René Fournier

Theoretical study of the structure of silver clusters

Neutral silver cluster isomers Agn (n=2 to 12) were studied by Kohn–Sham density functional theory. There is a strong even-odd oscillation in cluster stability due to spin subshell closing. Nearest-neighbor interatomic distances do not evolve continuously from the diatomic (2.53 A) to the bulk (2.89 A). After adding an empirical correction to the calculated values, we estimate that they are always near 2.68 A for 3⩽n⩽6, and near 2.74 A for 7⩽n⩽12. We find several low-energy isomers at all cluster sizes larger than seven atoms with one exception: Ag10 has a D2d twinned pentagonal bipyramid isomer predicted to be 0.20 eV more stable than any other isomer. The ellipsoidal jellium model predicts rather well the shapes of stable silver clusters. Other models (extended Huckel, empirical potential) fail to reproduce the energy ordering of cluster isomers. The structural attributes of low-energy silver cluster isomers Agn (n⩾7) are, in decreasing order of importance: a high mean coordination; a shape that conform...

Analytical gradient of the linear combination of Gaussian‐type orbitals—local spin density energy

An expression has been derived for the analytical evaluation of the energy gradient within the linear combination of Gaussian‐type orbitals—local spin density method. This expression is valid for any exchange‐correlation energy functional which can be represented in a density gradient expansion. In practice, because the exchange‐correlation terms are fitted with auxiliary functions, one has to introduce an approximation. Results are reported of tests on diatomics that show that it is possible to attain a typical accuracy of ±0.01 a.u. on equilibrium distances, relative to the energy minimum. The formulas for molecular integral derivatives that we implemented are based on the highly efficient recurrence formulas of Obara and Saika. We report here an additional formula for angular momentum transfer which is very useful for efficient programming of the gradient. In all cases studied, the time required to compute the gradient is a fraction of the time spent to solve the self‐consistent‐field Kohn–Sham equations.

Density functional study of the bonding in small silicon clusters

We report the ground electronic state, equilibrium geometry, vibrational frequencies, and binding energy for various isomers of Sin(n = 2–8) obtained with the linear combination of atomic orbitals‐density functional method. We used both a local density approximation approach and one with gradient corrections. Our local density approximation results concerning the relative stability of electronic states and isomers are in agreement with Hartree–Fock and Mo/ller–Plesset (MP2) calculations [K. Raghavachari and C. M. Rohlfing, J. Chem. Phys. 89, 2219 (1988)]. The binding energies calculated with the gradient corrected functional are in good agreement with experiment (Si2 and Si3) and with the best theoretical estimates. Our analysis of the bonding reveals two limiting modes of bonding and classes of silicon clusters. One class of clusters is characterized by relatively large s atomic populations and a large number of weak bonds, while the other class of clusters is characterized by relatively small s atomic p...

Theoretical study of the monocarbonyls of first‐row transition metal atoms

The results of density functional calculations on the most stable high‐spin and low‐spin states of MCO are given, where M=Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and Cu. The ground states are found to be high spin for M=Sc, Ti, V, Cr, and Cu (2S+1=4, 5, 6, 7, and 2, respectively) and low spin for M=Mn, Fe, Co, and Ni (2S+1=4, 3, 2, and 1, respectively). From Sc to Cu, the M–CO binding energies with respect to ground state products are estimated to be 9, 16, 26, 13, −14, 14, 30, 54, and 19 kcal/mol. Where comparison with experiment is possible, the estimates are apparently too large by about 6 kcal/mol (FeCO), 13 kcal/mol (NiCO), and 12 kcal/mol (CuCO). The high‐spin state MCO complexes with metal to the right of vanadium in the Periodic Table all have bent equilibrium geometries; all others are found to be linear. The calculated CO harmonic stretch frequencies generally overestimate the observed values, but follow a similar trend. The CO bond lengths, CO stretch frequencies, and metal–CO bond strengths all correla...

Theoretical study of linear and bent CrCO, NiCO, and CuCO

I performed density functional calculations on the electronic ground state of the monocarbonyls of chromium, nickel, and copper. CrCO and CuCO have bent equilibrium geometries with angles equal to 139.9° and 143.9° respectively, while NiCO is linear. The linear structures of CrCO and CuCO are less stable by 3 kcal/mol and are not minima, but have two imaginary frequencies. An analysis of the bonding suggests that the bent structures of CrCO and CuCO are more stable because the repulsion between the 5σ orbital of CO (essentially a lone pair on the carbon atom) and the half‐filled orbital on the metal is smaller in that geometry. The calculated Ni–CO bond energy 53 kcal/mol is 13 kcal/mol larger than the most recent experimental determination [L. S. Sunderlin et al., J. Am. Chem. Soc. 114, 2788 (1992)]. The calculated bond energies of CrCO and CuCO are 14 and 20 kcal/mol, respectively.I performed density functional calculations on the electronic ground state of the monocarbonyls of chromium, nickel, and copper. CrCO and CuCO have bent equilibrium geometries with angles equal to 139.9° and 143.9° respectively, while NiCO is linear. The linear structures of CrCO and CuCO are less stable by 3 kcal/mol and are not minima, but have two imaginary frequencies. An analysis of the bonding suggests that the bent structures of CrCO and CuCO are more stable because the repulsion between the 5σ orbital of CO (essentially a lone pair on the carbon atom) and the half‐filled orbital on the metal is smaller in that geometry. The calculated Ni–CO bond energy 53 kcal/mol is 13 kcal/mol larger than the most recent experimental determination [L. S. Sunderlin et al., J. Am. Chem. Soc. 114, 2788 (1992)]. The calculated bond energies of CrCO and CuCO are 14 and 20 kcal/mol, respectively.

Electronic spectroscopy of the niobium dimer molecule: Experimental and theoretical results

Rotationally resolved electronic spectra of the niobium dimer molecule are reported for the first time. The molecules were produced by laser vaporization of a niobium target rod and cooled in a helium supersonic expansion. The molecular beam containing niobium dimer molecules was interrogated in the range 400–900 nm using a pulsed dye laser to excite fluorescence. Numerous Ω=0←Ω=0 and Ω=1←Ω=1 vibronic transitions were discovered in the region 630–720 nm and investigated at 200 MHz resolution using the cw output of a single mode ring dye laser. The principal features were classified into five Ω=0←Ω=0 systems originating from a common lower state of 0+g symmetry, and three Ω=1←Ω=1 systems originating from a common lower state of 1g symmetry. The two lower states were assigned as the Ω=0 and Ω=1 spin–orbit components of the X 3Σ−g ground state, which is derived from the electron configuration 1π4u1σ2g2σ2g1δ2g. The two spin–orbit components are split by several hundred cm−1 due to a strong, second‐order isoco...

Predicted bond energies in peroxides and disulfides by density functional methods

We have performed self‐consistent linear combination of Gaussian‐type orbitals‐density functional calculations for the molecules YY, RY, RYY, RYR’, RYYR, and RYYR’ with Y=O,S and R,R’=H,CH3. The structures were optimized within the local spin density approximation while the Y–Y, Y–C, and Y–H bond dissociation energies (BDE) were calculated with both a local exchange‐correlation energy functional and a gradient corrected functional. Comparison of results obtained with the local and gradient corrected exchange‐correlation functionals provides more experience on the successes and failures of gradient corrections. Trends in BDEs and the nature of bonding in oxygen and sulfur containing analog molecules are analyzed on the basis of two observations: (1) the O atom is more electronegative than S, C, and H atoms; (2) a S atom can have a valency larger than two and has a greater ability for multiple bonding than oxygen. Finally, comparison with a number of experimental results suggest that the C–S BDE in CH3S, th...

Second and third derivatives of the linear combination of Gaussian type orbitals-local spin density energy

A practical formulation of the analytical second and third derivatives of the linear combination of Gaussian type orbitals–local spin density energy is presented. The equations obtained hold with little modification for density gradient corrected exchange‐correlation functionals. The efficiency and accuracy of future computer implementation of these equations are discussed.

Theoretical study of the structure of lithium clusters

Lithium clusters Lin (n=5 to 20) were studied by Kohn–Sham theory with local spin density and gradient-corrected energy functionals. We used a Tabu Search algorithm for structure optimization. The lowest energy Lin isomers that we found fall in two categories: (i) the pentagonal bipyramid, icosahedron, and related structures which are typical of most pair potentials, and (ii) structures containing centered square antiprisms which are reminiscent of the bulk bcc structure and have two characteristic peaks in the pair distribution function, one near 2.60 A and the other near 3.05 A. Calculated isomer energies and vibrational frequencies suggest that, at room temperature, many cluster sizes should show liquidlike behavior or coexistence of multiple isomers. The number of unpaired electrons “M” as a function of cluster size “n” generally alternates between 0 (singlet) and 1 (doublet), but some cluster sizes display anomalous spin magnetic moments M(n); they are M(13)=5, M(16)=2, M(17)=3, and M(18)=2. The Li7,...

Gaussian-based density functional methodology, software, and applications

We review some of the progress made by the Universite de Montreal group over the last few years, and especially over recent months, towards developing, testing, and applying Gaussianbased density functional techniques of increased accuracy, speed and functionality. These improvements include: the use of (relativistic) model core potentials, basis set preparation, more efficient integral evaluation (following Obara and Saika), the calculation of energy derivatives, automatic geometry optimization, calculation of vibrational frequencies, a “hybrid” method for simultaneous geometry and electronic structure optimization that incorporates elements of the Car-Parrinello approach along with conventional potential energy surface walkers, and the use of non-local functionals involving the gradient of the density. These elements have been incorporated into a software package called deMon that is being tested and applied over a wide range of systems and interaction types (organic and inorganic molecules, transition-metal complexes, clusters, and surface models, van der Waals interactions, hydrogen bonds).