Molecular Geometries by the Extended-HückelMolecular Orbital Method III: Band-structure calculations (original) (raw)
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Molecular Geometries by the Extended-Hueckel Molecular Orbital Method: A Comment
The Journal of Physical Chemistry, 1995
Bond length calculations with the extended Hiickel molecular orbital (EHMO) approximation can be improved by adding a two-body repulsive energy term and a distance-dependent Wolfsberg-Helmholz constant K = k exp(-GR). As demonstrated in the case of simple homonuclear two-level interactions, such a distance-dependent K leads to problems, however. This drawback of the otherwise very useful improvement of the EHMO method can be overcome by applying K = 1 + K exp(-G(R do)). do is equal to the sum of the orbital radii of the two adjacent atoms, and K is calculated from the weighted Wolfsberg-Helmholz formula. The new formula leads to good potential energy curves for diatomic and for polyatomic molecules.
Molecular geometries by the Extended Hueckel Molecular Orbital (EHMO) method
The Journal of Physical Chemistry, 1989
Bond length calculations with the extended Hiickel molecular orbital (EHMO) approximation can be improved by adding a two-body repulsive energy term and a distance-dependent Wolfsberg-Helmholz constant K = k exp(-GR). As demonstrated in the case of simple homonuclear two-level interactions, such a distance-dependent K leads to problems, however. This drawback of the otherwise very useful improvement of the EHMO method can be overcome by applying K = 1 + K exp(-G(R do)). do is equal to the sum of the orbital radii of the two adjacent atoms, and K is calculated from the weighted Wolfsberg-Helmholz formula. The new formula leads to good potential energy curves for diatomic and for polyatomic molecules.
A Theoretical Method for Calculating the Bond Integral Parameter for Atomic Orbitals
International Journal of Computational and Theoretical Chemistry, 2015
In molecular orbital theory, the bond integral parameter k is used to calculate the bond integral β for different molecular structures. The bond integral parameter k, which represents the ratio of bond integrals between two atoms of a diatomic molecule, is a function of the bond length. This parameter is usually obtained empirically; however, it will be shown that k can be determined analytically by utilizing the overlap integral S. k will be calculated for different atomic orbital combinations (ss,pp) of σ and π interactions as a function of bond length for a carbon-carbon diatomic molecule. The results, which are represented graphically, indicate that different atomic orbitals in different interactions can have the same, or very close to the same, k values. The graphs reveal some significant features for the different atomic orbital combinations with respect to magnitude and profile, as well as illustrate good agreement with experimental results, which validates the utilization of the overlap integral calculation method for the determination of the bond integral parameter k.
Journal of The American Chemical Society, 1973
The uu* +-u electronic transitions of symmetrical trihalide ions (I3-, IBr, ICl, and BrCl, are calculated in a molecular orbitaf approximation. The MO's are formed from linear combinations of npu halogen orbitals. For the zero-order calculations a modified Huckel theory is used. The calculations of the electronic transitions in the u system are refined by configuration interaction with complete neglect of differential overlap. The parameters p for the u bonds are based on the experimental electronic transitions of Br, , C1, , and I,. The method is applied to one transition of the 13-ion (4.25 eV) in order to obtain an equation for p. The agreement between the calculated values and the experimentally observed transitions appears to be a good one. A table of calculated charges and bond orders is also presented.
The Journal of Organic Chemistry, 1983
Three examples are given to supplement our previous observation of effective orbital interactions between T orbitals through a strained o bond to give extraordinarily long CC bonds. They are 3,5-disubstituted 2,6-diphenylpentacyclo[5.4.O.O2~6.O3~1o.O5~s]undecane-4,8,ll-trione (3b,c), pentacyclo[8.6.0.01~5.0z~g.06~1*] hexadeca-3,7,13,15-tetraene (4a), and anti-5,6-din -butyl-5,6-diphenyldecane (5a). One of the cyclobutane bonds in 3b,c and 4a, as well as the central bond of 5a, well exceeds 1.6 A. The operation of the through-bond coupling between phenyl or vinyl groups in these molecules has been inferred from combined molecular mechanics and semiempirical MNDO molecular orbital calculations. Effects of para substituents in 1,4-diphenylbicyclo[ 2.2.01 hexane (7c) have been studied computationally by using the MNDO method, and T donor groups such as 0and CO; are found to further elongate the central bond up to 0.02 A. Direct substitution of ?r donor groups at C1 and C4 of the bicyclo[2.2.0]hexane skeleton is predicted to be more effective in giving longer lengths for the CI-C4 bond. Strong steric interactions among alkyl side chains in 5 are analyzed.
A study of the orbital description of π-bonds in molecules by the FSGO method
Journal of Molecular Structure: THEOCHEM, 2002
The improvement of p-molecular orbitals is the center of attention in this research. The¯oating spherical gaussian orbital (FSGO) is found to be an appropriate method for this type of investigation. Three kinds of approaches have been selected to look at the problem. The ®rst one is an improvement of the p-MO in a molecule in such a way that a correct geometry and dipole moment are predicted which ensures a good electronic distribution in the molecule. Ethylene and vinyl lithium are selected for calculations to check the proposed wave function. The predicted geometry for ethylene gives the C±C, C±H bond lengths and an HCC angle, 2.547 (1.03%), 2.026 a.u. (20.83%) and 122.018 (0.57%), respectively. The obtained value for the vinyl lithium dipole moment is 6.65 Debye. In the second part, the concept of localization and delocalization of p-MOs has been studied in the FSGO methods. This part clearly demonstrates that the FSGO can handle both localization and delocalization. Cyclobutadiene has been chosen for this section. In the third approach, the more complicated p-systems i.e. p-MO adjacent to lone pair have been examined. Diazene N 2 H 2 (symmetric molecule no dipole moment) and formaldehyde H 2 CO (non-symmetric molecule with dipole moment) are selected for testing the proposed wave function. For diazene, the geometry is predicted as: N±N, N±H bond lengths and an NNH angle, 2.366 (0.04%), 1.921 a.u. (21.13%) and 105.758 (21.07%), respectively. The predicted geometry of formaldehyde shows the CyO, C±H bond length, HCO angle and dipole moment: 2.264(20.44%), 2.070 a.u. (20.33%), 121.738 (20.02%) and 2.23 Debye (24.44 %), respectively.
Molecular orbital theory is a conceptual extension of the orbital model, which was so successfully applied to atomic structure. As was once playfully remarked, "a molecule is nothing more than an atom with more nuclei." This may be overly simplistic, but we do attempt, as far as possible, to exploit analogies with atomic structure. Our understanding of atomic orbitals began with the exact solutions of a prototype problem – the hydrogen atom. We will begin our study of homonuclear diatomic molecules beginning with another exactly solvable prototype, the hydrogen molecule-ion \(H_{2}^{+}\).
Generalized Hybrid-Orbital Method for Combining Density Functional Theory with Molecular Mechanicals
ChemPhysChem, 2005
The generalized hybrid orbital (GHO) method has previously been formulated for combining molecular mechanics with various levels of quantum mechanics, in particular semiempirical neglect of diatomic differential overlap theory, ab initio Hartree-Fock theory, and self-consistent charge density functional tight-binding theory. To include electron-correlation effects accurately and efficiently in GHO calculations, we extend the GHO method to density functional theory in the generalized-gradient approximation and hybrid density functional theory (denoted by GHO-DFT and GHO-HDFT, respectively) using Gaussian-type orbitals as basis functions. In the proposed GHO-(H)DFT formalism, charge densities in auxiliary hybrid orbitals are included to calculate the total electron density. The orthonormality constraints involving the auxiliary Kohn-Sham orbitals are satisfied by carrying out the hybridization in terms of a set of Löwdin symmetrically orthogonalized atomic basis functions. Analytical gradients are formulated for GHO-(H)DFT by incorporating additional forces associated with GHO basis transformations. Scaling parameters are introduced for some of the one-electron integrals and are optimized to obtain the correct charges and geometry near the QM/MM boundary region. The GHO-(H)DFT method based on the generalized gradient approach (GGA) (BLYP and mPWPW91) and HDFT methods (B3 LYP, mPW1PW91, and MPW1K) is tested-for geometries and atomic chargesagainst a set of small molecules. The following quantities are tested: 1) the CC stretch potential in ethane, 2) the torsional barrier for internal rotation around the central CC bond in n-butane, 3) proton affinities for a set of alcohols, amines, thiols, and acids, 4) the conformational energies of alanine dipeptide, and 5) the barrier height of the hydrogenatom transfer between n-C 4 H 10 and n-C 4 H 9 , where the reaction center is described at the MPW1K/6-31G(d) level of theory.
International Journal of Quantum Chemistry, 2016
According to Koopmans theorem, the derivative of the energy of a canonical MO with respect to nuclear coordinates quantifies its bonding/antibonding character. This quantity allows predictions of bond length variation upon ionisation in a panel of 19 diatomic species. In polyatomic molecules, the derivative of a MO energy with respect to a given bond length reveals the nature and the degree of the bonding/antibonding contribution of this MO with respect to this bond. Accordingly, the HOMO "lone pairs" of CO and CN and the HOMO-2 of CH 3 CN are found to be antibonding with respect to the C-X bond (X = N, O), whereas the HOMO of N 2 is found to be bonding. With the same approach, the variation of the bonding character in the MOs of CO and CH 3 CN upon interaction with an electron acceptor (modelled through the approach of a proton) or by applying an electric field was studied.
International Journal of Quantum Chemistry, 2018
The derivative of molecular orbitals (MO) energies with respect to a bond length (dynamic orbital force, DOF) is used to estimate the bonding/antibonding character of valence MOs along this bond, with a focus on lone pair MOs, in a series of small molecules: AH (A = F, Cl, Br), AH2 (A = O, S, Se) AX3 (A = N, P, As; X = H, F) and H2CO. The HOMO DOF agrees with the calculated variation of bond length and force constant in the corresponding ground state cation, and of bond length variation by protonation. These results also agree with available experimental data. It is worthy to note that the p-type HOMOs in AH and AH2 are found bonding. The lone pair MO is bonding in NH3, while it is antibonding in PH3, AsH3, and AF3.