Optimizing potential energy functions for maximal intrinsic hyperpolarizability

Zhou, Juefei; Szafruga, Urszula B.; Watkins, David S.; Kuzyk, Mark G.

doi:10.1103/physreva.76.053831

Cited by 44 publications

(87 citation statements)

References 26 publications

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“…Kuzyk et al have studied a sub-problem of this, namely performing the optimization for the single-electron case with both one and two dimensional potentials. They suggest that implementing the qualitative (modulated) features observed in their optimized potentials might allow design of molecules with higher hyperpolarizabilities [4,5]. While these calculations have resulted in a number of potentials with large hyperpolarizabilities, they do not distinguish which features of the optimized potential are required for high β and which are artifacts of the minimization procedure or chosen parametrization.…”

Section: Introductionmentioning

confidence: 99%

“…In a notable series of papers, Kuzyk et al have shown [2][3][4][5] that all of the measured off-resonant first hyperpolarizabilities β zzz -specifically the second derivative of the polarization in a given direction z with respect to an electric field with vanishingly small frequency and wavevector in that direction -of known molecules are considerably smaller than a theoretical upper limit β max derived from the Thomas-Kuhn sum rules and the sum-overstates formula…”

Section: Introductionmentioning

confidence: 99%

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Maximizing the hyperpolarizability poorly determines the potential

et al. 2012

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We have optimized the zero frequency first hyperpolarizability β of a one-dimensional piecewise linear potential well containing a single electron by adjusting the shape of that potential. With increasing numbers of parameters in the potential, the maximized hyperpolarizability converges quickly to 0.708951 of the proven upper bound. The Hessian of β at the maximum has in each case only two large eigenvalues; the other eigenvalues diminish seemingly exponentially quickly, demonstrating a very wide range of nearby nearly optimal potentials, and that there are only two important parameters for optimizing β. The shape of the optimized wavefunctions converges with more parameters while the associated potentials remain substantially different, suggesting that the ground state wavefunction provides a superior physical description to the potential for the conditions that optimize the hyperpolarizability. Prospects for characterizing the two important parameters for near-optimum potentials are discussed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Maximizing the hyperpolarizability poorly determines the potential

et al. 2012

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“…We should point out that the quantum limits are obtained by assuming that the response is dominated by the contributions of three overlapping states, an ansatz that has been extensively verified numerically using Monte Carlo methods [20] as well as potential energy optimization. [21] There are no assumptions about the symmetry properties of the states. However, this does not imply that symmetry plays no role in he optimization of the second hyperpolarizability.…”

Section: Theorymentioning

confidence: 99%

A new dipole-free sum-over-states expression for the second hyperpolarizability

Pérez‐Moreno

Clays

Kuzyk

2008

The Journal of Chemical Physics

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A new dipole-free sum-over-states expression for the second hyperpolarizability The generalized Thomas-Kuhn sum rules are used to eliminate the explicit dependence on dipolar terms in the traditional sum-over-states (SOS) expression for the second hyperpolarizability to derive a new, yet equivalent, SOS expression. This new dipole-free expression may be better suited to study the second hyperpolarizability of non-dipolar systems such as quadrupolar, octupolar, and dodecapolar structures. The two expressions lead to the same fundamental limits of the offresonance second hyperpolarizability; and when applied to a particle in a box and a clipped harmonic oscillator, have the same frequency-dependence. We propose that the new dipole-free equation, when used in conjunction with the standard SOS expression, can be used to develop a three-state model of the dispersion of the third-order susceptibility that can be applied to molecules in cases where normally many more states would have been required. Furthermore, a comparison between the two expressions can be used as a convergence test of molecular orbital calculations when applied to the second hyperpolarizability. I. INTRODUCTIONThe sum-over-states (SOS) expressions have been used for more than three decades in the study of nonlinear optical phenomena, and are perhaps the most universally used equations in molecular nonlinear optics. The sum-over-states expression is obtained from quantum perturbation theory and is usually expressed in terms of the matrix elements of the dipole operator, −ex nm , and the zero-field energy eigenvalues, E n . [1,2,3] The SOS expressions for the first and second hyperpolarizability derived by Orr and Ward using the method of averages [2] are often used because they explicitly eliminate the unphysical secular terms that are present in other derivations.[1] These secular-free expressions contain summations over all excited states.Finite-state approximations are used to apply the theory to experimental results. Oudar and Chemla studied the first hyperpolarizability of nitroanilines by considering only two states, the ground and the dominant excited state. [4] Although the general validity of this "two-level" model has been questioned, especially in its use for extrapolating measurement results to zero frequency, the approximation is still widely used in experimental studies of the nonlinear properties of organic molecules.Several approaches have been used to develop approximate expressions for the second-hyperpolarizability in the off-resonance regime. [5,6,7] While such approximations are helpful, they systematically ignore some of the contributions to the SOS expression. As our goal is to derive a general expression that is equivalent to the traditional SOS one, we choose not to make any assumptions a priori about what type of contributions dominate the response. Furthermore, including all the possible contribution is necessary to properly describe the on-resonance behavior, even * Electronic address: Javier.PerezMoreno@fys.kuleuven.be ...

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“…In this work, we analyze the best device materials to gain an understanding of the amount of future improvements that are attainable by invoking the fundamental limits of the nonlinear-optical response of the hyperpolarizability. [24,25] Until a recent breakthrough in molecular design using modulation of conjugation (MOC), [26,27,28] the best molecules fell a factor of 30 short of the fundamental limit. [29] II.…”

Section: Introductionmentioning

confidence: 99%