## Visualizing the Contributions of Virtual States to Two-Photon Absorption Cross Sections by Natural Transition Orbitals of Response Transition Density Matrices

journal contribution

posted on 26.06.2017 by Kaushik D. Nanda, Anna I. Krylov#### journal contribution

Any type of content formally published in an academic journal, usually following a peer-review process.

Observables
such as two-photon absorption cross sections cannot be computed from
the wave functions of initial and final states alone because of their
nonlinear nature. Rather, they depend on the entire manifold of the
excited states, which follows from the familiar sum-over-states expressions
of second- and higher-order properties. Consequently, the interpretation
of the computed nonlinear optical properties in terms of molecular
orbitals is not straightforward and usually relies on approximate
few-states models. Here, we show that the two-photon absorption (2PA)
transitions can be visualized using response one-particle transition
density matrices, which are defined as transition density matrices
between the zero-order and first-order perturbed states. We also extend
the concept of natural transition orbitals to 2PA transitions. We
illustrate the utility of this new tool, which provides a rigorous
black box alternative to traditional qualitative few-states analysis,
by considering 2PA transitions in ethylene,

*trans*-stilbene, and*para*-nitroaniline.#### Read the peer-reviewed publication

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Response Transition Density Matrices Observablestransition orbitalsresponse one-particle transition density matricessum-over-states expressionsVirtual Statestransition density matricesfew-states analysisTwo-Photon Absorption Cross Sections2 PA transitionstwo-photon absorptionNatural Transition Orbitalshigher-order propertiesnonlinear naturefew-states modelswave functionsbox alternative

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#### Read the peer-reviewed publication

### Categories

### Keyword(s)

Response Transition Density Matrices Observablestransition orbitalsresponse one-particle transition density matricessum-over-states expressionsVirtual Statestransition density matricesfew-states analysisTwo-Photon Absorption Cross Sections2 PA transitionstwo-photon absorptionNatural Transition Orbitalshigher-order propertiesnonlinear naturefew-states modelswave functionsbox alternative