Benoı̂t Champagne

Assessment of conventional density functional schemes for computing the polarizabilities and hyperpolarizabilities of conjugated oligomers: An ab initio investigation of polyacetylene chains

DFT schemes based on conventional and less conventional exchange-correlation (XC) functionals have been employed to determine the polarizability and second hyperpolarizability of π-conjugated polyacetylene chains. These functionals fail in one or more of several ways: (i) the correlation correction to α is either much too small or in the wrong direction, leading to an overestimate; (ii) γ is significantly overestimated; (iii) the chain length dependence is excessively large, particularly for γ and for the more alternant system; and (iv) the bond length alternation effects on γ are either underestimated or qualitatively incorrect. The poor results with the asymptotically correct van Leeuwen–Baerends XC potential show that the overestimations are not related to the asymptotic behavior of the potential. These failures are described in terms of the separate effects of the exchange and the correlation parts of the XC functionals. They are related to the short-sightedness of the XC potentials which are relatively insensitive to the polarization charge induced by the external electric field at the chain ends.

Synthesis and Characterization of Teranthene: A Singlet Biradical Polycyclic Aromatic Hydrocarbon Having Kekulé Structures

A teranthene derivative has been successfully isolated in a crystalline form for the first time. Geometrical considerations and physical property investigations indicate that the molecule possesses prominent biradical character in the ground state.

Ab initio investigation of doping-enhanced electronic and vibrational second hyperpolarizability of polyacetylene chains

The effect of charging on the longitudinal second hyperpolarizability of polyacetylene (PA) chains containing up to nearly 70 carbon atoms has been investigated ab initio by characterizing chains with and without an explicit alkali atom (Li, Na, K) as dopant. Whereas charging dramatically enhances the static electronic and vibrational hyperpolarizabilities, γLe(0) and γLv, of an isolated chain at intermediate chain lengths, the presence of an alkali atom counterion substantially reduces this effect. As the size of the alkali atom increases, most properties, including the hyperpolarizabilities, approach those of the isolated chain. Detailed analysis shows that the behavior of γLe(0) is most simply explained in terms of a reduced electrostatic pinning potential due to increased distance between chain and counterion. At all chain lengths studied γLe(0) of PA is enhanced by alkali doping. For chains containing 50 carbon atoms (NC=50), the increase due to K doping is about 9×107 a.u., which more than doubles t...

Relationship between static vibrational and electronic hyperpolarizabilities of π-conjugated push–pull molecules within the two-state valence-bond charge-transfer model

The two-state valence-bond charge-transfer (VB-CT) model for π-conjugated push–pull molecules is analyzed to yield several parameter-independent relations between vibrational and electronic hyperpolarizabilities. Ab initio computational tests show that these relations are not satisfied. As a byproduct of the ab initio calculations, we have found cases where the static vibrational first hyperpolarizability is much larger than the static electronic first hyperpolarizability. Our results also shed light on a controversy regarding normal coordinate polarizability derivatives.

Differences between the exact sum-over-states and the canonical approximation for the calculation of static and dynamic hyperpolarizabilities

When molecules are subjected to static or dynamic uniform electric fields the effects are conveniently described in terms of dipole polarizabilities and hyperpolarizabilities. The fields act on both the electronic and vibrational motions simultaneously and, through perturbation theory, this leads to the exact sum-over-states (SOS) formulas for the (hyper) polarizabilities expressed in terms of vibronic states. As an approximation, the fields can be considered to act on the electronic motions first and subsequently, through the distorted electronic ground state potential surface, on the vibrational motions. This commonly used canonical or clamped nucleus approximation, leads to (hyper) polarizability expressions that are different from the SOS ones. In this paper we develop a compact first-order treatment of the differences and carry out a preliminary examination of the numerical repercussions. Our calculations also bear on a proposed theoretical relationship between the vibrational and electronic first hy...

Time-dependent Hartree–Fock schemes for analytical evaluation of the Raman intensities

Using the time-dependent Hartree–Fock method two analytical schemes are elaborated for determining the derivatives of frequency-dependent polarizability with respect to atomic Cartesian coordinates. The first scheme is iterative and consists in determining the mixed derivatives of the density matrix with respect to atomic Cartesian coordinates and dynamic electrical fields. The second takes advantage of the 2n+1 rule to express the polarizability derivatives in terms of first-order derivatives. Both schemes are implemented in the GAMESS program. They enable the fully analytical evaluation of the Raman intensities with inclusion of the frequency dispersion. The potential of these methods is illustrated by determining the polarizability derivatives and Raman intensities of small molecules.

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.

Correlated frequency-dependent electronic first hyperpolarizability of small push–pull conjugated chains

Abstract The longitudinal component of the dynamic electronic first hyperpolarizability of α,ω-nitro,amino-polyacetylene oligomers containing a small number of unit cells has been computed at the Hartree–Fock, Moller–Plesset and coupled-cluster levels with different atomic basis sets. Using frequency-dependent coupled-cluster results, we have tested the efficiency of the additive and multiplicative corrections to approximate the frequency-dependent correlated values. The multiplicative approach provides frequency-dependent electronic first hyperpolarizability values that are within a few percent of the true correlated ones whereas the additive correction leads to β L (−ω σ ; ω 1 , ω 2 ) too small by ∼20%. It turns out that the MP2/6-31G procedure is a suitable approach to reach a semi-quantitative accuracy.

Linear and nonlinear polarizabilities of polydiacetylene and polybutatriene chains: An ab initio coupled Hartree–Fock investigation

Ab initio Hartree–Fock 6-31G longitudinal polarizabilities and second hyperpolarizabilities of polydiacetylene and polybutatriene oligomers are computed and, then, extrapolated to the infinite polymer limit. Both the electronic and vibrational components are obtained with the latter evaluated in the double harmonic approximation. For static fields the electronic hyperpolarizability of the butatrienic form is almost 50 times larger than the acetylenic form; the ratio of the vibrational to the electronic component is 0.86 for the latter and 3.3 for the former. Thus, the two components are sensitive to the difference in bond length alternation (BLA) in different ways. Depending upon the particular nonlinear process it is shown that the vibrational hyperpolarizability may remain large even at optical frequencies. Three intense Raman-active k=0 modes dominate the vibrational component. At the level of theory used here these modes occur in the frequency range 1000–2500 cm−1 and they consist of changes in the BL...

Theoretical study of the second-order nonlinear optical properties of [N]helicenes and [N]phenylenes.

The second-order nonlinear optical properties of helicenes and phenylenes have been theoretically investigated at the time-dependent Hartree-Fock level using the Austin model 1 semiempirical Hamiltonian. Both the antisymmetric isotropic component of the first hyperpolarizability (beta) and its projection on the dipole moment (beta(parallel)) have been determined for increasingly large helical systems as well as for their analogs substituted by donor/acceptor pairs. It is found that (i) in nonsubstituted helicenes and phenylenes, beta increases monotonically with the size of the system and slightly depends on the nature of the helix; (ii) the corresponding beta(parallel) is mostly determined by the radial component of the first hyperpolarizability vector; (iii) in helicenes, beta(parallel) is positive and presents quasiperiodic oscillations with the helix; (iv) in phenylenes, beta(parallel) depends upon the size of the helix and it can be either positive or negative as a result of the differences in evolution with N of the radial components of the dipole moment and first hyperpolarizability. Substituting the helicenes and phenylenes by the prototypical NH2/NO2 donor/acceptor pair provides a diversity of effects on beta and beta(parallel) that encompasses decrease, increase, and change in sign.