Conical parametric scattering of a single extraordinary beam in BaTiO3 crystal

In this paper, the parametric scattering of a single extraordinary polarized beam of laser in BaTiO₃ photorefractive crystal has been investigated experimentally and theoretically. The resulting pattern consists of beam fanning, isotropic ring, and anisotropic one. Among all parts of scattering pattern, isotropic ring has not been studied as much as beam fanning and anisotropic ring, and there still are some differences in reports about it. Therefore, the study has mainly focused on this part. In this experimental configuration, isotropic ring is just visible in positive angles although the other parts of parametric scattering pattern can be visible from behind and in front of the crystal. In addition to steady state pattern in forward and backward directions, its transient behavior with the rotation of crystal has been studied. The results of experiments have been analyzed carefully, and their theoretical explanations have been presented based on the standard theory of parametric scattering in photorefractive crystals. It has been shown that this configuration corresponds to the so called parametric B-process scattering.     

Maximization of atomic information-entropy sum in configuration and momentum spaces

The maximum entropy procedure (MEP ) of Jaynes has been extended to the case involving constraints in complementary spaces. It has been rigorously shown that the sum of information entropies in position and momentum spaces is invariant to uniform scaling of the electron coordinates. A new MEP procedure requires that this sum of entropies must be maximized subject to the known constraints in both spaces. A specific application of this maximization procedure for synthesizing atomic-electron densities in coordinate and momentum spaces has been outlined.     

Tailoring approach for exploring electron densities and electrostatic potentials of molecular crystals

Experimental and theoretical studies of electron densities and the corresponding derived entities such as electrostatic potentials have been the primary means of understanding the chemical nature and electronic properties of crystalline substances. Conventional crystal calculation methods such as the embedded cluster models are capable of performing calculations on small and medium-sized molecules, while periodic ab initio methods can treat crystals with up to 200 atoms per unit cell. A linear scaling method, viz. the molecular tailoring approach, has recently been developed for obtaining ab initio quality one-electron properties. In the present study, the molecular tailoring approach is employed to generate electron density, electrostatic potential and interaction density maps with the ibuprofen crystal as a test case. The interaction density and electrostatic potential maps produced in the present work succinctly bring out the actual crystalline environment around a given reference molecule by including the interactions with atoms in its neighborhood. The results obtained from the molecular tailoring approach may thus be expected to enhance our understanding of the environment in the crystalline material with reasonably small computational effort.Contribution to the Jacopo Tomasi Honorary Issue     

The cyclodimerisation of 3-methyl-2-butenenitrile

3-Methyl-2-butenenitrile (1) cyclodimerised on treatment with lithium diisopropylamide in dimethoxyethane at temperatures between ?78°C and 0°C to 3-amino-4-cyano-1,5,5-trimethyl-1,3-cyclohexadiene (2) the structure of which was established by acid hydrolysis to the known 4-cyano-1,5,5-trimethyl-1-cyclohexene-3-one (3).     

Structure, reactivity and aromaticity of acenes and their BN analogues: a density functional and electrostatic investigation

Density functional calculations have been carried out on a series of linearly annelated acenes and their BN analogues. Even though borazine shows aromatic and reactivity behavior parallel with that of benzene, its condensed derivatives show patterns different from those of their hydrocarbon analogues. Nucleus independent chemical shift (NICS) values in acenes suggest that the aromaticity of the inner rings is more than that of benzene, whereas in BN-acenes there is no substantial change in the aromaticity of the individual rings. Molecular electrostatic potential (MESP) is employed to obtain further insights into the bonding and reactivity trends for these systems. The MESP topography patterns of acenes and BN-acenes are substantially different, with BN-acenes showing more localized pi electron features compared to those of acenes. The MESP values at the critical points (CPs) indicate overall lowering of aromaticity in these annelated systems. However, this change is gradual among the BN-acenes.     

Intramolecular hydrogen bond energy in polyhydroxy systems: a critical comparison of molecular tailoring and isodesmic approaches

The intramolecular hydrogen bond (H-bond) energies in several polyhydroxy systems are estimated using an isodesmic/homodesmic reaction approach as well as a molecular tailoring approach (MTA) [Deshmukh, M. M.; Gadre, S. R.; Bartolotti, L. J. J. Phys. Chem. A 2006, 110, 12519]. It is shown that the isodesmic/homodesmic reaction approach as advocated in the literature does not give true H-bond energy but includes the effect of strain energy due to the formation of a ring structure. Such a ring strain is duly accounted for in the MTA method. The isodesmic H-bond energies are found to be smaller than their MTA energy counterparts typically by the strain energy. The MTA is applied to decitol, a system with more than five different H-bonds for which an application of an appropriate isodesmic reaction is extremely difficult. It has been shown that the MTA method is able to predict not only the H-bond energies but also the trends in conformational energies for three different conformers of decitol studied in the present work.     

Atoms-in-molecules in momentum space: a Hirshfeld partitioning of electron momentum densities

A direct application of the Hirshfeld atomic partitioning (HAP) scheme is implemented for molecular electron momentum densities (EMDs). The momentum density contributions of individual atoms in diverse molecular systems are analyzed along with their topographical features and the kinetic energies of the atomic partitions. The proposed p-space HAP-based charge scheme does seem to possess the desirable attributes expected of any atoms in molecules partitioning. In addition to this, the main strength of the p-space HAP is the exact knowledge of the kinetic energy functional and the inherent ease in computing the kinetic energy. The charges derived from HAP in momentum space are found to match chemical intuition and the generally known chemical characteristics such as electronegativity, etc.     

Use of molecular electrostatic potential for quantitative assessment of inductive effect

Density functional theory computations at the B3LYP/6-31G(d,p) level have been carried out for three types of model compounds, viz. (i) 4-substituted bicyclo[2.2.2]octane carboxylic acids, (ii) anions of 4-substituted bicyclo[2.2.2]octane carboxylic acids and (iii) 4-substituted quinuclidines where the substituents are NO(2), CN, Cl, Br, CF(3), F, CHO, CH(2)Cl, COOH, COCH(3), CONH(2), OH, OCH(3), C(6)H(5), NH(2), H, CH(3), CH(2)CH(3), CH(CH(3))(2), and C(CH(3))(3) to study the dependencies between molecular electrostatic potential minimum (V(min)) and the inductive substituent constant sigma(I). All the three model systems show excellent linear correlation between V(min) and sigma(I) suggesting that the calculation of V(min) parameter in these systems offers a simple and efficient computational approach for the evaluation of inductive substituent constants. The calculated linear equation for the models (i), (ii), and (iii) are V(min) = 12.982 sigma(I)- 48.867, V(min) = 13.444 sigma(I)- 182.760, and V(min) = 18.100 sigma(I)- 65.785, respectively. Considering the simplicity of the quinuclidine model, V(min) value at the nitrogen lone pair region of a 4-substituted quinuclidine system is recommended for the evaluation of sigma(I). Further, the additivity effect of sigma(I) is tested on multiply substituted quinuclidine and bicyclo[2.2.2]octane carboxylic acid derivatives using the V(min) approach and the results firmly supported the additivity rule of inductive effect. The systems showing considerable deviations from the additivity rule are easily recognized as those showing either steric effect or intramolecular hydrogen bond interactions at the V(min) response site. However, the distance relation of sigma(I) is not well represented in the caged molecular systems.     

Refinement of electron momentum densities of ionic solids using an experimental energy constraint

It is demonstrated how one can refine a given approximate momentum density distribution using a constraint of the experimental electronic energy. The technique developed is based on the calculus of variations. This technique has been applied to ionic solids such as LiF, LiCIl NaF, NACl, MgO, KF and KCl.