Kaushik Hatua

Beryllium-Cyclobutadiene Multidecker Inverse Sandwiches: Electronic Structure and Second-Hyperpolarizability

Beryllium forms stable sandwich and inverse sandwich complexes with the cyclobutadiene molecule. Two types of multidecker complexes are designed. Multidecker inverse sandwiches are found to be thermally more stable than the corresponding sandwich complexes. The average distance between two consecutive metals and the two consecutive cyclobutadiene rings increase gradually on increasing size of the chosen inverse sandwich complexes. The density functional theory functionals B3LYP, BHHLYP, BLYP, M06, CAM-B3LYP, and B2PLYP in conjunction with the 6-311++G (d, p) basis set have been employed for calculating the third-order electric response properties of the chosen beryllium-cyclobutadiene complexes and the results obtained for each functional are found to have a consistent trend. Compared to the normal sandwich compounds the second-hyperpolarizability of inverse sandwiches is predicated to be larger, which fairly correlates with the extent of ground-state polarization. The significant enhancement of cubic polarizability of higher-order multidecker inverse sandwiches arises from the strong coupling between the ground and the low lying charge transfer excited states. The rather strong enhancement of second-hyperpolarizability on increasing size of the beryllium-multidecker inverse sandwiches may provide a new route to design efficient nonlinear optical materials.

RELATIONSHIPS BETWEEN DIFFERENT-ORDER POLARIZABILITIES AND GROUND STATE DIPOLE MOMENT

A number of charge transferring molecules with varying electron donor, acceptor and π-conjugative paths have been considered for the theoretical study of their NLO properties in terms of the linear polarizability and the ground state dipole moment. The equilibrium structures are calculated at the HF, MP2 and B3LYP levels, respectively. The longitudinal components of NLO coefficients are calculated by using HF, MP2, B3LYP, BHHLYP, CAM-B3LYP, and wB97XD methods for 6-31+G(p,d) and 6-311++G(p,d) basis sets. The hyperpolarizabilities obtained at different levels of calculation showed a fairly consistent trend. The relationships between hyperpolarizabilities, polarizability and ground state dipole moment have been proposed by considering only the two-level term in the standard sum-over-state (SOS) expressions and the generalized Thomas–Kuhn (TK) sum rule. The ab initio calculated first- and second-hyperpolarizabilities fairly correlate with the reduced 2-level contributions relating to the linear polarizability and ground state dipole moment. For a given length of conjugation the stronger enhancement of cubic polarizability arises from the increase of quadratic polarizability for comparable values of linear polarizability and dipole moment. The idea developed in the present work can be used to make a rational design of potential NLO-phores.

Double coned inverse sandwich complexes [M-(η4-C4H4)-M′] of Gr-IA and Gr-IIA Metals: theoretical study of electronic of structure and second hyperpolarizability

Double coned inverse sandwich complexes of Gr-IA and Gr-IIA metals have been considered for the theoretical study of electronic structure and second hyperpolarizability by employing density functional theory methods for different exchange and correlation functionals. For the investigated metal complexes the 6-311++G(d,p) basis set can give reliable values of NLO property. The chosen complexes are found to be thermally stable with respect to the dissociation into neutral fragments. Interesting charge transfer interaction has been noted. The replacement of a lighter metal atom with a heavier one leads to the significant enhancement of the longitudinal component of second hyperpolarizability. The relatively much stronger enhancement of second hyperpolarizability has been noted for the alkaline earth metal complexes compared to that of alkali metals. The emergence of second hyperpolarizability of alkali/alkaline earth metal inverse sandwich complexes can be explained qualitatively in terms of the two-state model. The largest magnitude of second hyperpolarizability (~107 au) has been predicted for the Ca-C4H4-Ca complex which may be ascribed to the smallest transition energy and the highest transition moment associated with the most intense linear transition.

Computational insight of the mechanism of Algar–Flynn–Oyamada (AFO) reaction

The present DFT investigation supports a previous conclusion of Dean et al. that hydroxylation occurs without epoxide intermediate at room temperature due to a strong electrostatic interaction of peroxide ions with π electrons of CC bonds of chalcone, and 3-hydroxyflavone has been found to be the major product. The calculated activation energy difference (ΔG#) of initial enolization followed by hydroxylation or simultaneous cyclization and hydroxylation has been found to be negligible (∼4 kcal mol−1). On the other hand, epoxide formation requires significant activation energy, which is supposed to occur at high temperatures. In addition, if epoxide is formed, the ring opens by an attack of phenolic oxygen, occurring preferentially at α position via a five-member transition state due to a low activation barrier height (19.82 kcal mol−1 in the gas phase and 19.55 kcal mol−1 in ethanol) compared to that of a six-member transition state (44.41 kcal mol−1 at B3LYP in the gas phase and 38.55 kcal mol−1 in ethanol). It is also observed that the solvation study does not affect the main conclusion of the paper. These findings also support the previous observation of Dean et al. Predicted ΔG# in different DFT functionals are consistent, although the total energy is significantly different.

INTERACTION OF BERYLLIUM WITH ACCEPTOR HYDROCARBONS: ELECTRONIC STRUCTURE AND SECOND HYPERPOLARIZABILITY

Some selected acceptor-Be hydrocarbon complexes have been considered for evaluation of second hyperpolarizability at different DFT functional. All the complexes have been found thermally stable and there is a significant increase of second hyperpolarizability compared to the ligands. Second hyperpolarizability has been explained in terms of charge transfer interaction. Co-operative interaction is required for maximization of second hyperpolarizability. Localized charge transfer in the vicinity of metal alone cannot increase second hyperpolarizability while charge delocalization over entire molecule is mandatory. Substitution by more electropositive metals e.g. Mg, Ca have greater enhancement in longitudinal component of γ. Basis set 6-311++G** is reasonable with respect to computational cost at aug-cc-pVnZs (n = D, T, Q) for evaluation of second hyperpolarizability for the present complexes.

Third-order NLO property of beryllium-pyridyne complexes

Six pyridyne isomers and their complexes with beryllium have been considered for the theoretical study of the third-order polarizability. The NLO properties are calculated by employing the DFT functionals BLYP, B3LYP, BHHLYP, B3PW91, BP86 and B2PLYP for the 6-311++G(d,p) basis set. The C-Be bond length in the complexes varies within 1.644 A–1.771 A indicating covalent interactions between the metal and pyridynes. The present investigation reveals that the magnitude of second-hyperpolarizability of pyridynes strongly enhances upon complex formation with beryllium. The maximum hyperpolarizability has been predicted for the 2,5-diberyllium pyridine complex. The lowest value of hyperpolarizability is obtained for the 2,3- and 3,4-diberyllium pyridine complexes. The chosen DFT methods predict almost identical pattern of variation of NLO property. The variation of second-hyperpolarizability has been satisfactorily explained by the excitation energy and transition dipole moment associated with the most dominant excited state.

Second hyperpolarizability of multimetallocenes [Cp–Mn–Cp] of Be, Mg and Ca

Multimetallocene complexes (Cp–Mn–Cp) of Be, Mg and Ca have been considered for the theoretical study of static second hyperpolarizability using a number of DFT functionals. Owing to the cooperative effect in bonding, beryllium forms multiberyllocene complexes (Cp–Ben–Cp) which have sufficient thermal stability with respect to dissociation into neutral fragments up to n = 10. On the other hand, multimetallocene complexes of Mg and Ca are found to be stable for n ≤ 5 which may be due to the weaker covalent bonding interaction between the larger metal atoms. The rather small variation of linear and cubic polarizabilities of Cp–Ben–Cp complexes beyond n = 5 arises from the rather weaker charge transfer transitions. The difference in NLO property among the investigated metal complexes arises from the extent of charge transfer from the terminal metal atoms and the distance between them. The charge transfer at longer distances in the ground state of Mg and Ca complexes leads to more intense electronic transition — the spectroscopic parameters of which strongly favors the enhancement of second hyperpolarizability.

Second hyperpolarizability of delta shaped disubstituted acetylene complexes of beryllium, magnesium, and calcium.

Present theoretical study involves the delta shape complexes of beryllium, magnesium, and calcium where the metal atom interacts perpendicularly with disubstituted acetylene. Most of the complexes are found to be fairly stable. The dependence of second-hyperpolarizability on the basis set with increasing polarization and diffuse functions has been examined which showed the importance of ‘f-type’ type polarization function for heavy metal (Mg, Ca) and ‘d-type’ polarization function for beryllium. Larger second hyperpolarizability has been predicted for complexes having significant ground state polarization and low lying excited states favoring strong electronic coupling. Transition energy plays the most significant role in modulating the second hyperpolarizability.

Static second hyperpolarizability of twisted ethylene: A comprehensive computational study

Twisted conformations of ethylene molecule have diradical character and the second hyperpolarizability of these conformations is best described by the multiconfigurational self consistence field theory (MCSCF) wave function. Present calculation indicates that unrestricted density functional theory (UDFT) predicts second hyperpolarizability which is qualitatively correct for the intermediate diradical region. However, for the two extremities, i.e. rear diradical region and near diradical region, the second hyperpolarizability obtained by UDFT methods differ significantly from the MRCISD result. The BHHLYP and LC-BLYP (μ=0.47) results of γxxxx are found to be in good agreement with the MRCISD result. Using the spin-projected UDFT methods almost similar results are obtained. The reasonably fair agreement between the calculated results of second hyperpolarizability obtained at the MRCISD and CASSCF(4,4) levels demonstrates that static electron correlation is the dominant feature of twisted ethylene.

Static second hyperpolarizability of Λ shaped alkaline earth metal complexes

A number of Λ shaped complexes of alkaline earth metals Be, Mg and Ca with varying terminal groups have been considered for the theoretical study of their second hyperpolarizability. The chosen complexes are found to be sufficiently stable and for a chosen ligand the stability decreases in the order: Be-complex > Ca-complex > Mg-complex. The calculated results of second hyperpolarizability obtained at different DFT functionals for the 6-311++G(d,p) basis set are found to be fairly consistent. The Λ shaped ligands upon complex formation with metals lead to strong enhancement of second hyperpolarizability. The highest magnitude of cubic polarizability has been predicted for the metal complex having > C(C2H5)2 group. For a chosen ligand, the magnitude of second hyperpolarizability increases in the order Be-complex < Mg-complex < Ca-complex which is the order of increasing size and electropositive character of the metal. The variation of second hyperpolarizability among the investigated metal complexes has been explained in terms of the transition energy and transition moment associated with the most intense electronic transition.