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.

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.

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.

Torsion-wagging tunneling and vibrational states in hydrazine determined from its ab initio potential energy surface.

Geometries, anharmonic vibrations, and torsion-wagging (TW) multiplets of hydrazine and its deuterated species are studied using high-level ab initio methods employing the second-order Mo̸ller-Plesset perturbation theory (MP2) as well as the coupled cluster singles and doubles model including connected triple corrections, CCSD(T), in conjunction with extended basis sets containing diffuse and core functions. To describe the splitting patterns caused by tunneling in TW states, the 3D potential energy surface (PES) for the large-amplitude TW modes is constructed. Stationary points in the 3D PES, including equivalent local minima and saddle points are characterized. Using this 3D PES, a flexible Hamiltonian is built numerically and then employed to solve the vibrational problem for TW coupled motion. The calculated ground state r(av) structure is expected to be more reliable than the experimental one that has been determined using a simplified structural model. The calculated fundamental frequencies allowed resolution of the assignment problems discussed earlier in the literature. The determined energy barriers, including the contributions from the small-amplitude vibrations, to the tunneling of the symmetric and antisymmetric wagging mode of 1997 cm(-1) and 3454 cm(-1), respectively, are in reasonable agreement with the empirical estimates of 2072 cm(-1) and 3312 cm(-1), respectively [W. Lodyga et al. J. Mol. Spectrosc. 183, 374 (1997)]. However, the empirical torsion barrier of 934 cm(-1) appears to be overestimated. The ab initio calculations yield two torsion barriers: cis and trans of 744 cm(-1) and 2706 cm(-1), respectively. The multiplets of the excited torsion states are predicted from the refined 3D PES.

Ab initio potential energy surface and intermolecular vibrations of the naphthalene-argon van der Waals complex.

The intermolecular potential energy surface (PES) of the naphthalene-argon (NpAr) complex is constructed using an ab initio method. The molecule-argon interaction energy is computed at the level of the second-order Møller-Plesset (MP2) theory combined with the augmented correlation consistent polarized valence double-ζ basis set. The analytical PES fitted to a large set of single energy values is further improved with the help of correction functions determined by calculations of the interaction energy at the coupled cluster level including single and double excitations supplemented by triple excitations performed for a limited set of intermolecular configurations. The PES determined is very flat near its four equivalent global minima of -493 cm(-1) located from both sides of the Np plane at a distance of 3.435 Å and shifted from the center of Np by ±0.43 Å along its long symmetry axis. The large-amplitude motion of Ar in the complex is investigated, and dynamical consequence of a strong intermode coupling is discovered in the excited vibrational states. The theoretical results obtained allow for the reassignment of the spectral bands observed in the electronic transition S(1) ← S(0) of the NpAr complex.

Ab initio characterization of the Mg-HF van der Waals complex.

The equilibrium structure and the three-dimensional potential energy surface of the Mg-HF van der Waals complex in its ground electronic state have been determined from accurate ab initio calculations using the coupled-cluster method, CCSD(T), in conjunction with the basis sets of triple- through quintuple-zeta quality. The core-electron correlation, high-order valence-electron correlation, and scalar relativistic effects were investigated. The Mg-HF complex was confirmed to be linear at equilibrium, with a vibrationless dissociation energy (into Mg and HF) D(e) of 280 cm(-1). The vibration-rotation energy levels of two isotopologues, (24)Mg-HF and (24)Mg-DF, were predicted using the variational method. The predicted spectroscopic constants can be useful in a further analysis of high-resolution vibration-rotation spectra of the Mg-HF complex.

Intermolecular potential energy surface of the water-carbon dioxide complex.

A complete intermolecular potential energy surface (PES) of the H(2)O-CO(2) complex has been constructed using a large scale ab initio calculations. This PES was sampled at 23,000 points of a five dimensional configuration space of the intermolecular coordinates. The interaction energy was calculated using the second order Moller-Plesset perturbation method in conjunction with the standard aug-cc-pVTZ basis set supplemented by bond functions. Single-point energy values were used to construct the analytical many-body representations of the PES that was further improved using a set of the interaction energy values calculated along the one-dimensional cuts of PES by employing the coupled cluster singles and doubles including connected triples method. The accurate data on the structure and energetics of the complex considered have been reported. The analysis of the PES determined revealed its complex structure. A few bifurcations were found on the minimum energy paths along the coordinates describing the radial and angular motions. For the torsional motion, four symmetrically equivalent potential barriers were found as a consequence of the bifurcations, so earlier models of this motion assuming two equivalent potential barriers were justified only for the lowest torsional states.

Ab initio characterization of the Ca-HCl van der Waals complex.

The equilibrium structure and three-dimensional potential energy surface of the Ca-HCl van der Waals complex in its ground electronic state have been determined from accurate ab initio calculations using the coupled-cluster method, CCSD(T), in conjunction with basis sets of quadruple- and quintuple-zeta quality. The core-electron correlation, high-order valence-electron correlation, and scalar relativistic effects were investigated. The Ca-HCl complex was confirmed to be linear at equilibrium, with the vibrationless dissociation energy (into Ca and HCl) D(e) of 287 cm(-1). The vibration-rotation energy levels of various Ca-HCl isotopomers were predicted using the variational method. The predicted spectroscopic constants can be useful in a further analysis of high-resolution vibration-rotation spectra of the Ca-HCl complex.

Ab initio intermolecular potential energy surfaces of the water-rare gas atom complexes.

Highly accurate analytical intermolecular potential energy surfaces (PESs) of the complexes composed of the water molecule and the rare gas (Rg) atom are presented for Rg=He, Ne, Ar, and Kr. These PESs were scanned using the supermolecule coupled cluster singles and doubles including connected triples method [CCSD(T)]. Efficient basis sets including the bond functions (3s3p2d1f1g) enabled the calculation of more than 430 single-point interaction energies for each complex. These energies were utilized to construct the analytical many-body representations of the PESs. They were refined using the interaction energies evaluated at the complete basis set limit in the PES stationary points. In addition, the corrections from the core correlation were calculated for the complexes including He, Ne, and Ar. The many-body PES of XeH(2)O was built using the ab initio energy values reported by Wen and Jager [J. Phys. Chem. A 110, 7560 (2006)]. The clear regularities of the equilibrium structure and the potential barriers were found in the RgH(2)O series. A comparison of the ab initio and experimental PESs of ArH(2)O [R. C. Cohen and R. J. Saykally, J. Chem. Phys. 98, 6007 (1993)] reveals their close similarity, except for the potential barriers corresponding to the planar saddle points. Their energetic order is different in both PESs. This suggests that an alternative PES with the reversed barriers, consistent with the ab initio ones, could be derived from the experimental data.

Rovibrational molecular hamiltonian in mixed bond-angle and umbrella-like coordinates.

A new exact quantum mechanical rovibrational Hamiltonian operator for molecules exhibiting large amplitude inversion and torsion motions is derived. The derivation is based on a division of a molecule into two parts: a frame and a top. The nuclei of the frame only are used to construct a molecular system of axes. The inversion motion of the frame is described in the umbrella-like coordinates, whereas the torsion motion of the top is described by the nonstandard torsion angle defined in terms of the nuclear vectors and one of the molecular axes. The internal coordinates chosen take into account the properties of the inversion and torsion motions. Vibrational s and rotational Omega vectors obtained for the introduced internal coordinates determine the rovibrational tensor G defined by simple scalar products of these vectors. The Jacobian of the transformation from the Cartesian to the internal coordinates considered and the G tensor specify the rovibrational Hamiltonian. As a result, the Hamiltonian for penta-atomic molecules like NH2OH with one inverter is presented and a complete set of the formulas necessary to write down the Hamiltonian of more complex molecules, like NH2NH2 with two inverters, is reported. The approach considered is essentially general and sufficiently simple, as demonstrated by derivation of a polyatomic molecule Hamiltonian in polyspherical coordinates, obtained by other methods with much greater efforts.

Structure and dynamics of the aniline-argon complex as derived from its potential energy surface.

The structure and dynamics of the van der Waals (vdW) complex of aniline (An) with argon (Ar) are studied using ab initio methods. The inversion potential of the aniline-argon (AnAr) complex perturbed by the weak vdW interaction is calculated taking into account subtle corrections from the zero-point energy of the vdW modes and from the frequency shifts of the An normal modes modified by the complexation. The intermolecular potential energy surface (PES) of the AnAr complex is determined by performing a large-scale computation of the interaction energy and the fitting of the analytical many-body expansion to the set of single-point interaction energies. The PES determined shows two deep local minima corresponding to the anti and syn AnAr conformers. The difference in the energies of these two minima is only 15 cm-1, but it is sufficient to localize the inversion wave functions and to form the two conformers. In the conformer anti (syn) of lower (higher) energy, Ar is bound to the An ring opposite (adjacent) the amino-hydrogens. In the additional local minima higher in energy, Ar approaches the aniline ring between the C-H bonds near its plane. An additional local minimum is located opposite of nitrogen between the two N-H bonds. The high-energy minima are, however, too flat to form stable conformers. The perturbation of the interaction of Ar with the phenyl ring by the NH2 group is described by the vdW hole, which is responsible for unusually strong intermode mixing in the excited intermolecular vibrational states. The analysis of these states calculated for the ground (S0) as well as the first excited electronic state (S1) resolves difficulties faced earlier with the assignment of the observed vibronic bands of AnAr.

Potential energy surface, van der Waals motions, and vibronic transitions in phenol-argon complex.

The structure and intermolecular vibrational energy levels of the phenol-Ar complex are calculated from its potential energy surface. This surface is constructed from a large set of the interaction energy values computed using second-order Moller-Plesset perturbation theory with the augmented correlation consistent polarized valence double-zeta basis set. The global minimum in the potential energy surface corresponds to a cluster structure with Ar located over the geometric center of the phenol ring at a distance of 3.510 A and shifted by 0.1355 A towards oxygen. The calculated dissociation energy of 371 cm(-1) is in accordance with the experiment. Additional local minima higher in energy are with Ar placed in the phenol plane. However, they are too shallow to form the bound states corresponding to planar isomers. The deformation of the potential energy surface shape, created by the interaction of Ar with the phenolic oxygen, is responsible for a pronounced intermode mixing. As a result, a set of hybrid stretching-bending states appears which cannot be described in terms of the standard models. The intermode coupling is reflected in the vibronic structure of the S1-S0 electronic transition. The intensities of the vibronic bands are calculated from the electronic transition dipole moment surfaces determined using the ab initio single-excitation configuration interaction method. They allow us to correct and complete the assignment of the spectra observed in phenol-Ar, as well as in the analogous complexes of phenol with Kr and Xe.

Potential-energy surface, van der Waals energy spectrum, and vibronic transitions in s-tetrazine-argon complex.

The van der Waals vibrational states and the structure of the vibronic spectrum of s-tetrazine-argon complex have been studied by the ab initio methods. The potential-energy surface of the ground S(0) electronic state of the complex has been constructed by fitting the analytical many-body expansion to a large set of the interaction energy values computed using the second-order Møller-Plesset perturbation theory combined with the standard aug-cc-pVDZ basis set. The equilibrium structure of the complex found is that with argon located above the tetrazine ring at a distance of 3.394 A. The calculated dissociation energy of 354 cm(-1) is compatible with the experiment. The van der Waals energy spectrum calculated from the potential-energy surface is explained analyzing a correlation with a simpler energy spectrum of benzene-argon. A new assignment of the S(0)-S(1) vibronic spectrum is proposed on the basis of the rigorous selection rules, vibrational energy levels in S(0) and S(1) states and vibronic transition intensities calculated from the electronic transition dipole moment surfaces.

Fully dimensional ab initio description of the structure and energetics of azabenzene-argon complexes.

The structure and energetics of van der Waals complexes of argon with azabenzenes: pyridine, pyrazine, pyrimidine, pyridazine, s-triazine, and s-tetrazine are studied using the second-order Moller-Plesset perturbation theory combined with well-balanced basis sets. The full optimization of the cluster structures and computation of the inter- and intramolecular vibrational frequencies is performed by eliminating the basis set superposition error. The argon equilibrium coordinates are calculated with the accuracy comparable to that reached by standard methods of the structure determination from the spectral data. A simple rule to predict the position of argon with respect to the geometric center of the azabenzene ring is found. The calculated harmonic frequencies of the intermolecular vibrational modes are scaled by the factor of 0.85 to eliminate systematic errors coming from the neglect of anharmonic effects. The scaled frequencies agree with the experimental ones to about 1 cm(-1), except for pyrimidine-argon and tetrazine-argon for which empirical fundamental frequency estimates are problematic. A simple relation connecting the intermolecular bending frequencies and the monomer quadrupole tensor is found. The perturbation of the monomer properties caused by complexation is analyzed. The modification of the monomer structure by the interaction with argon and its influence on the binding energy appears to be negligible in all complexes studied. However, this interaction affects appreciably the intramolecular modes and causes their frequency shifts. As a consequence, the dissociation energy of the complexes increases by about 5 cm(-1).

Potential-energy surface and van der Waals motions of p-difluorobenzene-argon cation.

The structure and dynamics of the van der Waals complex of argon with the p-difluorobenzene cation are investigated using the ab initio theory. The restricted open-shell Møller-Plesset second-order perturbation method combined with the augmented correlation-consistent polarized valence double-zeta basis set is employed to determine the electronic ground-state potential-energy surface of the cationic complex. This surface is extremely flat in a wide region of the configuration space of the Ar atom which moves almost freely over the monomer ring. However, it is bound to the monomer stronger in the cationic than in the neutral complex. Its binding energy is calculated to be 621 cm(-1) at a distance of 3.445 A from the monomer center. The calculated dissociation energy of 572 cm(-1) agrees perfectly with the experimental value of 572+/-6 cm(-1) [S. M. Belm, R. J. Moulds, and D. Lawrence, J. Chem. Phys. 115, 10709 (2001)]. The effect of a strong coupling of large-amplitude intermolecular motions on the character of van der Waals vibrational states is investigated. The vibrational structure of the spectrum of the complex is explained and its earlier assignment is partly corrected.

Potential-energy surface, dynamics of van der Waals motions, and vibronic transitions in p-difluorobenzene-argon complex.

The dynamics of van der Waals vibrational motions and vibronic spectrum of the complex of argon with p-difluorobenzene (ArDFB) are investigated using the ab initio method. The electronic ground-state potential-energy surface of the complex is calculated at the second-order Møller-Plesset level of theory using a well-balanced basis set aug-cc-pVDZ and its reduced version without tight polarization functions. The dissociation energy of 351 cm(-1) and the binding energy of 402 cm(-1) determined at the Ar distance of 3.521 Angstroms from the DFB ring well agree with the experimental data available. The character of calculated vibrational levels is analyzed and the effect of a strong coupling between the stretching and bending motions is investigated. A new class of hybrid states created by this coupling is found. To investigate the vibronic S(1)-S(0) spectrum, the surfaces of the electronic transition dipole moment are calculated using the ab initio method. From these surfaces, the vibronic transition intensities are determined and employed to assign the Franck-Condon- and Herzberg-Teller-induced transitions.

Well-balanced basis sets for second-order Møller-Plesset treatment of argon-aromatic molecule complexes.

Efficient ab initio method for studies of van der Waals complexes of argon and aromatic molecules is presented. It is based on the supermolecular second-order Møller-Plesset (MP2) perturbation theory combined with well-balanced basis sets. The error resulting from incompleteness of such basis sets is almost exactly canceled by the correlation error inherent in the MP2 method. Two basis sets adapted to the MP2 method are selected from various medium-sized basis sets. The standard augmented correlation consistent polarized valence double-zeta basis set and a smaller reduced version derived from it are shown to perform exceptionally well. They are employed in a large scale computation of the potential energy surfaces of argon-benzene and argon-fluorobenzene complexes. The results are critically compared with ab initio high level coupled-cluster calculations and experimental data available. The calculated MP2 equilibrium geometry, dissociation energy, and the vibrational states of the stretching mode are proved to be in excellent agreement with the experiment. However, the bending fundamentals are systematically overestimated by about 1 cm(-1). This deficiency is removed by introducing a simple correction function which improves the MP2 potential energy surface. This function can be easily determined and applied to arbitrary argon-aromatic molecule complexes. The MP2 method is compared to the density-functional theory. Local, semilocal, and hybrid models are tested and the results obtained clearly show that none of these models is capable of accurate description of the van der Waals interaction.