Ab initio calculation of electronic circular dichroism fortrans-cyclooctene using London atomic orbitals

Summary The second-quantization magnetic dipole operator that arises when London atomic orbitals are used as basis functions is derived. In atomic units, the magnetic dipole operator is defined as the negative of the first derivative of the electronic Hamiltonian containing the interaction with the external magnetic field. It is shown that for finite basis sets, the gauge origin dependence of the resulting magnetic dipole operator is analogous to that of the exact operator, and that the derived operator converges to the exact operator in the limit of a complete basis set. It is also demonstrated that the length expression for the rotatory strength in linear response calculations gives gauge-origin-independent results. Sample calculations ontrans-cyclooctene and its fragments are presented. Compared to conventional orbitals, the basis set convergence of the rotatory strengths calculated in the length form using London atomic orbitals is favourable. The rotatory strength calculated fortrans-cyclooctene agrees nicely with the corresponding experimental circular dichroism spectrum, but the spectra for the fragment molecules show little resemblance with that oftrans-cyclooctene.Dedicated to Prof. Jan Linderberg     

Ab initio calculation of maximum bond order hybrid orbitals

Summary The maximum bond order hybrid orbital (MBOHO) procedure is tested onab initio level by use of the density matrix in Löwdin orthogonalized atomic orbital basis. The direct MBOHO calculation based on the whole density matrix includes also the hybridization of the inner atomic orbitals, and the MBOHO calculation based on the valence orbital part of the density matrix considers only the hybridization of the valence atomic orbitals. The concrete MBOHO calculations based on theab initio calculation with STO-3G basis show that the components of the s atomic orbitals in MBOHOs and the maximum bond orders obtained from the two kinds of MBOHO calculations are very close to each other, and that the two kinds of MBOHOs all have the excellent correlativity with the nuclear spin-spin coupling constants.The project supported by National Natural Science Foundation of China and the Excellent Young University Teacher's Foundation of State Education Commission of China.     

Spin-orbit interaction in polyatomic molecules: Ab initio computations with Gaussian orbitals

Standard sets of Gaussian atomic orbitals (STO -3G , STO -4.31G ) are used to evaluate spin-orbit coupling constants in linear molecules (CO, NNN) and spin-orbit effects on singlet–triplet transition intensities in formaldehyde. All spin-other orbit effects have been included. In all cases spin-other orbit interactions form a large fraction of the matrix elements. Simple formulae to evaluate spin-orbit one- and two-electron integrals over atomic orbitals are presented. Standard molecular integral programs can be used for the computation of spin-orbit integrals.     

Gauge invariant gaussian orbitals and the ab initio calculation of diamagnetic susceptibility for molecules

It is shown that gauge terms can be introduced into the Gaussian functions used as the basis functions for an ab initio calculation of the energy of a molecule in the presence of a uniform magnetic field so that all the integrals become independent of the origin of the vector potential. The perturbation treatment of the diamagnetic susceptibility is considered in the molecular orbital approximation. The results show that the susceptibility can be calculated using only the unperturbed orbitals and their first-order corrections. All the integrals that arise can be expressed in terms of known functions.     

Ab initio calculation of the C/D ratio of magnetic circular dichroism

A procedure for calculating the magnetic circular dichroism C/D ratio from density functional theory calculations is discussed. The method is simplified considerably through the application of group theory and the irreducible-tensor method and only requires integrals of the magnetic dipole moment operator over a few orbitals and published tables of symmetry factors. The implementation of the method is tested through application to several small and medium-sized molecules.     

Ab initio calculation of molecular chiroptical properties

This review describes the first-principles calculation of chiroptical properties such as optical rotation, electronic and vibrational circular dichroism, and Raman optical activity. Recent years have witnessed a flurry of activity in this area, especially in the advancement of density-functional and coupled cluster methods, with two ultimate goals: the elucidation of the fundamental relationship between chiroptical properties and detailed molecular structure, and the development of a suite of computational tools for the assignment of the absolute configurations of chiral molecules. The underlying theory and the basic principles of such calculations are given for each property, and a number of representative applications are discussed.     

Ab initio MO calculation of force constants and dipole derivatives for the formamide dimer. An estimation of hydrogen-bond force constants

Ab initio SCF MO calculations (with the 4-31G basis set) have been carried out to determine the equilibrium geometry, vibrational frequencies, dipole-moment derivatives, and force constants for intermolecular modes of the formamide dimer and its d₄ and d₆ derivatives. The results are correlated with monomer calculations and experimental data for crystalline formamide.     

Ab initio relativistic calculation of the RbCs molecule

We apply the relativistic configuration-interaction valence-bond method to calculate various characteristics of the alkali-metal RbCs dimer. These include the electronic potentials and transition dipole moments between the ground and first excited states and permanent dipole moments of the X 1sigma+ and a 3sigma+ states of the ground configuration. In addition, we estimate the lifetime of the rovibrational levels of the X state due to blackbody radiation. These data can help experimentalists to optimize photoassociative formation of ultracold RbCs molecules and their longevity in a trap or in an optical lattice. Extended basis sets, constructed from Dirac-Fock and Sturm's orbitals, have been used to ensure convergence of our calculations. We compare our data with other theoretical and experimental results when they were available.     

Ab initio study of the NMR shielding constants and spin-spin coupling constants in cyclopropene

Summary Ab initio calculations of parameters which characterize the NMR spectrum are presented for the cyclopropene molecule. The London orbitals CHF (or GIAO-CHF, Gauge-Independent Atomic Orbital Coupled Hartree-Fock) results for the shielding constants are in good agreement with the experimental data, accurately determined, and with otherab initio values. The calculations of the NMR spin-spin coupling constants have been performed using the Multiconfiguration Time-Dependent Hartree-Fock (MC TDHF) approach. Different basis sets and MC SCF wavefunctions were used to estimate the accuracy of the results. Good agreement is obtained with the coupling constants estimated using the available experimental data.Dedicated to Professor Werner Kutzelnigg on the occasion of his 60th birthday     

Ab initio derivative calculation of vibrational circular dichroism

The recent formalism of Stephens for the calculation of rotational strength in vibrational circular dichroism has been implemented, exploiting the analytical derivative technique for ab initio Hartree-Fock wavefunctions.     

Ab initio calculation of magnetic shielding and susceptibility. Finite perturbation calculation of susceptibility with GIAO's

The magnetic susceptibility of hydrogen fluoride is calculated with four different basis sets of gauge invariant atomic orbitals (GIAO's). The Roothaan equations are solved for various values of the magnetic field strength and the susceptibility is deduced by a numerical differentiation of the energy.     

Ab initio study of force constants and intensities of 1,3,5-trioxane

The structure, vibrational force constants and infrared and Raman intensities have been calculated for 1,3,5-trioxane using a 3-21G basis set. These results have been used to identify some possible inaccuracies in experimental diffraction based structures and in vibrational assignments. It is demonstrated that there is a marked contrast between the trends in the vibrational force constants and in the King's effective atomic charges of the axial and equatorial CH bonds in the series cyclohexane, 1,4-dioxane and 1,3,5-trioxane. The axial CH stretching force constant decreases by 0.04 mdyne Å⁻¹ for each adjacent oxygen atom, whereas that of the equatorial CH bond increases by 0.15 mdyne Å⁻¹ per oxygen. In trioxane the effective atomic charge of the axial hydrogen is twice that of the equatorial. Atomic polar tensors are calculated in a bond oriented frame, and the effect of the oxygens on CH stretching and bending mode intensities discussed. Some properties are also calculated using the 4-31G basis.     

Ab initio SCF computation of force constants for CO2

Force constants for CO₂ have been evaluated using SCF wave functions. The effect ofd basis functions and geometry are investigated. Comparison with experimental values shows that a large error, due to neglect of electron correlation, occurs for theK ₁₂ interaction stretch force constant.     

Ab initio molecular orbitals study of the conformational preference in alpha-cyano-alpha-fluorophenylacetic acid ester

The origin of conformational preference in alpha-cyano-alpha-fluorophenylacetic acid (CFPA) methyl ester that is a model system of alpha-cyano-alpha-fluoro-p-tolylacetic acid (CFTA) esters was theoretically investigated by means of DFT and MP2 calculations. Two stable conformations having the C-F bond syn and anti to the C=O bond, respectively, were obtained for CFPA methyl ester. A small energy difference (0.9 kcal mol-1 at the MP2(fc)/6-31++G(d,p)) was found between the two conformations. From the molecular orbital analysis based on the Natural Bond Orbital analysis and supported by calculations using the Orbital Deletion Procedure technique, we found that sigma-(sigma*+pi*)(C=O) and sigma-sigma*(Ph) and pi(Ph)-sigma* hyperconjugations are the main factors responsible for the conformational preference. The role of the fluorine atom on the stereogenic center was also clarified.     

Ab initio rotational constants of interstellar species: Cyanoacetylene hydrogenated derivatives

By means of ab initio calculations, the rotational constants and dipole moments of H_nC₃N (n = 1, 3, 5, 7, and 9) species have been calculated at the HF / 6-31G * level of theory. Selected cases have been also calculated at the MP 2/6-31G * level and the influence of calculation level on rotational constant values is briefly discussed. Some of these species were discovered in the interstellar medium, while others have still not been detected there, although their existence is very probable. The results given here could help in their detection. © 1993 John Wiley & Sons, Inc.