“…Baur's (1987) report of a list of ionic radii for nitride crystals suggests, as observed for oxides, fluorides and sulfides, that molecular orbital (MO) calculations on hydronitride molecules should be capable of generating bond lengths and angles that reproduce those observed for nitride crystals. In fact, previous calculations on Si nitride (Julian and Gibbs 1985) and methyl-and silylsubstituted amine molecules (Julian and Gibbs 1988), show that the minimum energy bond lengths and angles not only match those observed for the molecules but also those observed for silicon nitride crystals. The present study (Buterakos 1990) was undertaken to learn whether the bond length -bond strength and bonded radii systematics observed for oxide and sulfide molecules and crystals also obtain for nitride molecules and crystals and whether the bonded radius of the nitride ion, rb(N), correlates with R(XN), as observed for the apparent radius of the nitride ion (O'Keeffe 1979).…”
Abstract. Bond lengths calculated for the coordination polyhedra in hydronitride molecules match average values observed for XN bonds involving main group X-cations in nitride crystals to within ~ 0.04 ~. As suggested for oxide and sulfide molecules and crystals, the forces that determine the average bond lengths recorded for coordinated polyhedra in hydronitride molecules and nitride crystals appear to be governed in large part by the atoms that comprise the polyhedra and those that induce local charge balance. The forces exerted on the coordinated polyhedra by other parts of the structure seem to play a small if not an insignificant role in governing bond length variations. Bonded radii for the nitride ion obtained from theoretical electron density maps calculated for the molecules increase linearly with bond length as observed for nitride crystals with the rock salt structure. Promolecule radii calculated for the molecules correlate with bonded and ionic radii, indicating that the electron density distributions in hydronitride molecules possess a significant atomic component, despite bond type.
“…Baur's (1987) report of a list of ionic radii for nitride crystals suggests, as observed for oxides, fluorides and sulfides, that molecular orbital (MO) calculations on hydronitride molecules should be capable of generating bond lengths and angles that reproduce those observed for nitride crystals. In fact, previous calculations on Si nitride (Julian and Gibbs 1985) and methyl-and silylsubstituted amine molecules (Julian and Gibbs 1988), show that the minimum energy bond lengths and angles not only match those observed for the molecules but also those observed for silicon nitride crystals. The present study (Buterakos 1990) was undertaken to learn whether the bond length -bond strength and bonded radii systematics observed for oxide and sulfide molecules and crystals also obtain for nitride molecules and crystals and whether the bonded radius of the nitride ion, rb(N), correlates with R(XN), as observed for the apparent radius of the nitride ion (O'Keeffe 1979).…”
Abstract. Bond lengths calculated for the coordination polyhedra in hydronitride molecules match average values observed for XN bonds involving main group X-cations in nitride crystals to within ~ 0.04 ~. As suggested for oxide and sulfide molecules and crystals, the forces that determine the average bond lengths recorded for coordinated polyhedra in hydronitride molecules and nitride crystals appear to be governed in large part by the atoms that comprise the polyhedra and those that induce local charge balance. The forces exerted on the coordinated polyhedra by other parts of the structure seem to play a small if not an insignificant role in governing bond length variations. Bonded radii for the nitride ion obtained from theoretical electron density maps calculated for the molecules increase linearly with bond length as observed for nitride crystals with the rock salt structure. Promolecule radii calculated for the molecules correlate with bonded and ionic radii, indicating that the electron density distributions in hydronitride molecules possess a significant atomic component, despite bond type.
“…Model a is related to the 10 heavy-atom adamantane- and hexamethylenetetramine-like clusters (Figure a and b) having the topology of the diamond and zinc-blende cubic unit cells (Figure c and d), respectively. Models b and c , corresponding to the 4−5 heavy-atom molecular systems with trigonal-pyramidal and tetrahedral structures, were included for comparison with the results of the experiments and previous calculations − (see Figures −8). Note that the adamantane and hexamethylenetetramine molecules were analyzed for the first time at the ab initio Hartree−Fock level by Guo and Goddard to obtain a force-field parameters (MSFF approach) suitable for predicting mechanical properties (bulk modulus) of carbon nitrides of the hexagonal structural phase, α-C 3 N 4 and β-C 3 N 4 …”
Section: Resultsmentioning
confidence: 99%
“…Other calculations: (j) refs and ; (k) refs and . (l) Experimental values: refs and (and references therein). 5 B3LYP/6-31G(d,p) optimized structures of the silylene-substituted derivative N 4 (CH 2 ) 6 - n (SiH 2 ) n ( n = 2) (model a ) of the hexamethylenetetramine molecule N 4 (CH 2 ) 6 (constructed by replacement of 2 C atoms with the equivalent number of Si atoms) and the silyl-substituted amine N(CH 3 ) 3- k (SiH 3 ) k ( k = 1) (model b ) which have been used to represent crystalline fragments of the cubic (defect zinc-blende) silicon−carbon nitride dz-Si x C 3 - x N 4 ( x = 1) (compound III ). (i) Calculated values of geometrical parameters (lengths in Å, angles in degrees, see Figure and text), this work.…”
Density functional B3LYP/6-31G(d,p) calculations have been carried out to study the structural peculiarities and physical properties of the series of cubic (defect zinc-blende) silicon-carbon nitrides with composition Si x C 3-x N 4 (x ) 0, 1, 2, 3). As model systems, we have considered six clusters with the structure of the adamantane molecule (CH) 4 (CH 2 ) 6 (I), hexamethylenetetramine-like molecules N 4 (CH 2 ) 6-n (SiH 2 ) n (II-V) (n ) 0, 2, 4, 6), and silicon-substituted adamantane molecule (SiH) 4 (SiH 2 ) 6 (VI). These 10 heavy-atom clusters have been used to simulate the crystalline fragments of diamond (I), cubic (defect zinc-blende) siliconcarbon nitrides (II-V), and cubic (zinc-blende) silicon solid (VI). It was found that the full B3LYP/6-31G(d,p) geometry optimization of these clusters allow us to reproduce the structures, unit cell parameters, and bulk modulus (hardness) of real crystals (I and VI) quite well and to predict the structural and mechanical properties of the hypothetical crystalline compounds (II-V).
“…The detailed example was worked out in this paper to serve as a template for more cumbersome algebraic expressions that will be discussed and applied in later papers. It is my hope eventually to work with more complex systems such as the silicon nitrides (6 ).…”
This paper develops an analytical method for calculating the transferable force constants in symmetrically complete coordinates directly from the nontransferable force constants in independent coordinates, allowing a direct treatment of the redundancy problem. In calculating the force constants for structures with tetrahedral symmetry, the interdependence of the tetrahedral angles must be considered to be a constraint on the potential energy function. The methane molecule is chosen as the simplest example of a tetrahedron. The potential energy of methane is a function of six equally weighted tetrahedral angles constrained such that the sum of the changes in angle over all six angles is zero. The calculations with independent coordinates are done with two different parameterizations, first with five tetrahedral angles and second with three tetrahedral angles and two dihedral angles. These are the two most useful and common parameterizations used in molecular orbital calculations. The methane tetrahedron is modeled with seven force constants; this paper demonstrates that only five independent variables-K r , K rr , (K rA -K rV ), (K θ -K V ), and (K θ -K A )-are needed. This agrees with the fact that the entire vibrational spectrum of methane can be calculated from only five force constants. Sample Gaussian 90 calculations are done with Slater-type orbital 3-21G* basis sets and compared with neutron dispersion data for diamond, silicon, germanium, and tin. This method can be extended to other constrained systems such as rings.
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