Geometry Optimization of Carbon Dioxide Clusters (CO₂)_n for 4 ≤ n ≤ 40

Abstract

Geometry optimization of carbon dioxide clusters (CO2)n with the size of 4 < or = n < or = 40 is performed by a heuristic and unbiased method combined with geometrical perturbations. Comparison with the global minima reported in the literature shows that the present method reproduces the global minima for clusters with n = 6, 8, 13, 19, 28, 30, and 32 and yields new global minima for (CO2)23, (CO2)25, and (CO2)35. For the other clusters under investigation, global minima are first reported in this article. Structural features of CO2 clusters and efficiency of the optimization method are discussed.

Theoretical investigation on structural properties of ethylene clusters (C2H4)n (n⩽25)

“…3). The non-icosahedral geometry is first observed for van der Waals homoclusters consisting of thirteen molecules; the clusters previously investigated (benzene [1], carbon dioxide [3], acetylene [4], ethane [2], and molecular nitrogen [16] clusters) take icosahedrons. This can be explained using the deviation of the tetramer geometry from a regular tetrahedron.…”

“…The method was applied to carbon dioxide clusters (CO 2 ) n (n ≤ 40) [3] and acetylene clusters (C 2 H 2 ) n (n ≤ 55) [4]. These clusters have three common features: (1) Transformation from cluster-specific geometries to the crystal-like ones is observed.…”

High resolution infrared spectroscopy of carbon dioxide clusters up to (CO2)13

“…Our original assignments 28 were based on calculations of the lowest-energy structures for (CO 2 ) N clusters reported by Takeuchi,46 who used the M-O-M empirical intermolecular potential. 37,38 This function has eight adjustable parameters and consists of atom-atom Lennard-Jones 12-6 terms for the C-C, C-O, and O-O interactions, plus five point charges distributed along the CO 2 axis.…”

“…Takeuchi reported detailed structural parameters for N = 4-40 in his Supporting Information section of Ref. 46 which enabled us to readily calculate the cluster rotational constants, A, B, and C. Subsequently, we made further calculations using the SAPT-s potential, a simplified function based on the high-level ab initio results of Bukowski et al 30 These numerical cluster simulations start with N molecules in random positions and orientations and adjust the {5(N − 1) − 1}-dimensional structure to find an energy minimum for (CO 2 ) N using the Powell method from Numerical Recipes. 47 This is repeated hundreds or thousands of times until we are reasonably confident that the true global minimum has been found.…”

The structural investigation on small methane clusters described by two different potentials

“…Geometrical features of molecular clusters have not been well elucidated. Many researchers have investigated structural features of two fundamental molecular clusters, CO 2 clusters [2][3][4][5][6][7] and water clusters [8][9][10][11][12][13][14][15][16][17][18]; small CO 2 clusters take structures based on the icosahedron and water clusters exhibit structures specific to hydrogen-bond networks. Methane clusters are also essential since methane is one of the simplest hydrocarbon molecules.…”