Ab Initio Molecular Dynamics of Dimerization and Clustering in Alkali Metal Vapors † ‡ Vitaly V

Article pubs.acs.org/JPCA Ab Initio Molecular Dynamics of Dimerization and Clustering in Alkali Metal Vapors † ‡ Vitaly V. Chaban and Oleg V. Prezhdo*, † Instituto de Cienciâ e Tecnologia, Universidade Federal de Saõ Paulo, 12231-280 Saõ Josédos Campos, SP Brazil ‡ Departments of Chemistry, Physics and Astronomy, University of Southern California, Los Angeles, California 90089, United States ABSTRACT: Alkali metals are known to form dimers, trimers, and tetramers in their vapors. The mechanism and regularities of this phenomenon characterize the chemical behavior of the first group elements. We report ab initio molecular dynamics (AIMD) simulations of the alkali metal vapors and characterize their structural properties, including radial distribution functions and atomic cluster size distribu- tions. AIMD confirms formation of Men, where n ranges from 2 to 4. High pressure sharply favors larger structures, whereas high temperature decreases their fraction. Heavier alkali metals maintain somewhat larger fractions of Me2,Me3, and Me4, relative to isolated atoms. A single atom is the most frequently observed structure in vapors, irrespective of the element and temperature. Due to technical difficulties of working with high temperatures and pressures in experiments, AIMD is the most affordable method of research. It provides valuable understanding of the chemical behavior of Li, Na, K, Rb, and Cs, which can lead to development of new chemical reactions involving these metals. ■ INTRODUCTION moderate temperatures and pressures, suggesting that higher Clusters of metals represent a vibrant field of research, in which imperfections result primarily from the formation of stable both experimental and theoretical methods are successfully tetramer molecules Li4,K4, and Cs4. The standard enthalpy for − 1 5 the formation of K4 from four potassium atoms in the vapor employed. All alkali metals are known to form diatomic − −1 molecules through the formation of weak metal−metal phase amounts to 146.0 kJ mol . In particular, it exceeds − ΔH bonds.6 11 The weak bond originates from the overlap between (K2) more than 2-fold. diffuse valence orbitals of two atoms, considered within the Urban and Sadlej applied a number of high-level ab initio one-electron approximation.12 Various heteronuclear alkali methods to investigate the basic electric properties of the alkali atom dimers, including dipole moment and dipole polar- metal dimers, such as NaLi, KNa, RbK, etc., are also possible. 12 − izability. The authors criticized density functional theory The metal metal bonding leads to a partial association of the − alkali metal vapors. The resulting structures constitute a (DFT) exchange correlation models for underestimation of − significant research interest.13 18 According to spectroscopic the parallel component of the dipole polarizability, as compared and vapor pressure studies, a significant fraction of dimers is to more accurate ab initio methods and experimental Downloaded via UNIV OF SOUTHERN CALIFORNIA on November 7, 2019 at 23:06:26 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. observations. expected in alkali metal vapors. The association increases with 22 the atomic mass of the element, Li < Na < K < Rb < Cs. Sarkisyan and co-workers devised an interesting method to Optical absorbance spectra of small clusters of alkali metals experimentally determine the metal dimer dissociation energy dimers, trimers, and tetramerspoint to the existence of by observing the dependence of the relative dimer density on distinct vibrational energy levels. The spectra are qualitatively temperature in the superheated vapor of cesium. The proposed different for larger clusters. For instance, the clusters containing method is also sensitive to the amount of the investigated ff 19,20 substance. Recently, an important simulation effort was more than 8 atoms exhibit collective e ects in their spectra. 6 The heat of dimerization decreases as the size of the element described by Donoso and co-workers. Trimers Li3,Na3,K3, 21 − increases. Ewing and co-workers employed the van’tHoff Rb3, and Cs3 were studied using Born Oppenheimer molecular equation to compute the standard enthalpies of dimerization, dynamics as clusters in a vacuum; Na7 was also simulated for ↔ comparison. Using fairly short simulations (8.0 ps) with using 2Me Me2. All enthalpies derived this way are negative: ΔH − −1 ΔH − −1 10 replicas per system, the authors derived reliable structural (Li2)= 76.5 kJ mol ; (K2)= 56.4 kJ mol ; ΔH − −1 and electric properties. Pseudorotation and crossover were (Cs2)= 48.5 kJ mol . Smaller dimerization enthalpies can be understood as generally weaker Me−Me bonds due to larger bond lengths. The same authors21 performed an analysis Received: May 7, 2016 of the PVT data of the lithium, potassium, and cesium vapors. Revised: June 10, 2016 They concluded that the degree of dimerization is significant at Published: June 13, 2016 © 2016 American Chemical Society 4302 DOI: 10.1021/acs.jpca.6b04609 J. Phys. Chem. A 2016, 120, 4302−4306 The Journal of Physical Chemistry A Article considered as two coupled phenomena determining movement Table 1. Simulated Systems, Their Key Parameters, and a of the atoms. Sampling Durations Dimerization of alkali metals constitutes an important density, mass, plane wave sampling fundamental phenomenon in chemistry, the understanding of no. metal temp, K kg m−3 amu cutoff,eV duration, ps which is valuable for developing new reactions and adjusting 1 Li 2100 28.8 138.82 100 100 yields of known chemistries. As exemplified above, the field 2 Li 2400 28.8 138.82 100 90 develops gradually. At this point, we are not aware of efforts to 3 Li 2700 28.8 138.82 100 70 simulate the vapor phase of the alkali metals at the atomic level 4 Li 3000 28.8 138.82 100 70 of precision. For the first time, we report ab initio molecular 5 Li 3300 28.8 138.82 100 70 dynamics (AIMD) simulations of the Li, Na, K, Rb, and Cs 6 Na 1800 95.4 459.80 76.5 100 vapors above and below the critical points of these simple 7 Na 2100 95.4 459.80 76.5 80 substances. The cluster analyses were performed to identify the 8 Na 2400 95.4 459.80 76.5 80 structure and percentages of the Men clusters, where n >1,in 9 Na 2700 95.4 459.80 76.5 70 the vapor phase. 10 K 1400 162.3 781.97 87.5 100 ■ METHODOLOGY 11 K 1700 162.3 781.97 87.5 90 12 K 2000 162.3 781.97 87.5 90 Adiabatic AIMD simulations were conducted within the DFT 13 K 2300 162.3 781.97 87.5 80 framework employing a pure DFT functional and a converged 14 Rb 1600 354.7 1709.36 91.4 100 plane-wave basis set. Plane waves constitute an efficient means 15 Rb 1800 354.7 1709.36 91.4 100 to optimize wave functions in the three-dimensional periodic 16 Rb 2000 354.7 1709.36 91.4 90 systems. Periodic boundary conditions allow simulating a 17 Rb 2200 354.7 1709.36 91.4 90 virtually infinite system, while eliminating undesirable boundary 18 Cs 1400 551.6 2658.11 165.2 100 effects. The exchange−correlation functional proposed by 19 Cs 1600 551.6 2658.11 165.2 100 Perdew, Burke, and Ernzerhof in the generalized gradient 20 Cs 1800 551.6 2658.11 165.2 90 23 approximation was employed. All core electrons were 21 Cs 2000 551.6 2658.11 165.2 90 24 simulated by the projector-augmented wave method, 22 Li 3300 14.7 138.82 100 100 providing high computational efficiency. The self-consistent 23 Li 3300 10.5 138.82 100 100 −5 field (SCF) convergence threshold was set to 10 Hartree. A 24 Li 3300 8.5 138.82 100 100 a minimum of three SCF iterations were conducted per time Each system contains 20 alkali atoms. step. The initial geometries were optimized prior to performing finite-temperature AIMD. The nuclear equations-of-motion were propagated with a 1.0 fs integration time step. The Cartesian coordinates of all atoms were saved every 100 time steps. The simulations were carried out in the constant temperature constant volume ensemble. The Nose thermostat was used to maintain constant temperature25 with the relaxation time constant equaling to 100 time steps. Empirical dispersion corrections were not employed, because the contribution of the van der Waals interaction to the overall interaction energy is much smaller than the metal−metal covalent bond energies. The Vienna Ab initio Simulation Package (VASP)26 was employed. Packmol27 was used to Figure 1. Experimental normal boiling temperatures (red solid line) generate initial configurations for the AIMD simulations. VMD 28 and critical temperatures (green dashed line) of the simple substances (Visual Molecular Dynamics, version 1.9.1) and Gabedit 30 29 composed of alkali metal atoms. Simple substance is a homogeneous (version 2) were the tools to manipulate particles and form of a chemical element existing in a free state. visualize atomic trajectories. Table 1 enumerates the simulated systems and the basic simulation parameters, such as the energy cutoff for plane Therefore, the maximum height of an RDF shows by what waves, simulated temperature, density, and sampling duration. factor the probability of finding an atom at a given distance Each simulated system contains 20 alkali metal atoms (Li, Na, from another atom exceeds the probability to find two atoms at K, Rb, Cs), which were distributed randomly in space at time an (infinitely) large distance in the periodic system. The cluster zero. The generated configurations were placed in cubic boxes analysis was performed on the basis of a geometric criterion. If of volumes varying between 8.0 × 103 and 2.7 × 104 Å.

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