Treatment of nonlinear optical properties due to large amplitude anharmonic vibrational motions: umbrella motion in NH3

A general reduced dimensionality finite field nuclear relaxation method for calculating vibrational nonlinear optical properties of molecules with large contributions due to anharmonic motions is introduced. In an initial application to the umbrella (inversion) motion of NH3 it is found that difficulties associated with a conventional single well treatment are overcome and that the particular definition of the inversion coordinate is not important. Future applications are described

Général de Sérigny [Serrigny] de Polytechnique [assistant au match de football Poytechnique contre St Cyr le 25-2-20 au stade Jean-Bouin] : [photographie de presse] / [Agence Rol]

Référence bibliographique : Rol, 58205

Early Variscan I-type pluton in the pre-Alpine basement of the Western Alps: The ca. 360 Ma Cogne diorite (NW-Italy)

Located at the internal border of the Grand-Saint-Bernard Zone, the diorite and its aureole lie on top of intensively studied Alpine eclogitic units but this pluton, poorly studied yet, has kept locally almost undeformed. The pluton intruded, at similar to 360 Ma, country-rocks mostly composed of dark shales with Na2O > K2O and minor mafic intercalations of tholeiitic basalt affinity. This association is characteristic of the Vanoise (France) basement series, where available age determinations suggest an Early Paleozoic age. Parts of the pluton, and of its hornfels aureole that is evidenced here for the first time, in the Punta Bioula section of Valsavaranche valley (NW-Italy), have been well-preserved from the Alpine deformation. Syn-emplacement hardening, dehydration-induced, probably prevented strain-enhanced Alpine recrystallization. Magmatic rock-types range continuously from subordinate mafic types at SiO2 similar to 48%, of hornblendite with cumulative or appinite affinities, to the main body of quartz diorite to quartz monzonite (SiO2 up to 62%). P-T estimates for the pluton emplacement, based on the abundance of garnet in the hornfelses, using also zircon and apatite saturation thermometry and Al-in-hornblende barometry, suggest T similar to 800-950 degrees C and minimum P in the 0.2-0.5 GPa range, with records of higher pressure conditions (up to 1-2 GPa?) in hornblendite phlogopite-cored amphibole. The high-K, Na > K, calcalkaline geochemistry is in line with a destructive plate-margin setting. Based on major element data and radiogenic isotope signature (epsilon Nd-360 Ma from -1.2 to + 0.9, Sr-87/Sr-86(360 MA) from 0.7054 to 0.7063), the parental magmas are interpreted in terms of deep-seated metabasaltic partial melts with limited contamination from shallower sources, the low radiogenic Nd-content excluding a major contribution from Vanoise tholeiites. There is no other preserved evidence for Variscan magmatism of similar age and composition in the Western Alps, but probable analogs are known in the western and northern parts of French Massif Central. Regarding the Alpine tectonics, not only the age of the pluton and its host-rocks (instead of the Permo-Carboniferous age previously believed), but also its upper mylonitic contact, suggest revisions of the Alpine nappe model. The Cogne diorite allegedly constituted the axial part of the E-verging ``pli en retour [backfold] du Valsavaranche'', a cornerstone of popular Alpine structural models: in fact, the alleged fold limbs, as attested here by field and geochemical data, do not belong to the same unit, and the backfold hypothesis is unfounded. (C) 2012 Elsevier B.V. All rights reserved.

Vibration and two-photon absorption

The rigorous and transparent treatment of the effects of nuclear vibrational motion in two-photon absorption (TPA) was discussed. Perturbation formula for diatomic molecules were developed and applied to the X¹Σ+–A¹Π transition in CO. The analysis showed that the vibrations played an important role in TPA, just as their role in the calculation of conventional nonlinear optical (NLO) hyperpolarizabilities

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

Anharmonicity contributions to the vibrational second hyperpolarizability of conjugated oligomers

Restricted Hartree-Fock 6-31G calculations of electrical and mechanical anharmonicity contributions to the longitudinal vibrational second hyperpolarizability have been carried out for eight homologous series of conjugated oligomers - polyacetylene, polyyne, polydiacetylene, polybutatriene, polycumulene, polysilane, polymethineimine, and polypyrrole. To draw conclusions about the limiting infinite polymer behavior, chains containing up to 12 heavy atoms along the conjugated backbone were considered. In general, the vibrational hyperpolarizabilities are substantial in comparison with their static electronic counterparts for the dc-Kerr and degenerate four-wave mixing processes (as well as for static fields) but not for electric field-induced second harmonic generation or third harmonic generation. Anharmonicity terms due to nuclear relaxation are important for the dc-Kerr effect (and for the static hyperpolarizability) in the σ-conjugated polymer, polysilane, as well as the nonplanar π systems polymethineimine and polypyrrole. Restricting polypyrrole to be planar, as it is in the crystal phase, causes these anharmonic terms to become negligible. When the same restriction is applied to polymethineimine the effect is reduced but remains quantitatively significant due to the first-order contribution. We conclude that anharmonicity associated with nuclear relaxation can be ignored, for semiquantitative purposes, in planar π-conjugated polymers. The role of zero-point vibrational averaging remains to be evaluated

Simple finite field nuclear relaxation method for calculating vibrational contribution to degenerate four-wave mixing

A simple extended finite field nuclear relaxation procedure for calculating vibrational contributions to degenerate four-wave mixing (also known as the intensity-dependent refractive index) is presented. As a by-product one also obtains the static vibrationally averaged linear polarizability, as well as the first and second hyperpolarizability. The methodology is validated by illustrative calculations on the water molecule. Further possible extensions are suggested

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

Field-induced coordinates for the determination of dynamic vibrational nonlinear optical properties

Three conjugated organic molecules that span a range of polarity and valence-bond/charge transfer characteristics were studied. It was found that dispersion can be insignificant, and that adequate treatment can be achieved with frequency-dependent field-induced vibrational coordinates (FD-FICs)

A variational approach for calculating Franck-Condon factors including mode-mode anharmonic coupling

We have implemented our new procedure for computing Franck-Condon factors utilizing vibrational configuration interaction based on a vibrational self-consistent field reference. Both Duschinsky rotations and anharmonic three-mode coupling are taken into account. Simulations of the first ionization band of Cl O2 and C4 H4 O (furan) using up to quadruple excitations in treating anharmonicity are reported and analyzed. A developer version of the MIDASCPP code was employed to obtain the required anharmonic vibrational integrals and transition frequencies

Nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties by means of electrical property expansions: Application to HF, CH4, CF4, and SF6

Electrical property derivative expressions are presented for the nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties. For CF4 and SF6, as opposed to HF and CH4, a term that is quadratic in the vibrational anharmonicity (and not previously evaluated for any molecule) makes an important contribution to the static second vibrational hyperpolarizability of CF4 and SF6. A comparison between calculated and experimental values for the difference between the (anisotropic) Kerr effect and electric field induced second-harmonic generation shows that, at the Hartree-Fock level, the nuclear relaxation/infinite frequency approximation gives the correct trend (in the series CH4, CF4, SF6) but is of the order of 50% too small

Variational calculation of static and dynamic vibrational nonlinear optical properties

The vibrational configuration interaction method used to obtain static vibrational (hyper)polarizabilities is extended to dynamic nonlinear optical properties in the infinite optical frequency approximation. Illustrative calculations are carried out on H2 O and N H3. The former molecule is weakly anharmonic while the latter contains a strongly anharmonic umbrella mode. The effect on vibrational (hyper)polarizabilities due to various truncations of the potential energy and property surfaces involved in the calculation are examined