Thermodynamic properties of van der Waals fluids from Monte Carlo simulations and perturbative Monte Carlo theory

Computer simulations have been performed for fluids with van der Waals potential, that is, hard spheres with attractive inverse power tails, to determine the equation of state and the excess energy. On the other hand, the first- and second-order perturbative contributions to the energy and the zero- and first-order perturbative contributions to the compressibility factor have been determined too from Monte Carlo simulations performed on the reference hard-sphere system. The aim was to test the reliability of this "exact" perturbation theory. It has been found that the results obtained from the Monte Carlo perturbation theory for these two thermodynamic properties agree well with the direct Monte Carlo simulations. Moreover, it has been found that results from the Barker-Henderson [J. Chem. Phys. 47, 2856 (1967)] perturbation theory are in good agreement with those from the exact perturbation theory.     

Rydberg states with quantum Monte Carlo

Calculations on Rydberg states are performed using quantum Monte Carlo methods. Excitation energies and singlet-triplet splittings are calculated for two model systems, the carbon atom (3P and 1P) and carbon monoxide ((1Sigma and 3Sigma). Kohn-Sham wave functions constructed from open-shell localized Hartree-Fock orbitals are used as trial and guide functions. The fixed-node diffusion quantum Monte Carlo (FN-DMC) method depends strongly on the wave function's nodal hypersurface. Nodal artefacts are investigated for the ground state of the carbon atom. Their effect on the FN-DMC results can be analyzed quantitatively. FN-DMC leads to accurate excitation energies but to less accurate singlet-triplet splittings. Variational Monte Carlo calculations are able to reproduce the experimental results for both the excitation energies and the singlet-triplet splittings.     

Energy transfer rates in inhomogeneous van der Waals clusters

The internal energy exchanges inside an inhomogeneous van der Waals cluster are investigated by means of molecular dynamic calculations. The very long time scales for relaxation of the high frequency degrees of freedom are examined within the framework of Nekhoroshev's theorem.     

Collisional stabilization of van der Waals states of ozone

The mixed quantum-classical theory developed earlier [M. Ivanov and D. Babikov, J. Chem. Phys. 134, 144107 (2011)] is employed to treat the collisional energy transfer and the ro-vibrational energy flow in a recombination reaction that forms ozone. Assumption is that the van der Waals states of ozone are formed in the O + O(2) collisions, and then stabilized into the states of covalent well by collisions with bath gas. Cross sections for collision induced dissociation of van der Waals states of ozone, for their stabilization into the covalent well, and for their survival in the van der Waals well are computed. The role these states may play in the kinetics of ozone formation is discussed.     

Electron impact ionization efficiency curves of van der Waals clusters

The study of van der Waals clusters is an area of growing interest and is being widely studied for a number of reasons. The measurement of the ionization efficiency (IE) curves have yielded a wealth of information by enabling ionization and appearance energies of ions to be determined which are essential for the calculation of thermochemical data. In the case of van der Waals clusters, the measurement ofIE curves enables one to determine the qualitative trends in the ionization potentials as a function of cluster size. In additionIE curves have also offered valuable insight into ionization related processes occurring in clusters. This paper will cover some of the more recent studies of Penning ionization, exciton induced decay and Coulomb explosion in van der Waals clusters through the use of electron impactIE curves.     

Reactions of O with CO van der Waals molecules and clusters

The reaction of O(³ P) with COR _m clusters to produce electronically excited CO₂ was studied under molecular beam conditions. It was found that the spectrum of the chemiluminescence produced extended from the blue all the way to the near infrared. The dependence of the total emission intensity on stagnation pressure was investigated for (CO) _m as well as for COR _m , R=He, Ne, Ar, N₂, CO₂ and SO₂. The low pressure data indicate that small (CO) _m polymers are more efficient than clusters of CO with other species in inducing the chemiluminescent reaction. The larger CO-rare gas clusters, however, exhibited larger reaction cross-sections than those of the CO polymers. Rare gas clusters ofm≧5, on the other hand have successively smaller cross sections for reaction. The reactivity of the CO₂ and SO₂ clusters seems to peak at aboutm=1 and then decreases for larger species. An equilibrium model for cluster formation was proposed and it was found capable of explaining and simulating the experimental observations. Contrary to what was reported from afterglow experiments, no barrier for the reaction was detected.     

Rotationally resolved ultraviolet spectra of benzene-noble gas van der Waals clusters

Sub-Doppler electronic spectra with hundreds of resolved rotational lines are now available for benzene-Ar dimers and trimers. From their analysis the structure of these clusters is precisely determined. The analysis of two bands, 6 ₀ ¹ and 16 ₀ ² , of C₆H₆ · Ar is presented in detail. It leads to accurate values of the van der Waals bond length in the electronic ground and excited state. The change in frequency upon clustering is found to be a factor of 17 larger for the overtone of the out-of-plane modev ₁₆ than for the in-plane vibrationv ₁. This can be tentatively explained by an interaction of the low frequency out-of-plane motion of the ring with the van-der-Waals motion of the Ar atom.     

Resolved high Rydberg spectroscopy of polyatomic molecules and van der Waals clusters

Using sub-Doppler double resonance excitation with Fourier-transform limited laser pulses and pulsed field ionization techniques we were able to resolve individual high n Rydberg states (45 < n < 110) below and above the lowest ionization energy of van der Waals clusters of benzene with the noble gases neon and argon. By choosing various selected J'K' intermediate rotational states we detected and assigned several Rydberg series with nearly vanishing quantum defect. They converge to different limits representing the rotational states in the vibrational states of the cluster cation. Even far above the ionization threshold sharp high-n Rydberg states with a width of 750 MHz are observed converging to intramolecular vibrational states located up to 800 cm-1 above the dissociation threshold of the cluster ion. This points to a slow dissociation rate of the cluster ion in the range of 3 x 10(5) s-1 < k < 5 x 10(8) s-1. In further studies single high Rydberg states of benzonitrile, a polyatomic molecule with an high dipole moment of 4.18 D, were detected in the range from n = 50 to 100. We plan to investigate the influence of the strong anisotropic dipole field of this molecule on the coupling between the high Rydberg electron and the molecular core.     

Path integral Monte Carlo approach for weakly bound van der Waals complexes with rotations: algorithm and benchmark calculations

A path integral Monte Carlo technique suitable for the treatment of doped helium clusters with inclusion of the rotational degrees of freedom of the dopant is introduced. The extrapolation of the results to the limit of infinite Trotter number is discussed in detail. Benchmark calculations for small weakly bound (4)He(N)--OCS clusters are presented. The Monte Carlo results are compared with those of basis set calculations for the He--OCS dimer. A technique to analyze the orientational imaginary time correlation function is suggested. It allows one to obtain information regarding the effective rotational constant for a doped helium cluster based on a model for the rotational Hamiltonian. The renormalization of the effective rotational constant for (4)He(N)--OCS clusters derived from the orientational imaginary time correlation function is in good agreement with experimental results.     

Quantum statistical mechanics with Gaussians: equilibrium properties of van der Waals clusters

The variational Gaussian wave-packet method for computation of equilibrium density matrices of quantum many-body systems is further developed. The density matrix is expressed in terms of Gaussian resolution, in which each Gaussian is propagated independently in imaginary time beta=(k(B)T)(-1) starting at the classical limit beta=0. For an N-particle system a Gaussian exp[(r-q)(T)G(r-q)+gamma] is represented by its center qinR(3N), the width matrix GinR(3Nx3N), and the scale gammainR, all treated as dynamical variables. Evaluation of observables is done by Monte Carlo sampling of the initial Gaussian positions. As demonstrated previously at not-very-low temperatures the method is surprisingly accurate for a range of model systems including the case of double-well potential. Ideally, a single Gaussian propagation requires numerical effort comparable to the propagation of a single classical trajectory for a system with 9(N(2)+N)/2 degrees of freedom. Furthermore, an approximation based on a direct product of single-particle Gaussians, rather than a fully coupled Gaussian, reduces the number of dynamical variables to 9N. The success of the methodology depends on whether various Gaussian integrals needed for calculation of, e.g., the potential matrix elements or pair correlation functions could be evaluated efficiently. We present techniques to accomplish these goals and apply the method to compute the heat capacity and radial pair correlation function of Ne(13) Lennard-Jones cluster. Our results agree very well with the available path-integral Monte Carlo calculations.     

Charge transfer and van der Waals states of jet-cooled dialkylaniline complexes with anthracene

We report here a study of the influence of a physical parameter (i.e. the ionization energy of different donor aromatic molecules) on the spectroscopic and dynamic properties of a series of molecular complexes A-D (A acceptor, D donor) where A is the anthracene molecule and D is one of the following dialkylanilines: dimethyl, diethyl, dipropyl or dibutyl. All complexes exhibit the same spectroscopic behavior already observed for dimethylaniline and diethylaniline cases and tentatively explained by the existence of two isomeric forms for each complex. Decay times and the broad band maximum frequency shifts for the exciplex-like emission type are experiencing a continuous variation in agreement with the change of the ionization energy of the donors. This is confirmed by calculations done using a very simple model based on the interactions between the diabatic A*D and A⁻D⁺ states of the complexes. This agreement is in favor of the initial assumption, that most physical parameters (complexation geometry, coupling between the diabatic states) are only weakly perturbed when changing the donor molecule and this despite an expected increased steric hindrance.     

Time-dependent density functional theory calculation of van der Waals coefficient of sodium clusters

In this paper we employ all-electron ab initio time-dependent density functional theory based method to calculate the long range dipole-dipole dispersion coefficient (van der Waals coefficient) C(6) of sodium atom clusters containing even number of atoms ranging from 2 to 20 atoms. The dispersion coefficients are obtained via Casimir-Polder relation [Phys. Rev. 3, 360 (1948)]. The calculations are carried out with two different exchange-correlation potentials: (i) the asymptotically correct statistical average of orbital potential (SAOP) and (ii) Vosko-Wilk-Nusair representation [Can. J. Phys. 58, 1200 (1980)] of exchange-correlation potential within local density approximation. A comparison with the other theoretical results has been performed. We also present the results for the static polarizabilities of sodium clusters and also compare them with other theoretical and experimental results. These comparisons reveal that the SAOP results for C(6) and static polarizability are quite accurate and very close to the experimental results. We examine the relationship between volume of the cluster and van der Waals coefficient, and find that to a very high degree of correlation C(6) scales as the square of the volume. We also present the results for van der Waals coefficient corresponding to cluster-Ar atom and cluster-N(2) molecule interactions.     

Augmented van der Waals equations of state: SAFT-VR versus Yukawa based van der Waals equation

Performance of the SAFT-VR equation of state developed for the hard sphere based simple fluids, namely the square-well, Sutherland and Yukawa fluids, is examined by comparing its results with simulation data and an augmented van der Waals (vdW) equation based on a Yukawa (Y) reference. Its shown that both for the equilibrium vapor-liquid data and data along selected isotherms in the liquid and supercritical fluid phases the vdW(Y) equation provides better results, particularly when going to lower temperatures.     

Geometries and excited-state dynamics of van der Waals dimers and higher clusters of 1-cyanonaphthalene

Mass-selected resonant two-photon ionization and infrared-ultraviolet double-resonance spectroscopies are combined with correlated (second Moller-Plesset perturbation) quantum chemistry calculation to probe electronic spectra and ground-state geometries of the jet-cooled dimer and higher clusters of 1-cyanonaphthalene. The results indicate that the dimer and trimer have stacked geometries, consistent with the highly efficient, rapid excimer formation that follows photoexcitation of the ground-state clusters.     

An ab initio study of van der Waals potential energy parameters for silver clusters

We employ ab initio calculations of van der Waals complexes to study the potential energy parameters (C(6) coefficients) of van der Waals interactions for modeling of the adsorption of silver clusters on the graphite surface. Electronic structure calculations of the (Ag(2))(2), Ag(2)-H(2), and Ag(2)-C(6)H(6) complexes are performed using a coupled-cluster approach that includes single, double, and perturbative triple excitations (CCSD(T)), M?ller-Plesset second-order perturbation theory (MP2), and spin-component-scaled MP2 (SCS-MP2) methods. Using the atom pair approximation, the C(6) coefficients for silver-silver, silver-hydrogen, and silver-carbon atom systems are obtained after subtracting the energies of quadrupole-quadrupole interactions from the total electronic energy.