Single-crystal X-ray diffraction analysis is the most direct and definitive technique for determining (or confirming) the geometric structure of chemical compound. In this paper, we describe the capacity of semi-empirical methods such as AM1, PM3, PM6 and NODCs for determining interatomic distances and bond angles for three compounds
P1 ((1S, 3R,8R)-2,2-dichloro-3,7,7,10-tetramethyl-tricyclo [6,4,0,01,3] dodec-9-ene), P2 (1S,3R,8R,9S,11R)-2,2,10,10-tetrachloro-3,7,7,11 tetramethyltetracyclo [6,5,0,01.2,09.116 ] tridecane) and P3 (1S,3R,8R,9S,11R)-2,2,10,10-tetrabromo-3,7,7,11 tetramethyltetracyclo [6,5,0,01.2,09.116 ] tridecane) including experimental data interatomic distances and bond angles are available. The results obtained show a good agreement with experimental reference values, a few exceptions, for semi-empirical methods AM1 and PM6 appear more reliable than PM3 and NODC.

In this work we used density functional theory (DFT) B3LYP/6-31G*(d) to study the stoichiometric reaction between the β-himachalene and dibromocarbene. We have shown that β-himachalene behaves as a nucleophile, while dibromocarbene behaves as an electrophile; that the chemical potential of dibromocarbene is superior to that of β-himachalene in absolute terms; and that β-himachalene reacts with an equivalent quantity of dibromocarbene to produce only one products P1: (1S,3R,8S) -2,2- dibromo -3,7,7,10

In this work, we carried out theoretical calculations to determine the structure of the hydrogen phosphate anion (HPO_{4}^{2-}) in the free state and its structure and position when intercalated between layers of the zinc and aluminum layered double hydroxide [Zn-Al-HPO_{4}]. We hypothesized that the anion might be intercalated either by forming strong bonds with zinc, or by means of hydrogen bonds with water molecules, and we performed a number of different calculations to determine which of the two hypotheses was correct. We used the DFT B3LYP/6-311G ab initio quantum method to calculate interatomic and interlayer distances, vibration frequencies and enthalpy of formation of the hydrogen phosphate anion in the free state and in the various models proposed, as well as the force constant of the Zn-O bond in the different chemical structures. Results obtained by DFT B3LYP/6-311G were compared to those obtained by experiment and by using the semi-empirical methods AM1 and PM3, and it was shown that results obtained by DFT B3LYP/6-311G correspond more closely to experimental results than those obtained by the two semi-empirical methods. Finally, we established that the hydrogen phosphate anion HPO_{4}^{2-} is intercalated between the two layers of the layered double hydroxide [Zn-Al-HPO_{4}] by means of hydrogen bonds with water molecules, while the phosphate anion PO_{4}^{3-} is bound to zinc atoms.

In the present work we used the quantum DFT method (density functional theory) B3LYP/6-311G (d, p) to determine the following: geometric optimization of interatomic distances in the reactants isopropyl dichloroacetate and isobutyraldehyde, transition states of the products obtained during the reaction between these two reactants, energies corresponding to reactants and products, electron density at certain atoms of the reactants, electrophilic and nucleophilic nature of the reactants, Fukui indices, condensed local softness values, local electrophilicity and nucleophilicity indices, certain thermodynamic values of the reaction (enthalpy, entropy, free enthalpy), location of the transition states, electronic populations of atoms and reactivity indexes calculated using natural population analysis (NPA), MK and CHelpG electrostatic population, analysis of potential energy surface and nature of the reaction mechanism.

In this work, we determined the tensors of screen as well as the chemicals shifts of the nuclear magnetic resonance of the carbon 13 (RMN 13C) of organic product: P1 :[(1S, 3R, 8R)-2,2- dichloro -3, 7, 7, 10-tetra- methyl-tricyclo [6, 4, 0, 01,3] dodec-9-ene], using methods: CSGT (Continuous Set of Gauge Transformations), IGAIM (a slight variation on the CSGT method) and GIAO (Gauge-Independent Atomic Orbital), using the method DFT by means of functional B3LYP / 6-311 (2d, p) for the geometrical optimization of this product. These methods are implanted in the software Gaussian09. The comparison of the theoretical results to the experimental results shows that the method GIAO is the most reliable. On the other hand we calculate the chemicals shifts of the carbon 13 (13C of the compound P2 :[(1S, 3R, 8R) -2, 2- dichloro-3, 7, 7, 10 -tetramethyl- tricycle [6, 4, 0, 01,3 ] dodec-9-

The reaction between α-trans-himachalene and dichlorocarbene has been studied using density functional theory (DFT) B3LYP/6-311G (d, p). The global electrophilicity and global nucleophilicity indices indicate that α-trans-himachalene behaves as a nucleophile while dichlorocarbene behaves as an electrophile. The majority product obtained by stoichiometric reaction between dichlorocarbene and α-trans-himachalene is (1R, 2S, 4R, 7S)-3,3-dichloro-8-methylene-4,12,12-trimethyl-tricyclo [5.5.0.02,4] dodecane (referred to here as P1(α)): in this reaction the attack takes place at the endocyclic double bond at the α side of α-trans-himachalene. The majority product obtained by the reaction between two equivalents of dichlorocarbene with α-trans-himachalene is (1R, 2S, 4R, 7S, 8R)-3,3,13,13-tetrachloro-4,12,12-trimethyl-tricyclo [5.5.0.02,4] -spiro[28] tetradecane (referred to here as P2(β)): here the attack takes place at the β side of the exocyclic double bond. P2(β) is also obtained by the equimolar reaction of P1(α) with dichlorocarbene. P1(α) and P2(β) are both exothermic. Analysis of local electrophilicity and local nucleophilicity indices demonstrates the chemo-, regio- and stereoselectivity of the reaction. Analysis of the potential energy surface shows that this reaction follows an asynchronous concerted mechanism. Calculating the intrinsic reaction coordinate (IRC) shows that the reaction mechanism can be characterized as "one-step" and "two-stage". Stationary points were characterized by frequency calculations in order to verify that the transition states had one and only one imaginary frequency.

In the work reported here we looked at the magnetic behaviour of a 3/2 spin system with crystalline anisotropy and transverse field. The spin Hamiltonian considered here contains terms which cannot be commuted further, giving rise to important quantum effects: quantum fluctuations and thermal fluctuations. We used the mean field approximation method to determine the expressions of magnetization along the z (longitudinal) axis and the x (transverse) axis, as well as the partition function. The thermal variations mz and mx for different values of the transverse field show that the latter inhibits order along the z axis and encourages spin confinement in the transverse plane.

In this work we used the AM1 and PM3 semi-empirical methods, together with density functional theory (DFT) B3LYP 6-311G, to determine the structure and position of the carbonate anion intercalated between layers of the zinc and aluminum layered double hydroxide [Al-Zn-Co3] at ambient temperature. We calculated interlayer distances, vibration frequencies, force constants and enthalpies of formation. We showed that at ambient temperature the CO32- anion is intercalated in the interlayer space by the formation of hydrogen bonds with water molecules. The results obtained using these three methods are compared to those obtained experimentally and those obtained using the Hartree-Fock STO-3G method.

The two quantum methods Hartree-Fock HF/6-31G* (d, p) and density functional theory DFT/3-21G* (d, p) were used to calculate the equilibrium of the Si-F and Si-Cl bonds in SiH_{3}X compounds where X may be F^{-} or Cl^{-} ; the atomic electron affinity of chloride (Cl^{-}), fluoride (F^{-}), chlorine (Cl) and fluorine (F); entropy (S), heat capacity (C_{v}), total energy and reaction enthalpy of fluorosilanes, chlorosilanes and silyl radicals; and bond angles and bond lengths of SiH_{3}F and SiH_{3}Cl. Inter-atomic distances of the Si-F and Si-Cl bonds in SiH_{3}F and SiH_{3}Cl calculated using HR and DFT are in good agreement with the experimental values. The optimal distance of the Si-F bond is shorter than that of the Si-Cl bond in SiH_{3}X. Electron affinities calculated using HF and DFT are not in agreement with those obtained experimentally. The values of entropy (S) increase in parallel with the increase in the number of fluorine atoms in the silanes. The geometric structures of SiH_{3}F and SiH_{3}Cl both belong to the C_{3v} point group. Their bond angles are slightly different. SiH_{3}F has slightly higher energy than SiH_{3}Cl. This might be due to the value of the bond angle in SiH_{3}F, which is 109.18

β-himachalene behaves as a nucleophile while dichlorocarbene behaves as an electrophile. Equimolar condensation of β-himachalene and dichlorocarbene results in a single product: (1S,3R,8R)-2,2-dichloro-3,7,7,10-tetramethyltricyclo[6,4,0,0^{1.3}]dodec-9-ene, also referred to as dichlorocarbene β-himachalene ? (referred to as P_{1} here), formed by reaction at the ? side of the C_{6}=C_{7} double bond of β-himachalene. This regioselectivity is controlled by the frontier orbitals, as is the reaction mechanism. Electron density is particularly high around the C_{6}=C_{7} double bond of the HOMO orbital. However when β-himachalene reacts with two equivalents of dichlorocarbene under the same conditions the result is two products: (1S,3R,8R,9S,11R)-2,2,10,10-tetrachloro-3,7,7,11-tetramethyltetracyclo[6,5,0,0^{1.2},0^{9.11}]tridecane and (1S,3R,8R,9R,11S)-3,7,7,11-tetrachloro-3,7,7,11-tetramethyltetracyclo[6,5,0,0^{1.2},0^{9.11}]tridecane (referred to here as P_{2} and P_{3} respectively). The same two products are also obtained when P_{1} reacts with one equivalent of dichlorocarbene. The attack takes place simultaneously at the ? and β sides of the C_{2}=C_{3} double bond. Study of the two reactions using the ab-initio quantum density functional theory method (B3LYP/6-31G(d)) shows that they are stereoselective, chemospecific, concerted and exothermic. P_{3} is formed in greater quantity than P_{2}.