Robert R. Birge

A theoretical analysis of the two‐photon properties of linear polyenes and the visual chromophores

A self‐consistent field molecular orbital formalism for calculating molecular two‐photon absorptivities is presented based on the combined use of the Pariser–Parr–Pople π‐electron method including full single and double excitation configuration interaction and Monson and McClain’s two‐photon orientational averaging procedures. The formalism is applied to a series of linear, nonlinear, and retinyl polyenes to study the effect of chain length, conformation, and polarity on the calculated two‐photon absorptivities for various photon polarization and propagation relationships. The calculations indicate that the low‐lying ’’1Ag*−’’ covalent state should be strongly two‐photon allowed in virtually all polyenes, whether polar, nonpolar, linear, or nonlinear, provided a strongly one‐photon allowed ’’1Bu*+’’ state is nearby. The two‐photon absorptivity of the ’’1Ag*−’’ state for two linearly polarized photons is predicted to increase with increasing polyene chain length. Linearly polarized light produces the stron...

The effect of solvent environment on molecular electronic oscillator strengths

A simple expression is derived for the effect of solvent environment on solute oscillator strength. The only parameters required are the refractive index of the solvent and a geometric factor which depends upon the shape of the molecule and the orientation of its transition moment. Whereas classical local field theories predict that oscillator strengths in all molecules should change in the same direction with increasing solvent polarizability, our theory correctly predicts a decrease in the oscillator strength of the π*←π transition of β‐carotene and an increase in the oscillator strength of the π*←n transition in pyrazine. The theory is based on perturbation of the ground and excited states of the solute by point–dipole interactions between solvent and solute transition moments. Although our expression is derived for nonpolar solutes in nonpolar solvents, experimental evidence indicates that it may be equally applicable to nonpolar solutes in polar solvents.A simple expression is derived for the effect of solvent environment on solute oscillator strength. The only parameters required are the refractive index of the solvent and a geometric factor which depends upon the shape of the molecule and the orientation of its transition moment. Whereas classical local field theories predict that oscillator strengths in all molecules should change in the same direction with increasing solvent polarizability, our theory correctly predicts a decrease in the oscillator strength of the π*←π transition of β‐carotene and an increase in the oscillator strength of the π*←n transition in pyrazine. The theory is based on perturbation of the ground and excited states of the solute by point–dipole interactions between solvent and solute transition moments. Although our expression is derived for nonpolar solutes in nonpolar solvents, experimental evidence indicates that it may be equally applicable to nonpolar solutes in polar solvents.

Calculation of molecular polarizabilities using an anisotropic atom point dipole interaction model which includes the effect of electron repulsion

The point dipole interaction model for molecular polarizability recently proposed by Applequist, Carl, and Fung is modified by replacing isotropic atomic point dipoles with anisotropic atomic point dipoles. The modified formalism, which is invariant to coordinate transformations, requires an additional empirical parameter for each atom type (ξA, the atomic anisotropy constant) and a single, global parameter applicable to all nonconjugated systems (κ, the repulsion exponent). The atomic polarizability tensor in the molecular environment is evaluated as a function of interatomic electron repulsion. This latter quantity is shown to be related to the degree to which bonding diminishes the polarizability of an atomic center in the direction (s) of the covalent bond (s). The anisotropic atom point dipole interaction model generates identical mean molecular polarizabilities as in the isotropic procedures of Applequist et al., while reducing the average error in the calculated molecular polarizability components ...

Two‐photon spectroscopy of diphenylbutadiene. The nature of the lowest‐lying 1Ag*−ππ* state

A two‐photon excitation spectrum of all‐trans 1,4‐diphenyl‐1,3‐butadiene is taken in EPA solvent glass at 77 K. The system origin of the lowest‐lying 1Ag*− ππ* state is observed at 27 900±20 cm−1, 130 cm−1 below the system origin of the strongly allowed 1Bu*+ state. The vibronic analysis and the Franck–Condon intensity distribution indicate considerable bond order reversal in the 1Ag*− state localized in the polyene portion of the molecule. Configurational analysis using PPP–SCF–MO–CISD procedures predicts that the bond order reversal is primarily associated with a LUMO←HOMO double excitation. Although the bond order reversal is polyene localized, the electronic transition is calculated to be highly delocalized with 55% of the ’’optical’’ electron density on the phenyl groups. A single intermediate state approximation based on the strongly allowed 1Bu*+ state is demonstrated to adequately describe the two‐photon absorptivity and polarization properties of the lowest‐lying 1Ag*− state. The remarkably short...

Calculation of Raman intensities for the ring‐puckering vibrations of trimethylene oxide and cyclobutane. The importance of electrical anharmonicity

Raman intensities are calculated for the ring‐puckering vibration of trimethylene oxide (TMO) and cyclobutane using an anisotropic atom–point dipole interaction model to calculate the elements of the molecular polarizability tensor. Three different models for the ring‐puckering motion are examined: (i) a model in which the methylene groups are held rigid to the molecular frame as the ring puckers, (ii) a dynamical model in which the methylene groups rock (TMO and cyclobutane) and wag (TMO) as the ring puckers, and (iii) a second rigid model in which all of the polarizability of the molecule is localized on the atoms of the ring skeleton. All three models for the ring‐puckering motion predict unusually large second‐order terms in the expansion of the polarizability tensor elements in the ring puckering coordinate [‖∂2amn/∂Z2)0‖≳0]. These terms result in intense Dv = 2 overtone transitions. The calculated relative intensities of the members of the Dv = 2 overtone progression are in good agreement with those...

Calculation of molecular polarizabilities using a semiclassical Slater‐type orbital‐point dipole interaction (STOPDI) model

The point dipole interaction model for molecular polarizability proposed by Applequist, Carl, and Fung [J. Am. Chem. Soc. 94, 2952 (1972)] is modified by replacing the point dipole interaction tensor with a descaled distributed charge interaction tensor. Our procedure is based on the descaled tensor algorithm proposed by Thole [Chem. Phys. 59, 341 (1981)] and uses a Slater‐type orbital (STO) function to represent the charge distribution. The resulting STOPDI formalism calculates mean molecular polarizabilities and the components of the molecular polarizabilities with errors comparable to experimental uncertainty. Furthermore, these procedures require only one optimized parameter per atom, the average atomic polarizability. The formalism is invariant to coordinate transformations and avoids the discontinuities and/or false resonances that are characteristic of previous classical and semiclassical formalisms. The STOPDI algorithm requires less parameterization and computation time than the anisotropic atom ...

Two‐photon excitation spectroscopy of a substituted all‐trans hexatriene (iso‐tachysterol). Spectroscopic assignments of the low‐lying 1‘‘1Bu*+’’ and 2‘‘1Ag*−’’ ππ* states

The two‐photon excitation spectrum of the substituted all‐trans hexatriene, iso‐tachysterol, is taken in EPA (77 K). Comparison of this spectrum with the one‐photon absorption and fluorescence spectra indicate that the system origin of the 2’’ 1A*−’’g state lies slightly below the 1’’ 1B*+’’u system origin in EPA (77 K). (AIP)

The experimental determination of ground state dipole moments from dielectric constant measurements using ellipsoidal cavity correction factors

An equation is derived from the Onsager–Bottcher formalism to calculate permanent dipole moments of molecules of ellipsoidal shape from dielectric constant data. An expression is also derived which allows dipole moments calculated by spherical cavity formalisms to be corrected without repeating the experiment. This expression is applied to literature values calculated using the Debye equation, and it is shown that the correction brings the published values for nonspherical molecules closer to the vapor phase values. Tables of the ellipsoidal shape factor Aa as a function of the ratios of the axes of the molecular ellipsoid are presented. Interpolation algorithms can be used in conjunction with the above tables to calculate Aa to at least three significant digits.

Calculation of Raman intensities for the ring‐puckering vibrations of 2,5‐dihydropyrrole and trimethyleneimine. Electrical versus mechanical anharmonicity in asymmetric potential wells

Raman intensities are calculated for the ring‐puckering transitions of 2,5‐dihydropyrrole (DHP) and trimethyleneimine (TMI) using an anisotropic atom–point dipole interaction model to evaluate the elements of the molecular polarizability tensor. The calculated relative intensities for the members of the Δv = 1 and Δv = 2 ring‐puckering progressions for DHP are in good agreement with those observed. The calculations predict that the observed Δv = 2 overtones of DHP occur not because of the first‐order allowedness expected for these transitions in the asymmetric double‐minimum potential well which governs the ring‐puckering motion, but rather because of unusually large second‐order terms in the expansions of the polarizability tensor elements in the puckering coordinate [‖(∂2αμν/∂Z2)0‖≫0]. Raman intensities are calculated for the ring‐puckering transitions of TMI using the two different potential functions which have been proposed for the puckering motion. It is found that the intensities calculated for the...

Calculation of Raman intensities for the ring‐puckering vibrations of cyclopentene and 2,5‐dihydrofuran

Raman intensities are calculated for the ring‐puckering vibrations of cyclopentene and 2,5‐dihydrofuran using an anisotropic atom–point dipole interaction model to calculate the elements of the molecular polarizability tensor. Large second‐order terms are calculated for both molecules in the expansions of the molecular polarizability tensor elements in the ring‐puckering coordinate [‖(∂2αμν/∂Z2)0‖≫0]. These terms result in intense calculated Δv = 2 overtone transitions, in agreement with experimental observations. The calculations predict that the Δv = 2 transitions of cyclopentene are one to two orders of magnitude more intense than the Δv = 1 fundamentals, while the two sets of transitions are comparable in intensity in 2,5‐dihydrofuran. Although the shape of the band contours precludes observation of the Δv = 1 transitions for either molecule, the calculations suggest that the fundamental transitions of cyclopentene would not be observable even if the band shape were amenable to observation.