Theoretical study of spectroscopical properties of Na and Na2 in argon clusters and matrices

Accommodation of a dimer in an Ar-like lattice: exploring the generic structural motifs

A global optimization strategy is applied to Lennard-Jones models describing the stable trapping sites of a dimer in the face-centered cubic Ar-like lattice. Effective volumes of the trapping sites, quantified as the number of host atoms dislodged from the lattice, are mapped onto the parameter space defined by the strength and range of the dimer interaction potentials. The two models considered differ in the host-guest interaction and give very different maps that reflect the effect of local lattice relaxation. A hierarchical complete-linkage clustering technique is applied to identify generic structural types of the dimer accommodations. The dominant types found and enlisted maintain the symmetry of the isolated dimer and possess high tetrahedral and octahedral symmetry of the host environment with respect to the dimer atoms or center and can be roughly classified as the "whole" or "per atom" dimer accommodations. The results are compared to the analysis of the analogous model for trapped atoms and realistic model for trapped alkaline-earth metal dimers. Implications for matrix isolation spectroscopy are discussed.

Spin-orbit coupling in the dissociative excitation of alkali atoms at the surface of rare gas clusters: A theoretical study

We analyze the role of the spin-orbit (SO) coupling in the dissociative dynamics of excited alkali atoms at the surface of small rare gas clusters. The electronic structure of the whole system is deduced from a one-electron model based on core polarization pseudo-potentials. It allows us to obtain in the same footing the energy, forces, and non-adiabatic couplings used to simulate the dynamics by means of a surface hopping method. The fine structure state population is analyzed by considering the relative magnitude of the SO coupling ξ, with respect to the spin-free potential energy. We identify three regimes of ξ-values leading to different evolution of adiabatic state population after excitation of the system in the uppermost state of the lowest np (2)P shell. For sufficiently small ξ, the final population of the J=12 atomic states, P12, grows up linearly from P12=13 at ξ = 0 after a diabatic dynamics. For large values of ξ, we observe a rather adiabatic dynamics with P12 decreasing as ξ increases. For intermediate values of ξ, the coupling is extremely efficient and a complete transfer of population is observed for the set of parameters associated to NaAr3 and NaAr4 clusters.

Absorption Spectroscopy, a Tool for Probing Local Structures and the Onset of Large-Amplitude Motions in Small KAr(n) Clusters at Increasing Temperatures

Photoabsorption spectra of KArn (n = 1-10) are simulated at temperatures ranging between 5 and 25 K. The calculations associate a Monte Carlo (MC) method to sample cluster geometries at temperature T, with a one-electron ab initio model to calculate the ground-state and excited-state energies of the cluster. The latter model replaces the K(+) core electrons and all the electrons of the Ar atoms by appropriate pseudopotentials, complemented by core polarization potentials. It also provides the necessary oscillator strengths to simulate the spectra. Global optimization by basin-hopping is used in combination with MC simulation at low temperature (5 K) to identify the most stable isomer and remarkable isomers of ground-state KArn clusters, which are stable with respect to deformations of the order of those expected with Zero Point Energy motions. The absorption spectra calculated for each of these isomers at 5 K suggest that absorption spectroscopy can probe sensitively the local environment of K atom: surface location of K with respect to a close-packed Ar moiety, number of Ar atom in close vicinity, and local symmetry about K. Simulation at increasing temperatures, up to the evaporation limit of K out of the cluster, shows the onset of large amplitude motions above 20 K, when the K atom experiences a variety of local environments.

Water clusters in an argon matrix: infrared spectra from molecular dynamics simulations with a self-consistent charge density functional-based tight binding/force-field potential

The present theoretical study aims at investigating the effects of an argon matrix on the structures, energetics, dynamics, and infrared (IR) spectra of small water clusters (H2O)n (n = 1-6). The potential energy surface is obtained from a hybrid self-consistent charge density functional-based tight binding/force-field approach (SCC-DFTB/FF) in which the water clusters are treated at the SCC-DFTB level and the matrix is modeled at the FF level by a cluster consisting of ∼340 Ar atoms with a face centered cubic (fcc) structure, namely (H2O)n/Ar. With respect to a pure FF scheme, this allows a quantum description of the molecular system embedded in the matrix, along with all-atom geometry optimization and molecular dynamics (MD) simulations of the (H2O)n/Ar system. Finite-temperature IR spectra are derived from the MD simulations. The SCC-DFTB/FF scheme is first benchmarked on (H2O)Arn clusters against correlated wave function results and DFT calculations performed in the present work, and against FF data available in the literature. Regarding (H2O)n/Ar systems, the geometries of the water clusters are found to adapt to the fcc environment, possibly leading to intermolecular distortion and matrix perturbation. Several energetical quantities are estimated to characterize the water clusters in the matrix. In the particular case of the water hexamer, substitution and insertion energies for the prism, bag, and cage are found to be lower than that for the 6-member ring isomer. Finite-temperature MD simulations show that the water monomer has a quasifree rotation motion at 13 K, in agreement with experimental data. In the case of the water dimer, the only large-amplitude motion is a distortion-rotation intermolecular motion, whereas only vibration motions around the nuclei equilibrium positions are observed for clusters with larger sizes. Regarding the IR spectra, we find that the matrix environment leads to redshifts of the stretching modes and almost no shift of the bending modes. This is in agreement with experimental data. Furthermore, in the case of the water monomer and dimer, the magnitudes of the computed shifts are in fair agreement with the experimental values. The complex case of the water hexamer, which presents several low-energy isomers, is discussed.

Understanding of matrix embedding: a theoretical spectroscopic study of CO interacting with Ar clusters, surfaces and matrices

Through benchmark studies, we explore the performance of PBE density functional theory, with and without Grimme's dispersion correction (DFT-D3), in predicting spectroscopic properties for molecules interacting with rare gas matrices.

Potential energy curves and spin-orbit coupling of light alkali-heavy rare gas molecules

The potential energy curves of the X, A, and B states of alkali-rare gas diatomic molecules, MKr and MXe, are investigated for M = Li, Na, K. The molecular spin-orbit coefficients a(R)=<(2)Π(½)|Ĥ(SO)|(2)Π(½)> and b(R)=<(2)Π(-½)|Ĥ(SO)|(2)Σ(½)> are calculated as a function the interatomic distance R. We show that a(R) increases and b(R) decreases as R decreases. This effect becomes less and less important as the mass of the alkali increases. A comparison of the rovibrational properties deduced from our calculations with experimental measurements recorded for NaKr and NaXe shows the quality of the calculations.

Nonadiabatic molecular dynamics of photoexcited Li2(+) Ne(n) clusters

We investigate the relaxation of photoexcited Li(2)(+) chromophores solvated in Ne(n) clusters (n = 2-22) by means of molecular dynamics with surface hopping. The simplicity of the electronic structure of these ideal systems is exploited to design an accurate and computationally efficient model. These systems present two series of conical intersections between the states correlated with the Li+Li(2s) and Li+Li(2p) dissociation limits of the Li(2)(+) molecule. Frank-Condon transition from the ground state to one of the three lowest excited states, hereafter indexed by ascending energy from 1 to 3, quickly drives the system toward the first series of conical intersections, which have a tremendous influence on the issue of the dynamics. The states 1 and 2, which originate in the Frank-Condon area from the degenerated nondissociative 1(2)Π(u) states of the bare Li(2)(+) molecule, relax mainly to Li+Li(2s) with a complete atomization of the clusters in the whole range of size n investigated here. The third state, which originates in the Frank-Condon area from the dissociative 1(2)Σ(u)(+) state of the bare Li(2)(+) molecule, exhibits a richer relaxation dynamics. Contrary to intuition, excitation into state 3 leads to less molecular dissociation, though the amount of energy deposited in the cluster by the excitation process is larger than for excitation into state 1 and 2. This extra amount of energy allows the system to reach the second series of conical intersections so that approximately 20% of the clusters are stabilized in the 2(2)Σ(g)(+) state potential well for cluster sizes n larger than 6.

Vibrational relaxation of NO-(v=1) in icosahedral (Ar)12NO- clusters

Relaxation dynamics of NO(-)(v=1) in icosahedral (Ar)(12)NO(-) clusters are studied using classical dynamics and semiclassical procedures over the temperature range of 100-300 K. The minimum energy of the equilibrium configuration (-9875 cm(-1)) needed in the study is determined by varying the cluster size z in (Ar)(z)NO(-). NO(-)(v=1) is embedded in the cluster, which is filled with low frequency motions: 39 cm(-1) for the argon modes, 77 cm(-1) for the Arc...NO(-) substructure vibration, 109 cm(-1) for the librational frequency of restricted rotation, and 128 cm(-1) for oscillatory local translation. Dynamics calculations show that in the early time period (<20 ps), part of the vibrational energy rapidly transfers to rotation, but most energy transfers to Ar atoms on a long time scale (approximately 1 ns). The long time scale leads to the relaxation rates of 0.403 ns(-1) at 100 K and 0.453 ns(-1) at 300 K. The rates calculated using analytical formulations vary nearly linearly from 0.288 ns(-1) at 100 K to 0.832 ns(-1) at 300 K. Although the temperature dependence is stronger in the latter, both approaches give the rates on a nanosecond time scale. The principal energy transfer pathway is from NO(-) vibration to Ar vibrations via oscillatory local translation, while the NO(-) rotation is in a librational state. The energy transfer probabilities are two orders of magnitude larger than the vibration-to-translation probabilities in the gas phase collision Ar-NO(-)(v=1).

Light absorption during alkali atom-noble gas atom interactions at thermal energies: a quantum dynamics treatment

The absorption of light during atomic collisions is treated by coupling electronic excitations, treated quantum mechanically, to the motion of the nuclei described within a short de Broglie wavelength approximation, using a density matrix approach. The time-dependent electric dipole of the system provides the intensity of light absorption in a treatment valid for transient phenomena, and the Fourier transform of time-dependent intensities gives absorption spectra that are very sensitive to details of the interaction potentials of excited diatomic states. We consider several sets of atomic expansion functions and atomic pseudopotentials, and introduce new parametrizations to provide light absorption spectra in good agreement with experimentally measured and ab initio calculated spectra. To this end, we describe the electronic excitation of the valence electron of excited alkali atoms in collisions with noble gas atoms with a procedure that combines l-dependent atomic pseudopotentials, including two- and three-body polarization terms, and a treatment of the dynamics based on the eikonal approximation of atomic motions and time-dependent molecular orbitals. We present results for the collision induced absorption spectra in the Li-He system at 720 K, which display both atomic and molecular transition intensities.

Rydberg states of small NaArn* clusters

The 4s and 5s Rydberg excited states of NaAr(n)* clusters are investigated using a pseudopotential quantum-classical method. While NaAr(n) clusters in their ground state are known to be weakly bound van der Waals complexes with Na lying at the surface of the argon cluster, isomers in 4s or 5s electronically excited states of small NaAr(n)* clusters (n< or =10) are found to be stable versus dissociation. The relationship between electronic excitation and cluster geometry is analyzed as a function of cluster size. For both 4s and 5s states, the stable exciplex isomers essentially appear as sodium-centered structures with similar topologies, converging towards those of the related NaAr(n)+ positive ions when the excitation level is increased. This is consistent with a Rydberg-type picture for the electronically excited cluster, described by a central sodium ion solvated by an argon shell, and an outer diffuse electron orbiting around this NaAr(n)+ cluster core.

Simple DFT model of clusters embedded in rare gas matrix: Trapping sites and spectroscopic properties of Na embedded in Ar

We present a theoretical model to study the dynamics of metallic clusters embedded in a rare gas matrix. We describe the active electrons of the embedded cluster using time dependent density functional theory, while the surrounding matrix is described in terms of classical molecular dynamics of polarizable atoms. The coupling between the cluster and the rare gas atoms is deduced from the work of Gross and Spiegelmann [J. Chem. Phys. 108, 4148 (1998)] and reformulated explicitly in a simple and efficient density functional form. The electron rare gas interaction takes the form of an averaged dipole fluctuation term, which retains the van der Waals long range interaction, and a short range repulsive pseudopotential, which accounts for the Pauli repulsion of the electron by the rare gas atom. We applied our model to Na clusters embedded in Ar matrix. For the latter we developed an efficient local pseudopotential, which allows studying systems containing more than 10(3) Ar atoms. We show that large systems are indeed necessary to account properly for long range polarization of the matrix, that competes with the matrix confinement effect. We focus our study on Na(2), Na(4), and Na(8). For each system, we have determined the geometry of the most favorable trapping site by means of damped molecular dynamics. We present the effect of matrix embedding on the optical absorption spectrum. For Na(2), the trapping site can be unambiguously identified by comparison of the absorption spectrum with experiment. For Na(4) the spectrum of the embedded cluster is significantly different from the free cluster spectrum, while for Na(8) differences are less pronounced.