The effect of halogen atom on the molecular quadratic nonlinearity of half sandwich complexes in the presence of an acceptor

Half sandwich complexes of the type [CpM(CO)(n)X] {X=Cl, Br, I; If, M=Fe, Ru; n=2 and if M=Mo; n=3} and [CpNiPPh3X] {X=Cl, Br, I} have been synthesized and their second order molecular nonlinearity (beta) measured at 1064 nm in CHCl3 by the hyper-Rayleigh scattering technique. Iron complexes consistently display larger beta values than ruthenium complexes while nickel complexes have marginally larger beta values than iron complexes. In the presence of an acceptor ligand such as CO or PPh3, the role of the halogen atom is that of a pi donor. The better overlap of Cl orbitals with Fe and Ni metal centres make Cl a better pi donor than Br or I in the respective complexes. Consequently, M-pi interaction is stronger in Fe/Ni-Cl complexes. The value of beta decreases as one goes down the halogen group. For the complexes of 4d metal ions where the metal-ligand distance is larger, the influence of pi orbital overlap appears to be less important, resulting in moderate changes in beta as a function of halogen substitution. (C) 2006 Elsevier B.V. All rights reserved.

Mono(Eta(5)-cyclopentadienyl)metal(II) complexes with thienyl acetylide chromophores: synthesis, electrochemical studies, and first hyperpolarizabilities

A series of mono(eta(5)-cyclopentadienyl)metal-(II) complexes with nitro-substituted thienyl acetylide ligands of general formula [M(eta(5)-C5H5)(L)(C C{C4H2S}(n)NO2)] (M = Fe, L = kappa(2)-DPPE, n = 1,2; M = Ru, L = kappa(2)-DPPE, 2 PPh3, n = 1, 2; M = Ni, L = PPh3, n = 1, 2) has been synthesized and fully characterized by NMR, FT-IR, and UV-Vis spectroscopy. The electrochemical behavior of the complexes was explored by cyclic voltammetry. Quadratic hyperpolarizabilities (beta) of the complexes have been determined by hyper-Rayleigh scattering (HRS) measurements at 1500 nm. The effect of donor abilities of different organometallic fragments on the quadratic hyperpolarizabilities was studied and correlated with spectroscopic and electrochemical data. Density functional theory (DFT) and time-dependent DFT (TDDFT) calculations were employed to get a better understanding of the second-order nonlinear optical properties in these complexes. In this series, the complexity of the push pull systems is revealed; even so, several trends in the second-order hyperpolarizability can still be recognized. In particular, the overall data seem to indicate that the existence of other electronic transitions in addition to the main MLCT clearly controls the effectiveness of the organometallic donor ability on the second-order NLO properties of these push pull systems.

Quadratic Nonlinearity of One- and Two-Electron Oxidized Metalloporphyrins and Their Switching in Solution

We report the quadratic nonlinearity of one- and two-electron oxidation products of the first series of transition metal complexes of meso-tetraphenylporphyrin (TPP). Among many MTPP complexes, only CuTPP and ZnTPP show reversible oxidation/reduction cycles as seen from cyclic voltammetry experiments. While centrosymmetric neutral metalloporphyrins have zero first hyperpolarizability, β, as expected, the cation radicals and dications of CuTPP and ZnTPP have very high β values. The one- and two-electron oxidation of the MTPPs leads to symmetry-breaking of the metal−porphyrin core, resulting in a large β value that is perhaps aided in part by contributions from the two-photon resonance enhancement. The calculated static first hyperpolarizabilities, β0, which are evaluated in the framework of density functional theory by a coupled perturbed Hartree−Fock method, support the experimental trend. The switching of optical nonlinearity has been achieved between the neutral and the one-electron oxidation products but not between the one- and the two-electron oxidation products since dications that are electrochemically reversible are unstable due to the formation of stable isoporphyrins in the presence of nucleophiles such as halides.

Numerically Exact Study of Polarizabilities and Hyperpolarizabilities of Correlated Conjugated Organic Models

Polarizabilities and Hyperpolarizabilities of conjugated organic chains are calculated using correlated model Hamiltonians. While correlations reduce the Polarizabilities and extend the range of linear response, the Hyperpolarizabilities essentially are unaffected by the same. This explains the apparently large Hyperpolarizabilities of conjugated electronic systems.

NDDO-based CI methods for the prediction of electronic spectra and sum-over-states molecular hyperpolarization

NDDO-based (AM1) configuration interaction (CI) calculations have been used to calculate the wavelength and oscillator strengths of electronic absorptions in organic molecules and the results used in a sum-over-states treatment to calculate second-order-hyperpolarizabilities. The results for both spectra and hyperpolarizabilities are of acceptable quality as long as a suitable CI-expansion is used. We have found that using an active space of eight electrons in eight orbitals and including all single and pair-double excitations in the CI leads to results that agree well with experiment and that do not change significantly with increasing active space for most organic molecules. Calculated second-order hyperpolarizabilities using this type of CI within a sum-over-states calculation appear to be of useful accuracy.

Geometry and quadratic nonlinearity of charge transfer complexes in solution using depolarized hyper-Rayleigh scattering

We report large quadratic nonlinearity in a series of 1:1 molecular complexes between methyl substituted benzene donors and quinone acceptors in solution. The first hyperpolarizability, beta(HRS), which is very small for the individual components, becomes large by intermolecular charge transfer (CT) interaction between the donor and the acceptor in the complex. In addition, we have investigated the geometry of these CT complexes in solution using polarization resolved hyper-Rayleigh scattering (HRS). Using linearly (electric field vector along X direction) and circularly polarized incident light, respectively, we have measured two macroscopic depolarization ratios D = I-2 omega,I-X,I-X/I-2 omega,I-Z,I-X and D' = I-2 omega,I-X,I-C/I-2 omega,I-Z,I-C in the laboratory fixed XYZ frame by detecting the second harmonic scattered light in a polarization resolved fashion. The experimentally obtained first hyperpolarizability, beta(HRS), and the value of macroscopic depolarization ratios, D and D', are then matched with the theoretically deduced values from single and double configuration interaction calculations performed using the Zerner's intermediate neglect of differential overlap self-consistent reaction field technique. In solution, since several geometries are possible, we have carried out calculations by rotating the acceptor moiety around three different axes keeping the donor molecule fixed at an optimized geometry. These rotations give us the theoretical beta(HRS), D and D' values as a function of the geometry of the complex. The calculated beta(HRS), D, and D' values that closely match with the experimental values, give the dominant equilibrium geometry in solution. All the CT complexes between methyl benzenes and chloranil or 1,2-dichloro-4,5-dicyano-p-benzoquinone investigated here are found to have a slipped parallel stacking of the donors and the acceptors. Furthermore, the geometries are staggered and in some pairs, a twist angle as high as 30 degrees is observed. Thus, we have demonstrated in this paper that the polarization resolved HRS technique along with theoretical calculations can unravel the geometry of CT complexes in solution. (C) 2011 American Institute of Physics. doi:10.1063/1.3514922]

Geometry and quadratic nonlinearity of charge transfer complexes in solution: A theoretical study

In this paper, we have computed the quadratic nonlinear optical (NLO) properties of a class of weak charge transfer (CT) complexes. These weak complexes are formed when the methyl substituted benzenes (donors) are added to strong acceptors like chloranil (CHL) or di-chloro-di-cyano benzoquinone (DDQ) in chloroform or in dichloromethane. The formation of such complexes is manifested by the presence of a broad absorption maximum in the visible range of the spectrum where neither the donor nor the acceptor absorbs. The appearance of this visible band is due to CT interactions, which result in strong NLO responses. We have employed the semiempirical intermediate neglect of differential overlap (INDO/S) Hamiltonian to calculate the energy levels of these CT complexes using single and double configuration interaction (SDCI). The solvent effects are taken into account by using the self-consistent reaction field (SCRF) scheme. The geometry of the complex is obtained by exploring different relative molecular geometries by rotating the acceptor with respect to the fixed donor about three different axes. The theoretical geometry that best fits the experimental energy gaps, beta(HRS) and macroscopic depolarization ratios is taken to be the most probable geometry of the complex. Our studies show that the most probable geometry of these complexes in solution is the parallel displaced structure with a significant twist in some cases. (C) 2011 American Institute of Physics. doi:10.1063/1.3526748]

First-order hyperpolarizabilities of octupolar aromatic molecules: symmetrically substituted triazines

The first hyperpolarizabilities of some symmetrically substituted triazines have been measured and compared with those of the corresponding symmetrically substituted benzenes. The octupolar triazines have higher quadratic polarizabilities than the corresponding octupolar benzenes. The triazine ring seems to be a better central acceptor than the benzene ring, but if it acts as a donor as in sym-triphenyl triazine, the nonlinearity improves further.

Photographic investigations in molecular spectroscopy

The determination of the energy levels and the probabilities of transition between them, by the formal analysis of observed electronic, vibrational, and rotational band structures, forms the direct goal of all investigations of molecular spectra, but the significance of such data lies in the possibility of relating them theoretically to more concrete properties of molecules and the radiation field. From the well developed electronic spectra of diatomic molecules, it has been possible, with the aid of the non-relativistic quantum mechanics, to obtain accurate moments of inertia, molecular potential functions, electronic structures, and detailed information concerning the coupling of spin and orbital angular monenta with the angular momentum of nuclear rotation. The silicon fluori1e molecule has been investigated in this laboratory, and is found to emit bands whose vibrational and rotational structures can be analyzed in this detailed fashion.

Like silicon fluoride, however, the great majority of diatomic molecules are formed only under the unusual conditions of electrical discharge, or in high temperature furnaces, so that although their spectra are of great theoretical interest, the chemist is eager to proceed to a study of polyatomic molecules, in the hope that their more practically interesting structures might also be determined with the accuracy and assurance which characterize the spectroscopic determinations of the constants of diatomic molecules. Some progress has been made in the determination of molecule potential functions from the vibrational term values deduced from Raman and infrared spectra, but in no case can the calculations be carried out with great generality, since the number of known term values is always small compared with the total number of potential constants in even so restricted a potential function as the simple quadratic type. For the determination of nuclear configurations and bond distances, however, a knowledge of the rotational terms is required. The spectra of about twelve of the simpler polyatomic molecules have been subjected to rotational analyses, and a number of bond distances are known with considerable accuracy, yet the number of molecules whose rotational fine structure has been resolved even with the most powerful instruments is small. Consequently, it was felt desirable to investigate the spectra of a number of other promising polyatomic molecules, with the purpose of carrying out complete rotational analyses of all resolvable bands, and ascertaining the value of the unresolved band envelopes in determining the structures of such molecules, in the cases in which resolution is no longer possible. Although many of the compounds investigated absorbed too feebly to be photographed under high dispersion with the present infrared sensitizations, the location and relative intensities of their bands, determined by low dispersion measurements, will be reported in the hope that these compounds may be reinvestigated in the future with improved techniques.

On the required shape corrections to the local density and generalized gradient approximations to the Kohn-Sham potentials for molecular response calculations of (hyper)polarizabilities and excitation energies

It is well known that shape corrections have to be applied to the local-density (LDA) and generalized gradient (GGA) approximations to the Kohn-Sham exchange-correlation potential in order to obtain reliable response properties in time dependent density functional theory calculations. Here we demonstrate that it is an oversimplified view that these shape corrections concern primarily the asymptotic part of the potential, and that they affect only Rydberg type transitions. The performance is assessed of two shape-corrected Kohn-Sham potentials, the gradient-regulated asymptotic connection procedure applied to the Becke-Perdew potential (BP-GRAC) and the statistical averaging of (model) orbital potentials (SAOP), versus LDA and GGA potentials, in molecular response calculations of the static average polarizability alpha, the Cauchy coefficient S-4, and the static average hyperpolarizability beta. The nature of the distortions of the LDA/GGA potentials is highlighted and it is shown that they introduce many spurious excited states at too low energy which may mix with valence excited states, resulting in wrong excited state compositions. They also lead to wrong oscillator strengths and thus to a wrong spectral structure of properties like the polarizability. LDA, Becke-Lee-Yang-Parr (BLYP), and Becke-Perdew (BP) characteristically underestimate contributions to alpha and S-4 from bound Rydberg-type states and overestimate those from the continuum. Cancellation of the errors in these contributions occasionally produces fortuitously good results. The distortions of the LDA, BLYP, and BP spectra are related to the deficiencies of the LDA/GGA potentials in both the bulk and outer molecular regions. In contrast, both SAOP and BP-GRAC potentials produce high quality polarizabilities for 21 molecules and also reliable Cauchy moments and hyperpolarizabilities for the selected molecules. The analysis for the N-2 molecule shows, that both SAOP and BP-GRAC yield reliable energies omega(i) and oscillator strengths f(i) of individual excitations, so that they reproduce well the spectral structure of alpha and S-4.(C) 2002 American Institute of Physics.

Exchange potential from the common energy denominator approximation for the Kohn-Sham Green's function: Application to (hyper)polarizabilities of molecular chains

An approximate Kohn-Sham (KS) exchange potential v(xsigma)(CEDA) is developed, based on the common energy denominator approximation (CEDA) for the static orbital Green's function, which preserves the essential structure of the density response function. v(xsigma)(CEDA) is an explicit functional of the occupied KS orbitals, which has the Slater v(Ssigma) and response v(respsigma)(CEDA) potentials as its components. The latter exhibits the characteristic step structure with "diagonal" contributions from the orbital densities \psi(isigma)\(2), as well as "off-diagonal" ones from the occupied-occupied orbital products psi(isigma)psi(j(not equal1)sigma). Comparison of the results of atomic and molecular ground-state CEDA calculations with those of the Krieger-Li-Iafrate (KLI), exact exchange (EXX), and Hartree-Fock (HF) methods show, that both KLI and CEDA potentials can be considered as very good analytical "closure approximations" to the exact KS exchange potential. The total CEDA and KLI energies nearly coincide with the EXX ones and the corresponding orbital energies epsilon(isigma) are rather close to each other for the light atoms and small molecules considered. The CEDA, KLI, EXX-epsilon(isigma) values provide the qualitatively correct order of ionizations and they give an estimate of VIPs comparable to that of the HF Koopmans' theorem. However, the additional off-diagonal orbital structure of v(xsigma)(CEDA) appears to be essential for the calculated response properties of molecular chains. KLI already considerably improves the calculated (hyper)polarizabilities of the prototype hydrogen chains H-n over local density approximation (LDA) and standard generalized gradient approximations (GGAs), while the CEDA results are definitely an improvement over the KLI ones. The reasons of this success are the specific orbital structures of the CEDA and KLI response potentials, which produce in an external field an ultranonlocal field-counteracting exchange potential. (C) 2002 American Institute of Physics.

Additional compact formulas for vibrational dynamic dipole polarizabilities and hyperpolarizabilities

Compact expressions, complete through second order in electrical and/or mechanical anharmonicity, are given for the dynamic dipole vibrational polarizability and dynamic first and second vibrational hyperpolarizabilities. Certain contributions not previously formulated are now included

Simple finite field method for calculation of static and dynamic vibrational hyperpolarizabilities: curvature contributions

In the static field limit, the vibrational hyperpolarizability consists of two contributions due to: (1) the shift in the equilibrium geometry (known as nuclear relaxation), and (2) the change in the shape of the potential energy surface (known as curvature). Simple finite field methods have previously been developed for evaluating these static field contributions and also for determining the effect of nuclear relaxation on dynamic vibrational hyperpolarizabilities in the infinite frequency approximation. In this paper the finite field approach is extended to include, within the infinite frequency approximation, the effect of curvature on the major dynamic nonlinear optical processes

Finite field treatment of vibrational polarizabilities and hyperpolarizabilities: on the role of the Eckart conditions, their implementation, and their use in characterizing key vibrations

In the finite field (FF) treatment of vibrational polarizabilities and hyperpolarizabilities, the field-free Eckart conditions must be enforced in order to prevent molecular reorientation during geometry optimization. These conditions are implemented for the first time. Our procedure facilities identification of field-induced internal coordinates that make the major contribution to the vibrational properties. Using only two of these coordinates, quantitative accuracy for nuclear relaxation polarizabilities and hyperpolarizabilities is achieved in π-conjugated systems. From these two coordinates a single most efficient natural conjugation coordinate (NCC) can be extracted. The limitations of this one coordinate approach are discussed. It is shown that the Eckart conditions can lead to an isotope effect that is comparable to the isotope effect on zero-point vibrational averaging, but with a different mass-dependence

Determination of vibrational polarizabilities and hyperpolarizabilities using field-induced coordinates

An analytical set of field-induced coordinates is defined and is used to show that the vibrational degrees of freedom required to completely describe nuclear relaxation polarizabilities and hyperpolarizabilities is reduced from 3N-6 to a relatively small number. As this number does not depend upon the size of the molecule, the process provides computational advantages. A method is provided to separate anharmonic contributions from harmonic contributions as well as effective mechanical from electrical anharmonicity. The procedures are illustrated by Hartree-Fock calculations, indicating that anharmonicity can be very important