Ab initio assessment of the electronic structure of 5α-reduced progestins

Progesterone (P) yields to 5α-reduced progestins, namely 5α-pregnanedione (DHP), tetrahydroprogesterone (THP), and allopregnanolone (ALLO-P). The geometries and electronic structure of these steroids were assessed by ab initio calculations using the 6-31G* basis set. The parameters measured were bond distances, valence angles, and dihedral angles. Likewise, the following were calculated: total energy; frontier orbitals, i.e., highest occupied molecular orbital (HOMO); lowest unoccupied molecular orbital (LUMO); dipole moment; atomic charges; and electrostatic potentials. The frontier orbitals of P were located at the π-double bond. However, the HOMO of the 5α-progestins was extended into the molecule, while the LUMO was confined at the C20 carbonyl group. The atomic charges, electronic density surfaces and electrostatic potentials showed patterns according to the stereochemical arrangement of the C3 and C20 carbonyl and hydroxyl functional groups. Interestingly, P and THP showed the larger dipole moment and high electronic density at the A-ring because the double bond and the 3α-hydroxy group, respectively. The present results might explain to some extent the metabolism of the studied progestins. Similarly, some physicochemical properties, such as dipole moments and electrostatic potentials, seem related with important biological actions such as uterine contractility and control of gonadotropin secretion. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 329–338, 1998     

Excited orbitals of sulphur in aliphatic and unsaturated sulphides

The energies of some electron configurations of sulphur in organic sulphides involving 3d and 4s orbitals have been derived by simulating the radial and angular perturbation of the molecular environment on sulphur valence orbitals, with electrostatic potentials. In order to discuss the relevance of the electron configurations in the molecular valence state and the role of the excited orbitals 4s and 3d to bonding, the energies were minimized in respect of size and orientation of sulphur valence orbitals. Interatomic exchange terms were included and the importance of interatomic exchange terms involving the electrons on carbons is discussed. The results are indicative for a negligible participation of 3d and 4s orbitals of sulphur to the ground state of aliphatic and unsaturated sulphides.     

Are there atomic orbitals in a molecule?

Effective atomic orbitals (AOs) have been calculated by the method of the "fuzzy atoms" analysis by using the numerical molecular orbitals (MOs) obtained from plane-wave DFT calculation, i.e., without introducing any atom-centered functions. The results show that in the case of nonhypervalent atoms there are as many effective AOs with non-negligible occupation numbers, as many orbitals are in the classical minimal basis set of the given atom. This means that, for nonhypervalent systems, it is possible to present the MOs as sums of effective atomic orbitals that resemble very much the atomic minimal basis orbitals of the individual atoms (or their hybrids). For hypervalent atoms some additional orbitals basically of d-type are also of some importance; they are necessary to describe the back-donation to these positive atoms. It appears that the d-type orbitals play a similar role also for strongly positive carbon atoms. The method employed here is also useful to decide whether the use of polarization functions of a given type is a matter of conceptual importance or has only a numerical effect.     

Orbital overlap and chemical bonding

The chemical bonds in the diatomic molecules Li(2)-F(2) and Na(2)-Cl(2) at different bond lengths have been analyzed by the energy decomposition analysis (EDA) method using DFT calculations at the BP86/TZ2P level. The interatomic interactions are discussed in terms of quasiclassical electrostatic interactions DeltaE(elstat), Pauli repulsion DeltaE(Pauli) and attractive orbital interactions DeltaE(orb). The energy terms are compared with the orbital overlaps at different interatomic distances. The quasiclassical electrostatic interactions between two electrons occupying 1s, 2s, 2p(sigma), and 2p(pi) orbitals have been calculated and the results are analyzed and discussed. It is shown that the equilibrium distances of the covalent bonds are not determined by the maximum overlap of the sigma valence orbitals, which nearly always has its largest value at clearly shorter distances than the equilibrium bond length. The crucial interaction that prevents shorter bonds is not the loss of attractive interactions, but a sharp increase in the Pauli repulsion between electrons in valence orbitals. The attractive interactions of DeltaE(orb) and the repulsive interactions of DeltaE(Pauli) are both determined by the orbital overlap. The net effect of the two terms depends on the occupation of the valence orbitals, but the onset of attractive orbital interactions occurs at longer distances than Pauli repulsion, because overlap of occupied orbitals with vacant orbitals starts earlier than overlap between occupied orbitals. The contribution of DeltaE(elstat) in most nonpolar covalent bonds is strongly attractive. This comes from the deviation of quasiclassical electron-electron repulsion and nuclear-electron attraction from Coulomb's law for point charges. The actual strength of DeltaE(elstat) depends on the size and shape of the occupied valence orbitals. The attractive electrostatic contributions in the diatomic molecules Li(2)-F(2) come from the s and p(sigma) electrons, while the p(pi) electrons do not compensate for nuclear-nuclear repulsion. It is the interplay of the three terms DeltaE(orb), DeltaE(Pauli), and DeltaE(elstat) that determines the bond energies and equilibrium distances of covalently bonded molecules. Molecules like N(2) and O(2), which are usually considered as covalently bonded, would not be bonded without the quasiclassical attraction DeltaE(elstat).     

六聚同多酸阴离子M_6O_(19)~(n-)(M=Mo,W,n=2;M=Nb,Ta,n=8)电子结构和化学性质的密度泛函理论研究

采用B3LYP方法在LanL2DZ水平上计算了六聚同多阴离子 (M6On-19,M =Mo和W ,n =2 ;M =Nb和Ta ,n =8)的电子结构 ,分析了它们的前线轨道、分子静电势 (MEP) .计算结果表明 ,Nb6O8-19和Ta6O8-19是电子给体 ,而Mo6O2 -19和W6O2 -19则是电子受体 ,这与它们在溶液中具有不同的化学性质是一致的     

Electronic structure of the ground state of the benzyl radical

Results from the -electron approximation are given for the total energy, spin-density distribution, and electron density, which have been derived by configuration interaction via self-consistent orbitals for closed and open shells and with allowance for all singly excited configurations and some doubly excited ones. Some singly excited configurations do not mix with the ground-state configuration in the first order of perturbation theory but make a contribution to the latter greater than do some of the configurations that do mix. Incorporation of all singly excited configurations results in a lower ground-state energy if orbitals for a closed shell are used instead of those for an open one. Calculations via closed-shell orbitals lead to an inhomogeneous electron-density distribution, which is gradually smoothed out as the set of configurations is expanded. The spin-density distribution is very much dependent on the number of configurations used and on the orbitals employed in them.     

Ab initio intermolecular energies between Li+ and H2 near the van der waals minimum: comparison between a perturbative procedure and an SCF supermolecule treatment

The electrostatic, exchange, polarization, and dispersion energies are computed without using the multipole expansion. It is seen that the overlap between the orbitals of the interacting molecules must be taken into account to describe qualitatively the first order term. The neglect of overlap in the polarization term overestimates the attractive energy around the van der Waals minimum. An interpretation of the polarization phenomena in terms of molecular orbitals is proposed. The results are compared with SCF calculations and the use of small basis sets is considered.     

An ab initio study of the effect of the 3d orbitals of phosphorus on the properties of the phosphate group

A large number of properties of the dimethylphosphate anion (DMP^?), model system for the phosphate group of the nucleic acids and the phospholipid components of membranes, has been investigated by the SCF ab initio procedure including the 3d orbitals of the phosphorus atom in the gaussian basis set and the results of the computations were compared with similar results obtained previously without taking these orbitals into account. The properties investigated include the conformational states of DMP with respect to the torsion about the P-O_ester bonds, the distribution of the electronic charges, the molecular electrostatic potentials generated by DMP^?, the characteristics of the molecular orbitals, particularly the electronic isodensity maps, the hydration scheme. Qualitatively, the introduction of the 3d orbitals modifies little the general aspects of the results obtained for most of the properties studied. On the quantitative level significant, although generally not great, modifications may be noticed with respect to some features of these properties. One of the strongest influences of the introduction of the 3d orbitals concerns the decrease of the net electronic charges in DMP^?.     

Near homogeneous variation of potentials in large systems and the electronic structure of molecular quantum dots

It is shown from Kohn-Sham (KS) density-functional theory that in a large molecular system, the Coulomb potential, molecular electrostatic potential, and KS effective potential may exhibit an approximately homogeneous variation in space, in response to a small change of the electron number. The homogeneous variation of potentials underlies the constant interaction (CI) model of quantum dots (QDs) and is related to the delocalization and invariance of KS orbitals, the identical shift of KS levels, and a natural definition of the QD capacitance. Calculation results of a fullerene C60 and a single-walled carbon nanotube are presented. Although the homogeneity of the potential variation is not perfect, it seems to lead to fairly good approximation of the CI model to the addition energy spectra of these systems.     

Transferability of some properties of localized molecular orbitals

The localized molecular orbitals of some related ten- and eighteen-electron systems have been studied. The transferability of the kinetic, self-interaction, Coulomb and exchange interaction energies on localized orbitals have been shown. The standard deviation of the kinetic and of the interaction energies (including exchange) are less than 2.5% except for lone pair orbitals of the oxygen atoms where the standard deviation is close to 4%.     

Partial charges by multipole constraint. Application to the amino acids

Atom-centered partial charges which exactly reproduce the lowest several multipoles of a molecule's charge distribution can be obtained in a straightforward and convenient manner from the output of existing electronic structure calculations. The multipole constraint method is demonstrated by a computation of partial charges for the twenty common amino acids. The electron density employed here, derived from a semiempirical MNDO calculation, incorporates Slater-type orbitals which imbue it with the exponential fall-off vital to electronic tunneling calculations. In addition, a procedure based on these charges is described which divides the original electron density into two components, a large component with a simple electrostatic potential, and a much smaller residual whose several lowest multipoles vanish.     

Dyson orbitals for ionization from the ground and electronically excited states within equation-of-motion coupled-cluster formalism: theory, implementation, and examples

Implementation of Dyson orbitals for coupled-cluster and equation-of-motion coupled-cluster wave functions with single and double substitutions is described and demonstrated by examples. Both ionizations from the ground and electronically excited states are considered. Dyson orbitals are necessary for calculating electronic factors of angular distributions of photoelectrons, Compton profiles, electron momentum spectra, etc, and can be interpreted as states of the leaving electron. Formally, Dyson orbitals represent the overlap between an initial N-electron wave function and the N-1 electron wave function of the corresponding ionized system. For the ground state ionization, Dyson orbitals are often similar to the corresponding Hartree-Fock molecular orbitals (MOs); however, for ionization from electronically excited states Dyson orbitals include contributions from several MOs and their shapes are more complex. The theory is applied to calculating the Dyson orbitals for ionization of formaldehyde from the ground and electronically excited states. Partial-wave analysis is employed to compute the probabilities to find the ejected electron in different angular momentum states using the freestanding and Coulomb wave representations of the ionized electron. Rydberg states are shown to yield higher angular momentum electrons, as compared to valence states of the same symmetry. Likewise, faster photoelectrons are most likely to have higher angular momentum.     

On the use of isovalued surfaces to determine molecule shape and reaction pathways

Summary Novel insights into local molecule structure and reactivity can be gained from viewing isovalued surfaces of the molecular electron density, electrostatic potential and molecular orbitals rendered as colored, 3-D objects. For example, drawing positive and negative electrostatic isopotential surfaces partitions the molecule into regions subject to nucleophilic or electrophilic attack. Similarly, coloring isodensity surfaces to indicate the magnitude of the gradient of the electron density maps the molecule surface into regions of high and low electronegativity.A basic understanding of reaction mechanisms can also come from viewing and manipulating isovalued surfaces. A theory of molecular interactions, based upon second-order perturbation theory, provides for the decomposition of the intermolecular interaction energy into steric, electrostatic and orbital interactions. Color figures illustrate the docking of reactant molecular densities, electrostatic potentials and orbitals on low-energy pathways. The figures are used to visualize the steric, electrostatic and orbital contributions to molecular interaction energy. The visualization not only identifies low-energy reaction pathways, but it frequently reveals local interactions which determine the magnitude of the total interaction energy. Similar insight is not easily obtained by simple evaluation of the total interaction energy. Approximate transition states, built from structures along low-energy approach pathways, are excellent starting points for transition state searches.CAChe^TM Technical Report No. 1, Tektronix Inc., Beaverton, OR.     

Evaluation of the charge penetration energy between non-orthogonal molecular orbitals using the Spherical Gaussian Overlap approximation

An overlap dependent formula for evaluating the charge penetration energy between non-orthogonal molecular orbitals is derived using the Spherical Gaussian Overlap approximation. When combined with an accurate multipole representation of the electrostatic energy, such as in the effective fragment potential method, ab initio electrostatic energies are generally reproduced to within 0.2 kcal/mol for a variety of molecular dimers and basis sets. The only larger error is for the DMSO dimer, where the electrostatic energy is overestimated by 0.7 kcal/mol.     

Atomic orbitals in molecules: general electronegativity and improvement of Mulliken population analysis

An approach of atomic orbitals in molecules (AOIM) has been developed to study the atomic properties in molecules, in which the molecular orbitals are expressed in terms of the optimized minimal atomic orbitals. The atomic electronegativities are calculated using Pauling's electronegativity of free atom and are employed to find the electronegativity equilibrium in molecules and to describe the amphoteric properties of the transition metals from the groups 4 to 10. AOIM can also improve the numerical stability and accuracy of the original Mulliken population analysis.     

Hyperconjugation Is the Source of Helicity in Perfluorinated n-Alkanes

Hyperconjugative, steric, and electrostatic effects were evaluated as possible sources of the helicity in linear perfluorinated alkanes through analysis of natural bond orbitals and classical electrostatics. Contrary to previous rationalizations, which indicate dominating steric or electrostatic effects, this analysis indicates that hyperconjugative stabilization through σ_CC→σ*_CF interactions are the underlying driving force for the origin of the observed helicity in perfluoroalkanes.     

Hyperconjugation Is the Source of Helicity in Perfluorinated n‐Alkanes

Hyperconjugative, steric, and electrostatic effects were evaluated as possible sources of the helicity in linear perfluorinated alkanes through analysis of natural bond orbitals and classical electrostatics. Contrary to previous rationalizations, which indicate dominating steric or electrostatic effects, this analysis indicates that hyperconjugative stabilization through σ_CC→σ*_CF interactions are the underlying driving force for the origin of the observed helicity in perfluoroalkanes.     

Electrostatic isopotential maps for large biomolecules

A new method for the calculation of electrostatic isopotential maps, based on completely transferable bond orbitals, is proposed. According to the simple form of the potential term the amount of computational work is proportional to the first power of the number of valence electrons. Slater-type atomic orbitals are used to construct the bond orbitals, thus all integrals can be calculated explicitly. The subtilisin charge-relay system is studied as an example. It is found, in agreement with the results of Beppu and Yomosa, that the two protons transfer in a stepwise manner.     

Quantum chemical study of electronic and structural properties of retinal and some aromatic analogs

The electronic and structural properties of retinal and four analogs were studied using semiempirical, ab initio Hartree-Fock, and density functional theory methods with the aim to evaluate the effects caused by some structural modifications in the ring bound to the polyenic chain and compared with the all-E-trans-retinal molecule. Therefore, some properties such as bond lengths, bond angles, atomic charges derived from electrostatic potential charges from electrostatic potential using grid based method as well as frontier orbitals of the polyenic chain were analyzed. Furthermore, the transition energies of the molecules were also calculated using the Zerner's intermediate neglect of differential overlap-spectroscopic, time-dependent Hartree-Fock, and time-dependent density functional theory methods. The results indicate that in spite of the structural modifications of retinal derivatives in comparison with all-E-trans-retinal, their properties seem similar. Thus, these molecules may behave similarly to all-E-trans-retinal and possibly be attempted in the search of novel molecular devices.     

Comparative study of the electronic structure of pregnanolones by ab initio theory

Pregnanedione (5β‐pregnane, 3,20‐dione), pregnanolone (3β‐hydroxy‐5β‐pregnan‐20‐one), and epipregnanolone (3α‐hydroxy‐5β‐pregnan‐20‐one) result from the 5β‐reduction of progesterone [4‐pregnene, 3‐20‐dione (P)]. These P metabolites induce anesthesia and smooth muscle relaxation (nongenomic actions). In the present study, geometries and electronic structure of these steroids were assessed by ab initio calculations using the 6‐31G* basis set. Consequently, bond distances, valence angles, and dihedral angles were measured. In addition total energy, frontier orbitals, i.e., highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO), dipole moment, and electrostatic potentials were calculated. Total energy was higher for P, followed by pregnanedione. Pregnanolones, the hydroxylated progestins, showed the lower energies. Concerning frontier orbitals, P showed the highest HOMO energy and the lowest LUMO energy. Pregnanedione showed lower HOMO and LUMO energy values than pregnanolone and epipregnanolone. P showed both HOMO and LUMO located at the A ring, including the π bond at C4, C5, and the carbonyl at C3. The HOMO in pregnanedione was included mostly in the A ring and the C3 carbonyl group, while the LUMO was shared by the carbonyl groups at C3 and C20. The frontier orbitals of pregnanolone and epipregnanolone were quite similar. The HOMO in both steroids included the B, C, and D rings and the carbonyl at C20. The LUMO was also similar in both pregnanolones including mostly the carbonyl at C20. The dipole moment was shorter for P and pregnanedione and directed toward the acetyl side chain at C17. Pregnanolone and epipregnanolone showed the dipole moment vector larger and directed toward the A ring. The electrostatic potentials were related mostly with the lone pairs of electrons from the oxygens. By the total energy and frontier orbitals energies of the hormones studied, it is concluded that the metabolism of progesterone toward its 5β‐reduced metabolites might be rationalized from the theoretical chemistry point of view. Besides, the importance of the A/B ring cis configuration, dipole moment, and electrostatic potential are highlighted as possible improving elements of molecular interactions to explain the nongenomic biological action of 5β‐reduced progestins. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 433–440, 1999