Molecular Orbital Coefficients Research Articles

Theoretical investigation of EPR and molecular orbital coefficient parameters for [Cu(hsm) 2(sac) 2] complex

In this study, the molecular orbital coefficients and the spin Hamiltonian parameters of bis(histamine-saccharinate) copper(II) complex, [Cu(hsm) 2(sac) 2], are calculated theoretically. Two d– d transition spectra and four EPR parameters g ∥ , g ⊥ , A ∥ , A ⊥ for the Cu(II) complex are calculated by using crystal-field theory. The calculated values are in good agreement with the experimental values. The g and A parameters have indicated that the paramagnetic centre is axially symmetric. Having the relations of g ∥ > g ⊥ > g e and A ∥ > A ⊥ for Cu 2+ ions, it can be concluded that Cu 2+ ions are located in distorted octahedral sites (D 4h) elongated along the z-axis and that the ground state of the paramagnetic electron is d x 2 - y 2 ( 2 B 1 g state).

Parallelism between charge redistribution and delocalization. Applications to organic reactions

The study is devoted to interrelations between two perturbative expansions for molecules and molecular systems, namely between terms of power series for one-electron density matrices on the one hand, and those for respective representation matrices of non-canonical (localized) molecular orbitals (MOs) on the other hand, as well as to the relevant implications. As the most outstanding example of the latter, simple proportionalities are established between alterations in populations of basis orbitals due to chemical interaction and delocalization coefficients of respective localized MOs (LMOs). The proof of these proportionalities is valid for members of power series to within the fifth order inclusive that were shown previously to be sufficient for investigations of the most important organic reactions. As a result, classical interpretations of early stages of these reactions in terms of shifts of respective localized pairs of electrons (cf. the so-called ‘curly arrow chemistry’) acquire a quantum-chemical support. Moreover, the results of the present study allow comparisons of relative extents of delocalization of LMOs for alternative routes of the same process. On this basis, predominant (allowed) routes of organic reactions are shown to be characterized by enhanced delocalization of respective principal pairs of electrons as compared to alternative (forbidden) routes. Raktažodžiai: localized molecular orbitals, Brillouin theorem, organic reactions, delocalization, curly arrow chemistry

The Fukui matrix: a simple approach to the analysis of the Fukui function and its positive character

The Fukui matrix is introduced as the derivative of the one-electron reduced density matrix with respect to a change in the number of electrons under constant external potential. The Fukui matrix extends the Fukui function concept: the diagonal of the Fukui matrix is the Fukui function. Diagonalizing the Fukui matrix gives a set of eigenvectors, the Fukui orbitals, and accompanying eigenvalues. At the level of theory used, there is always one dominant eigenvector, with an eigenvalue equal to 1. The remaining eigenvalues are either zero or come in pairs with eigenvalues of the same magnitude but opposite sign. Analysis of the frontier molecular orbital coefficient in the eigenvector with eigenvalue 1 gives information on the quality of the frontier molecular orbital picture. The occurrence of negative Fukui functions can be easily interpreted in terms of the nodal character of the dominant eigenvector versus the characteristics of the remaining eigenvectors and eigenvalues.

The use of unsymmetrical one-range addition theorems of Slater type orbitals for the calculation of intermolecular Coulomb interaction energy

The formulae at Hartree–Fock level are derived for the energy of Coulomb interaction between molecules containing any number of closed and open shells. These formulae are expressed in terms of linear combination coefficients of molecular orbitals and multicenter integrals of Slater type orbitals and interaction potentials produced by the charges of the molecules. As an example of application, by the use of unsymmetrical one-range addition theorems of Slater type orbitals the Hartree–Fock–Roothaan calculations have been performed for the energy of interaction produced by the ground states of two molecules H2O.

Evaluation of potential of electric field produced by molecule using symmetrical one-range addition theorems for Coulomb-Yukawa like correlated interaction potentials of integer and noninteger indices

Using symmetrical one-range addition theorems the series expansion formulae in terms of multicenter charge density expansion coefficients for noninteger n Slater type orbitals (STO), parameters of Coulomb-Yukawa like correlated interaction potentials (CIP) of noninteger indices and linear combination coefficients of molecular orbitals are established for the potential of electrostatic field produced by the charges of molecule. The final results are useful for the study of interaction between atomic-molecular systems containing any number of closed and open shells when the Hartree–Fock–Roothaan (HFR) approximation and the explicitly correlated methods based upon the use of STO as basis functions and Coulomb–Yukawa like CIP are employed. As an example of application, the calculations have been performed for the Coulomb interaction potential produced by the ground state of CH 2 molecule \({(1a_1^2 2a_1^2 1b_1^2 3a_1^1 1b_1^1,^3B_1 )}\).

EPR and optical absorption studies of VO2+ ion doped magnesium citrate decahydrate single crystals

An X-band electron paramagnetic resonance (EPR) study of VO2+ ions in magnesium citrate decahydrate single crystals was done at room temperature. Detailed EPR analysis indicated the presence of two magnetically inequivalent VO2+ sites. Both the vanadyl complexes were found to take up substitutional positions. The angular variation of the EPR spectra in three planes a*b, bc and ca* were used to determine principal g and A tensors. For the two sites the spin Hamiltonian parameters are site I: gx=2.0976, gy=1.9093, gz=1.9505, |Ax|=73, |Ay|=115, |Az|=237×10−4 cm−1; site II: gx=2.0735, gy=1.9235, gz=1.9699, |Ax|=72, |Ay|=111, |Az|=233×10−4 cm−1. An optical absorption study was also performed at room temperature, and absorption bands were assigned to various transitions. The theoretical band positions were estimated using energy expressions, and good agreement with experimental values was found. By correlating EPR and optical data, different molecular orbital coefficients were evaluated; the nature of the bonding in the crystal is discussed.

Optimized basis sets for the calculation of indirect nuclear spin-spin coupling constants involving the atoms B, Al, Si, P, and Cl

The aug-cc-pVTZ-J series of basis sets for indirect nuclear spin-spin coupling constants has been extended to the atoms B, Al, Si, P, and Cl. The basis sets were obtained according to the scheme previously described by Provasi et al. [J. Chem. Phys. 115, 1324 (2001)]. First, the completely uncontracted correlation consistent aug-cc-pVTZ basis sets were extended with four tight s and three tight d functions. Second, the s and p basis functions were contracted with the molecular orbital coefficients of self-consistent-field calculations performed with the uncontracted basis sets on the simplest hydrides of each atom. As a first illustration, we have calculated the one-bond indirect spin-spin coupling constants in BH(4)(-), BF, AlH, AlF, SiH(4), SiF(4), PH(3), PF(3), H(2)S, SF(6), HCl, and ClF at the level of density functional theory using the Becke three parameter Lee-Yang-Parr and the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes.

Experimental and computational studies on zwitterionic (E)-2-(1-(2-(4-methylphenylsulfonamido)ethyliminio)ethyl) phenolate

The Schiff base compound (E)-2-(1-(2-(4-methylphenylsulfonamido)ethyliminio)ethyl) phenolate has been synthesised and characterized by IR, UV–Vis, and X-ray single-crystal determination. Ab initio calculations have been carried out for the title compound using the density functional theory (DFT) and Hartree–Fock (HF) methods at 6-31G(d) basis set. The calculated results show that the DFT/B3LYP and HF can well reproduce the structure of the title compound. Using the TD-DFT and TD-HF methods, electronic absorption spectra of the title compound have been predicted and a good agreement with the TD-DFT method and the experimental ones is determined. Molecular orbital coefficient analyses reveal that the electronic transitions are mainly assigned to n → π* and π → π* electronic transitions. To investigate the tautomeric stability, optimization calculations at B3LYP/6-31G(d) level were performed for the NH and OH forms of the title compound. Calculated results reveal that the OH form is more stable than NH form. In addition, molecular electrostatic potential and NBO analysis of the title compound were performed at B3LYP/6-31G(d) level of theory.

Investigations on the Spin Hamiltonian Parameters and the Local Structures for Various Rh2+ Centers in NaCl

The spin Hamiltonian parameters (the g factors, the hyperfine structure constants, and the superhyperfine parameters) and the local structures for various Rh2+ centers OI, OII, and RTAX in NaCl are theoretically investigated from the perturbation formulas of these parameters for a 4d7 ion in tetragonally and orthorhombically elongated octahedra. The related molecular orbital coefficients and the ligand unpaired spin densities are determined quantitatively from the cluster approach in a uniform way. The centers OI, OII (orthorhombic) or RTAX (tetragonal) are attributed to the substitutional Rh2+ on Na+ site, associated with two, one or none next nearest neighbour cation vacancies VNa along [100] (or [010]) axis, respectively. The ligand octahedra in the orthorhombic centers OI and OII are found to suffer the relative elongations ΔZ ≈0.071 and 0.068 °A along the [001] axis due to the Jahn-Teller effect, and the intervening ligand(s) in the VNa and the Rh2+ may undergo the inward displacements ΔX ≈ 0.001 and 0.011 A° towards Rh2+, respectively. As for the tetragonal center RTAX, the uncompensated [RhCl6]4− cluster is found to experience the relative elongation ΔZ ≈ 0.067 °A along the [001] axis of the Jahn-Teller nature. The calculated spin Hamiltonian parameters based on the above local structures show good agreement with the observed values for all the centers.

Theoretical studies of the local structures and EPR parameters for various Rh 2+ centers in AgCl

The local structures and electron paramagnetic resonance (EPR) parameters (the g factors, the hyperfine structure constants and the superhyperfine parameters) for various Rh 2+ centers in AgCl are theoretically studied using the perturbation formulas of these parameters for a 4d 7 ion in tetragonally and orthorhombically distorted octahedra. These defects include the tetragonally and orthorhombically elongated centers at low temperatures (labeled as T L and O L) and the tetragonally compressed center at high temperature (labeled as T H). The centers T L and O L are attributed to the substitutional Rh 2+ on Ag + site, associated with none and one next nearest neighbour cation vacancy V Ag along [1 0 0] (or X) axis, respectively. The ligand octahedron in the orthorhombic center O L is found to suffer the relative elongation Δ Z OL ≈ 0.079 Å along [0 0 1] (or Z) axis due to the Jahn–Teller effect, and the intervening ligand Cl − in the V Ag and the Rh 2+ may experience the inward displacement Δ X ≈ 0.008 Å towards the central Rh 2+. In the center T L, the uncompensated [RhCl 6] 4− cluster is found to suffer the relative elongation Δ Z TL ≈ 0.116 Å along [0 0 1] axis due to the Jahn–Teller effect. As for the center T H, one V Ag occurs in the next nearest neighbour site along [0 0 1] axis, which may compel the intervening Cl − in the V Ag and the Rh 2+ to shift towards the central Rh 2+ by an amount Δ Z H ≈ 0.112 Å. In the calculations of the superhyperfine parameters, the related molecular orbital coefficients and the ligand unpaired spin densities are determined quantitatively from the cluster approach in a uniform way. The theoretical EPR parameters based on the above local structures show good agreement with the experimental data for all the centers.

Investigations of the spin Hamiltonian parameters for the cubic Mn2+ centers in ZnX (X = S, Se, Te) and CdTe

The spin Hamiltonian parameters (g factors and the hyperfine structure constants) for the cubic Mn2+ centers in ZnX (X = S, Se, Te) and CdTe are investigated theoretically using the perturbation formulas of these parameters for a tetrahedral 3d5 cluster containing both the crystal-field and charge-transfer contributions. The relevant molecular orbital coefficients are uniformly determined from the cluster approach, and the calculated spin Hamiltonian parameters are in good agreement with the observed values. The g-shifts of the g factors related to the pure spin value gs (≈ 2.0023) arising from the charge transfer contributions are opposite (positive) in sign and much larger in magnitude than those from the crystal field contributions. On the other hand, the contributions from the charge-transfer mechanism to the hyperfine structure constants are the same in sign and about 20%–30% in magnitude of those from the crystal-field mechanism. The importance of the charge transfer contributions increases significantly with the increase of the covalency and the spin–orbit coupling coefficient of the ligand, i.e., S2− < Se2− < Te2−.

EPR and optical absorption studies of Cu 2+ ions doped magnesium citrate decahydrate single crystals

X-band electron paramagnetic resonance (EPR) studies of Cu 2+ ions in magnesium citrate decahydrate single crystals are done at room temperature. Detailed EPR analysis indicates the presence of only one Cu 2+ site. Cu 2+ is found to take up substitutional position at Mg site. The angular variation of the EPR spectra in three planes a* b, bc and ca* are used to determine principal g and A tensors. The spin Hamiltonian parameters are: g x = 2.0346, g y = 2.1400, g z = 2.3874, A x = 57, A y = 76, A z = 99 (×10 −4) cm −1. The optical absorption study is also carried out at room temperature and absorption bands are assigned to various transitions. The theoretical band positions are estimated using energy expressions and a good agreement is obtained with the experimental values. By correlating EPR and optical data, different molecular orbital coefficients are evaluated and the nature of bonding in the complex is discussed.

First-order nonadiabatic couplings from time-dependent hybrid density functional response theory: Consistent formalism, implementation, and performance

First-order nonadiabatic coupling matrix elements (NACMEs) are key for phenomena such as nonradiative transitions and excited-state decay, yet a consistent and practical first principles treatment has been elusive for molecules with more than a few heavy atoms. Here we present theory, implementation using Gaussian basis sets, and benchmarks of first-order NACMEs between ground and excited states in the framework of time-dependent hybrid density functional theory (TDDFT). A time-dependent response approach to NACMEs which avoids explicit computation of excited-state wave functions is outlined. In contrast to previous approaches, the present treatment produces exact analytical derivative couplings between time-dependent Kohn-Sham (TDKS) determinants in a finite atom-centered basis set. As in analytical gradient theory, derivative molecular orbital coefficients can be eliminated, making the computational cost independent of the number of nuclear degrees of freedom. Our expression reduces to the exact Chernyak-Mukamel formula for first-order NACMEs in the complete basis-set limit, but greatly improves basis-set convergence in finite atom-centered basis sets due to additional Pulay type terms. The Chernyak-Mukamel formula is shown to be equivalent to the Hellmann-Feynman contribution in analytical gradient theory. Our formalism may be implemented in TDDFT analytical excited-state gradient codes with minor modifications. Tests for systems with up to 147 atoms show that evaluation of first-order NACMEs causes total computation times to increase by an insignificant 10% on average. The resolution-of-the-identity approximation for the Coulomb energy (RI-J) reduces the computational cost by an order of magnitude for nonhybrid functionals, while errors are insignificant with standard auxiliary basis sets. We compare the computed NACMEs to full configuration interaction (FCI) in benchmark results for diatomic molecules; hybrid TDDFT and FCI are found to be in agreement for regions of the potential energy curve where the Kohn-Sham ground-state reference is stable and the character of the excitation is properly captured by the present functionals. With these developments, nonadiabatic molecular dynamics simulations of molecular systems in the 100 atoms regime are within reach.

Electron Paramagnetic Resonance and Optical Absorption of VO2+ Doped Bis (glycinato) Mg (II) Monohydrate Single Crystals

We investigate the electron paramagnetic resonance (EPR) of VO2+ ions in bis (glycinato) Mg (II) monohydrate single crystals at room temperature. Detailed EPR. analysis indicates the presence of only one VO2+ site. The vanadyl complexes are found to take up the substitutional position. The angular variation of the EPR spectra in three planes a*b, be and ca* are used to determine principal g and A tensors. The values of spin Hamiltonian parameters are gx = 2.1447×10−4, gy = 1.9974×10−4, gz = 1.9131×10−4, Ax = 49×10−4, Ay = 60×10−4, Az = 82×10−4 cm−1. The optical absorption study is also carried out at room temperature and absorption bands are assigned to various transitions. The theoretical band positions are obtained using energy expressions and a good agreement is found with the experimental data. By correlating EBB. and optical data, different molecular orbital coefficients are evaluated and the nature of bonding in the crystal is discussed.

Monocyclic Electrocyclic Transition States are Neither Favoured Nor Disfavoured if the Incipient Ring Bears More Than Two Odd Substituents

A general case is presented that supports the conclusion that incipient π-bond orders, op1,j, are approximately zero if the incipient alternant ring bears more than two odd substituents. Hence, corresponding electrocyclic transition states are neither favoured nor disfavoured. The case is made using permethylene polyenes. After presentation of the novel application of dense Sachs’ subgraphs to the problem of convenient, rapid access to permethylene polyene characteristic polynomials, permethylene polyenes are shown to belong to the newly defined Hückel symmetrenes. Employing novel expressions for permethylene polyene molecular orbital coefficients, a general relationship for pairs of terms that lead to π-bond orders, op1,j, is obtained that, in turn, allows the key generalization to be made.

Evaluation of intermolecular interaction energy using one-range addition theorems for $${\psi ^\alpha}$$ – ETO and Coulomb-Yukawa like correlated interaction potentials with integer and noninteger indices

Using one-range addition theorems for complete orthonormal sets of \({\psi^\alpha }\) – exponential type orbitals (α = 1, 0, −1, −2, . . .) intruduced by the author, the series expansion relations are established for the energy of interaction between molecules which have any number of closed and open shells. The final results are expressed through the linear combination coefficients of molecular orbitals, the parameters of Coulomb-Yukawa like correlated interaction potentials with integer and noninteger indices and the multicenter overlap integrals. The formulas obtained are useful for the study of interaction between atomic-molecular systems when the \({\psi^\alpha}\) – exponential type orbital basis functions in Hartree-Fock-Roothaan and explicitly correlated methods are employed.

Investigations on the g factors and superhyperfine parameters for various tetragonal Ni + centers in RbCaF 3

The anisotropic g factors g ∥ and g ⊥ and the planar F − superhyperfine parameters A ∥ and A ⊥ in the tetragonal impurity Ni + I, II and III centers (as well as the axial F − superhyperfine parameters A ∥ ′ and A ⊥ ′ in I center) on the substitutional Ca 2+ site in RbCaF 3 are theoretically investigated in a uniform way using the perturbation formulas of these parameters for a 3d 9 ion in tetragonally elongated octahedra. In the calculations, the ligand unpaired spin densities are determined quantitatively from the related molecular orbital coefficients based on the cluster approach. These defects are attributed to the substitutional Ni + associated with none, one and two axial nearest neighbour F − vacancies for I, II and III centers, respectively. Ni + I center is found to suffer the relative elongation (≈5%) along the [0 0 1] (or C 4) axis due to the Jahn–Teller effect, while the tetragonal elongation distortions are mainly ascribed to the axial vacancies in II and III centers. The local structures of the various impurity centers are discussed.

Use of Coulomb-Yukawa Like Correlated Interaction Potentials of Integer and Noninteger Indices and One-range Addition Theorems for Ψα-ETO in Evaluation of Potential of Electric Field Produced by Molecule

Using Coulomb-Yukawa like correlated interaction potentials of integer and noninteger indices the series expansion formulae in terms of multicenter overlap integrals of three complete orthonormal sets of <TEX>${\psi}^{\alpha}$</TEX>‒exponential type orbitals and linear combination coefficients of molecular orbitals are established for the potential of electrostatic field produced by the charges of molecule, where <TEX>$\alpha$</TEX> = 1, 0, ‒1, ‒2,<TEX>${\cdots}$</TEX>. The formulae obtained can be useful for the study of interaction between atomic--molecular systems containing any number of closed and open shells when the <TEX>${\psi}^{\alpha}$</TEX>‒exponential type basis functions and Coulomb-Yukawa like correlated interaction potentials are used in the Hartree-Fock-Roothaan and explicitly correlated approximations. The final results are valid for the arbitrary values of parameters of correlated interaction potentials and orbitals. As an example of application, the calculations have been performed for the potential energy of interaction between electron and molecule <TEX>$H_2O$</TEX> using combined Hartree-Fock-Roothaan equations suggested by the author.

Investigations on the defect structure and the EPR parameters for AgBr:Ir2+

The defect structure and the EPR parameters (the g factors, the hyperfine structure constants and the superhyperfine parameters) for the tetragonal Ir(2+) center in AgBr are theoretically investigated using the perturbation formulas of these parameters for a 5d(7) ion in tetragonally elongated octahedra. In the calculations, the contributions from the ligand orbital and spin-orbit coupling interactions and the local lattice (elongation) distortion due to the Jahn-Teller effect are taken into account. Related molecular orbital coefficients and the ligand unpaired spin densities are determined quantitatively using a cluster approach. The impurity center is attributed to the substitutional [IrBr(6)](4-) cluster on host Ag(+) site, which suffers the relative elongation of about 0.08 angstrom along C(4) axis due to the Jahn-Teller effect. The calculated EPR parameters based on the above Jahn-Teller elongation show good agreement with the observed values.

EPR and UV studies of VO2+ ions in potassium d-gluconate monohydrate single crystals

Abstract Electron paramagnetic resonance (EPR) of VO2+ doped potassium hydrogen d -gluconate single crystals and powder have been examined at room temperature. Single crystal rotations in each of the three mutually orthogonal crystalline planes namely ac, ba and ca indicate two different VO2+ complexes. Each complex is located in different chemical environments, each environment containing two magnetically inequivalent VO2+ sites in distinct orientations occupying substitutional positions in the lattice and showing a very large angular dependence. The powder spectrum also clearly indicates four different VO2+ complexes, confirming the single crystal analysis. Crystalline field around the VO2+ ion is nearly axial. The optical absorption spectrum of VO2+ ions in the crystal lattice is also studied at room temperature. The characteristic spectrum of the VO2+ ions has two absorption bonds. The bond positions are at 17 857 and 11 235 cm–1. Spin Hamiltonian parameters and molecular orbital coefficients are calculated from the EPR and the optical data, and results are discussed.