excitations, CCSD(T), and triple-zeta quality basis sets with midbond functions. The SAPT and CCSD(T) results are in close agreement and provide the best representation of these points to date. The potential was used in calculations of vibration–rotation-tunneling (VRT) levels of the dimer by a method appropriate for large amplitude intermolecular motions and tunneling between multiple equivalent minima in the potential. The resulting VRT levels were analyzed with the use of the permutation-inversion full cluster tunneling (FCT) group G576 and a chain of subgroups that starts from the molecular symmetry group Cs(M) of the rigid dimer at its equilibrium Cs geometry and leads to G576 if all possible intermolecular tunneling mechanisms are feasible. Further information was extracted from the calculated wave functions. It was found, in agreement with the experimental data, that for all of the 54 G576 symmetry species (with different nuclear spin statistical weights) the lower VRT states have a tilted T-shape (TT) structure; states with the parallel-displaced structure are higher in energy than the ground state of A+1 symmetry by at least 30 cm−1. The dissociation energy D0 equals 870 cm−1, while the depth De of the TT minimum in the potential is 975 cm−1. Hindered rotation of the cap in the TT structure and tilt tunneling lead to level splittings on the order of 1 cm−1. Also intermolecular vibrations with excitation energies starting at a few cm−1 were identified. A further small, but probably significant, level splitting was assigned to cap turnover, although in scans of the potential surface we could not find a plausible ‘reaction path’ for this process. Rotational constants were extracted from energy levels calculated for total angular momentum J = 0 and 1, and from expectation values of the inertia tensor. Although the end-over-end rotational constant B + C agrees well with the measured microwave spectra, there is disagreement with the measurements concerning the (a)symmetric rotor character of the benzene dimer. It is concluded from calculations for the 54 nuclear spin species that the microwave spectrum should show overlapping contributions from many different species. Another interesting conclusion regards the role of the quantum number K, for a prolate near-symmetric rotor the projection of the total angular momentum on the prolate axis. For the benzene dimer, K has a substantial effect on the energy levels associated with the intermolecular motions of the complex.