Volume 92, Issue 12, 15 June 1990
Index of content:
92(1990); http://dx.doi.org/10.1063/1.458239View Description Hide Description
Polarized, depolarized, isotropic, difference, and reduced Raman spectra were obtained from vitreous silica, irreversibly compacted at 600 °C and 50 kbar, to a m b i e n t densities as high as 2.73 g cm−3. The 60 cm−1 ‘‘Boson’’ peak; and, the intense optic, Si–O–Si bending peak at 440 cm−1 including its low‐frequency shoulders at ≊210–240 and ≊340 cm−1; were observed to move strongly upward in position, but at two different rates with density rise. The two peak frequencies behave e x p e r i m e n t a l l y like spherical transverse acoustic (TA) or shear (S), and spherical longitudinal acoustic (LA) or pressure (P) stress waves of an isotropic elastic solid. In contrast, downward frequency shifts were observed for the transverse optic (TO) 1060 cm−1 and longitudinal optic (LO) 1200 cm−1 modes in the Si–O stretching region, but at a b s o l u t e rates e q u a l, respectively, to those of the 60 and 440 cm−1 peak frequencies thus linking optic as well as acoustic modes to the elastic modulii.
The TO and LO splitting was shown from a phonon coupling model to result from very strong interaction between the optic modes and the low‐frequency S and P modes. The frequency decreases of the TO and LO modes indicate a decrease in the Si–O stretching force constants, related to a decrease in the mean Si–O–Si bridging angle, from ≊144° to ≊120°, inferred from frequency increases at 440 and ≊800 cm−1. A decrease in the mean O–2nd‐O distance also occurs, but severe distortion of the SiO4 tetrahedra does not seem probable to densities of 2.73 g cm−3. The d i l a t a t i o n a l P‐mode wavelength ≥5 Å corresponds to volume‐related distances, e.g., Si–2nd‐O, O–2nd‐O, or Si–2nd‐Si. The shear mode wavelength is larger (≊13 Å) and similar to the structural correlation length, estimated roughly from x‐ray data, where G(r)≊1. Both S and P modes involve small coherence volumes, and both may have negligible group velocities, i.e., standing waves. The low‐frequency Sscattering is weakly to completely depolarized, but the higher‐frequency Pscattering may be strongly polarized, falling near or just below (BeF2, B2O3, GeO2, SiO2, ZBLAL) the f i r s t v e r y s t r o n g m i n i m u m in the Raman depolarization ratio, located above the S mode.
This new criterion locates the a c t u a l P mode of fused silica within the ≊200–350 cm−1 shoulder region. This region is intense in the density of states, determined by neutron inelastic scattering (NIS). S and P modes are resolved in the Raman spectra of several glasses, but their relation to the low‐order spherical acoustic stress waves of isotropic media has, heretofore, not been widely recognized.
92(1990); http://dx.doi.org/10.1063/1.458240View Description Hide Description
The diatomic molecule NbS has been observed for the first time by laser‐induced fluorescence at low resolution in a supersonic molecular beam following expansion of a CS2/He (1:100) mixture through a laser‐produced plasma of niobium atoms. Two band systems have been observed in the visible (400–700 nm); a strong one and a weaker one. The strong one has its origin near 15 670 cm−1 and is shown to belong to the C 4Σ−–X 4Σ− system. The weaker one has its origin likely at 15 215 cm−1 and is attributed to the 2Σ+–X 4Σ− 1/2 system. The latter system is observed owing to the 2Σ+(σ1δ2)∼C 4Σ− 1/2 (δ2σ*1) perturbation induced by the spin–orbit operators. This perturbation has been characterized through vibrational energy shifts, vibronic lifetimes, and analysis of the perturbation matrix elements. This enables direct determination of the large second‐order spin–orbit splittings in the C 4Σ− and X 4Σ− states.
In the ground state, the splitting which is due to the isoconfigurational 〈2Σ+‖H so‖X 4Σ−〉 interaction element has been established to be 63 cm−1 and is independent of the vibrational energy content. In the C state, the spin–orbit splitting arises from two interactions; one due to the isoconfigurational 〈2Σ+‖H so‖C 4Σ−〉 interaction and the other to the 〈2Σ−(σ1δ2), (v+1)‖H so‖C 4Σ−(δ2σ*1),v〉 interaction. The former interaction splits the C 4Σ− 3/2 and C 4Σ− 1/2 components by about 63 cm−1, as in the ground X 4Σ− state again independent of the vibrational energy content. The second interaction which becomes negligible at v(C 4Σ−)≥4 shifts the C 4Σ− (v=0,1,2,3) levels to lower wave numbers by 18, 15, 11, and 5 cm−1, respectively. From a Franck–Condon analysis, the electronic part of the molecular matrix elements 〈2Σ+(σ1δ2), v’‖H so‖C 4Σ−(δ2σ1*),v‘〉 is estimated to be 57 cm−1. Other molecular parameters such as vibrational frequencies and anharmonicities, radiative lifetimes, Franck–Condon factors, mixing coefficients, and approximate bond lengths are reported and discussed.
The permanent dipole moment of TiN and the nuclear magnetic hyperfine structure in its X 2Σ+ and A 2Π electronic states92(1990); http://dx.doi.org/10.1063/1.458241View Description Hide Description
The permanent dipole moment of TiN in its X 2Σ+ and A 2Σ states has been determined from the complete resolution of the first‐ and second‐order Stark splitting of the Q 2 1(1.5)+R 2(0.5) line of the (0,0) band of the A 2Π–X 2Σ+ system. Values of 3.56±0.05 D (2σ) and 4.63±0.04 D (2σ) have been derived for the X and A states respectively, from least‐squares fits to plots of Stark splitting vs electric field strength. Electric fields up to 12 kV/cm have been employed avoiding voltage breakdown. The zero‐field spectrum shows resolution of the nuclear magnetic hyperfine structure of the 47TiN and 49TiN isotopes. This hyperfine structure is that of the ground X 2Σ+ state only and is shown to follow closely the coupling case b βS . The value of the Fermi contact parameter is −570 MHz which implies a 4s occupation of the 9σ molecular orbital (MO) of 72%. The results are compared with calculated and available experimental values for early first‐row transition metal oxides and nitrides.
92(1990); http://dx.doi.org/10.1063/1.458242View Description Hide Description
The infrared absorptionspectrum of the ν3 fundamental band of the CD3 radical has been detected by diode laserabsorption spectroscopy. The CD3 radical was produced by excimer laserphotolysis of CD3I at 248 nm or (CD3)2CO at 193 nm. Molecular parameters of the v 3=1 vibrational state were determined from a least‐squares fit to 62 rotation–vibration transitions. In this fit, molecular parameters describing the ground state were constrained to those obtained from previous spectroscopic studies of the ν2 parallel IR band [J. M. Frye, T. J. Sears, and D. Leitner, J. Chem. Phys. 8 8, 5300 (1988)]. The molecular parameters determined in the present work are the band origin ν0=2381.088 60(84), B’=4.758 737(40), C’=2.373 297(34), (ζC)3=0.476 278(72), q 3=0.003 76(59), D ’ N =0.000 187 9(5), D N K =−0.000 341 0(12), D ’ K =0.000 143 7(8), η N =−0.000 005 5(36), η’ K =0.000 060(35), and q N =0.000 063(17), all in cm− 1 with one standard deviation in parentheses. The derived molecular parameters were compared with those for the CH3 radical v 3=1 level determined previously [T. Amano, P. Bernath, C. Yamada, Y. Endo, and E. Hirota, J. Chem. Phys. 7 7, 5284 (1982)]. The molecular parameters of the v 3=1 state of the CD3 and CH3 radicals follow the expected isotopic relationships. We have also found that the determined molecular parameters reasonably satisfy the approximate planarity relationships [J. K. G. Watson, J. Mol. Spectrsoc. 6 5, 123 (1977)] and the sign of the l‐type doubling constant is consistent with a planar equilibrium structure.
Photodissociation dynamics of H2S at 121.6 nm and a determination of the potential energy function of SH(A 2Σ+)92(1990); http://dx.doi.org/10.1063/1.458243View Description Hide Description
A new and improved version of the technique of H atom photofragment translational spectroscopy has been applied to a study of H2S photodissociation at 121.6 nm. The primary fragmentation pathways leading to H+SH(A) fragments and H+H+S(1 D) atoms are observed to dominate the product yield; the yield of H atoms formed in conjunction with ground state SH(X) fragments is undetectably small. The majority of the SH(A) fragments are formed in their v=0 level with a rotational state population distribution that spans all possible bound and quasibound rotational levels. The experimental determination of the energies of these hitherto unobserved high rotational states has enabled a refinement of the SH(A) potential energy function, an improved estimate of the SH(A) well depth (9280±600 cm− 1), and thus of the SH(X) ground state bond dissociation energyD 0 0 (S–H)=3.71±0.07 eV. All aspects of the observed energy disposal in the title photodissociation process may be understood, qualitatively, if it is assumed that (i) the primary fragmentations occur on the B̃ 1 A 1potential energy surface and (ii) Flouquet’s a b i n i t i o calculations of portions of this surface [Chem. Phys. 1 3, 257 (1976)] correctly predict its gross topological features.
On the use of combination/overtone band resonance Raman excitation profiles for understanding the vibronic coupling mechanism in the 700 nm absorption band of azulene92(1990); http://dx.doi.org/10.1063/1.458244View Description Hide Description
Finite temperature model expressions for the excitation profiles of second‐order Stokes resonance Raman (RR) scattering are derived within the framework of the time correlator theory for systems with simultaneous linear electron–phonon coupling and linear non‐Condon coupling. These expressions have all the advantages common to solutions from the time correlator theory, allowing convenient and efficient multimode modeling procedures. These results, together with those obtained elsewhere for the second‐order profiles of systems within the Condon approximation, but having mode mixing and frequency shifts, are applied to the RR scattering originating from the 700 nm absorption band of azulene. For this system, it was shown previously that the measuredoptical absorption and fundamental RR profiles cannot discriminate between a mode mixing model, invoked to account for the measured relative intensities of the fundamental profiles of two modes, and an equally successful non‐Condon model; nor can recent quantum‐chemistry calculations by others for this system. With our new model expressions for the s e c o n d‐order profiles, we calculate here the profiles of the combination/overtone bands involving these two modes, using either the same mode mixing model parameters, or the same non‐Condon model parameters which were previously successful for the absorption and fundamental profiles. Our results show that the second‐order profiles predict a clear discrimination between the two models.
92(1990); http://dx.doi.org/10.1063/1.458245View Description Hide Description
The harmonic vibrational frequencies of the Be3 and Be4 clusters have been determined using a b i n i t i oelectronic structure calculations. Large atomic natural orbital (ANO) basis sets have been used in conjunction with high levels of correlation treatment. These include multireference configuration‐interaction (MRCI) and single and double coupled‐cluster (CCSD) methods, and the CCSD method augmented with a correction for connected triple excitations [CCSD(T)]. In general, all three treatments agree very well. The only substantial disagreement is for the totally symmetric stretching mode in Be3, where the CCSD method yields a harmonic frequency that is 57 cm− 1 smaller than the MRCI value. The fundamental vibrational frequencies of Be3 and Be4 have been determined using second‐order perturbation theory to obtain anharmonic corrections; Be3 is treated as a symmetric top and Be4 as a spherical top. Full CCSD(T) quartic force fields were used to determine anharmonic constants, vibration–rotation interaction constants, and quartic and sextic centrifugal distortion constants. The anharmonic corrections for the two vibrational modes of Be3 reduce the frequencies by less than 5%, which is typical for bond‐stretching vibrations. The a 1 and e vibrations of Be4 exhibit somewhat smaller anharmonic corrections that decrease the frequency by about 3%. However, the only IR active mode of Be4 [ω3(t 2)] displays a large p o s i t i v e anharmonic correction of +111 cm− 1, or almost 20%. Finally, IR intensities have been determined using the double harmonic approximation.
92(1990); http://dx.doi.org/10.1063/1.458246View Description Hide Description
A detailed implementation of the polarization energy and its derivatives into a molecular dynamics program is described. In order to examine the effect of the polarization energy on the calculated free energy differences, we have computed the free energy of solvation, with coordinate coupling, of normal alkanes, tetraalkylmethane, tetraalkylammonium ions and some closed shell ions in water. The pattern of the computed free energy change is compared with the results of our earlier simulations where the polarization energy was not included in the calculation. It is found that in the majority of the cases the polarization energy contribution to the free energy change is additive. The results of the simulations are also compared with the available experimental data.
Stimulated Raman probing of supercooling and phase transitions in large N2 clusters formed in free jet expansions92(1990); http://dx.doi.org/10.1063/1.458247View Description Hide Description
High resolution stimulated Raman spectroscopy(SRS) has been used to examine N2 and N2/He free jet expansions and also equilibrium samples of N2 from 15 to 110 K. The jet spectra show the formation of large liquid clusters which supercool and subsequently freeze to form crystalline β‐N2solid and, in He expansions, undergo a further transformation to a partially annealed α‐N2 form. CW‐SRS frequency and linewidth data obtained for equilibrium samples of the condensed phases of N2 yielded frequency–temperature relations used in deducing internal temperatures for the clusters produced in the expansion experiments. Analysis of the cooling curves indicates a mean cluster diameter of 35 nm and favors a prompt freezing process rather than a gradual conversion of liquid to solid in a single cluster on the microsecond time scale of the experiments. Supercooling limits of 34 to 44 K are deduced for the liquid, far below the triple point temperature of 63.2 K at which equilibrium samples freeze. Some evidence for surface versus bulk contributions to the spectra is seen in the asymmetric line shapes observed for liquid clusters in the condensation region. The results show that the high spectral and spatial resolution of nonlinear Raman methods such as SRS and CARS provide a unique probe of the condensation processes in free jet expansions.
92(1990); http://dx.doi.org/10.1063/1.458248View Description Hide Description
Stimulated emission pumping (SEP) spectroscopy has been used to investigate rovibrational level mixing in the ground singlet state of methyl glyoxal. A low resolution (0.35 cm−1) SEP survey spectrum allows accurate frequency assignments for 15 normal vibrations and seven hindered rotor levels. High resolution (0.05 cm−1) SEP spectra are reported for selected vibrational bands, including the fundamental vibrations of the symmetric carbonyl stretch and symmetric carbonyl bend. A van der Waals interaction between the neighboring carbonyl oxygen and methyl hydrogens is found to influence mixing of the carbonyl vibrations, affirming the results of previous studies.
92(1990); http://dx.doi.org/10.1063/1.458249View Description Hide Description
Time correlation functions of the scattered light intensity are studied in aqueous solutions of charged rod‐like fd‐virus (L=880 nm, d=6 nm) at various ionic strengths. The short time behavior of the correlation function is dominated by the static structure factor S(q) which is also independently determined from static light scattering experiments. Comparison of correlation functions of solutions with high ionic strength (screened Coulomb interaction) and those of solutions with liquid‐like nearest neighbor order (strong Coulomb interaction) shows different single particle diffusion coefficients on medium time scales at high scattering vectors, where mainly single particle properties are observed by light scattering. The single particle diffusion coefficient decreases with increasing structure peak height of the solutions. At low scattering vectors an extra slow mode component of the correlation function is observed for solutions with Coulomb interaction.
92(1990); http://dx.doi.org/10.1063/1.458250View Description Hide Description
Rotational transitions between J≤3 levels within the K=0 manifold have been observed for H2O–CO, HDO–CO, D2O–CO, H2O–1 3CO, HDO–1 3CO, and H2 1 7O–CO using the molecular beam electric resonance and Fourier transform microwave absorption techniques. ΔM J =0→1 transitions within the J=1 level were also measured at high electric fields. A tunneling motion which exchanges the equivalent hydrogens gives rise to two states in the H2O and D2O complexes. The spectroscopic parameters for H2O–CO in the spatially symmetric tunneling state are [∼(B 0) =2749.130(2)MHz, D 0=20.9(2)kHz, and μ a =1.055 32(2)D] and in the spatially antisymmetric state are [∼(B 0) =2750.508(1)MHz, D 0=20.5(1)kHz, and μ a =1.033 07(1)D]. Hyperfine structure is resolved for all isotopes. The equilibrium structure of the complex has the heavy atoms approximately collinear. The water is hydrogen bonded to the carbon of CO; however the bond is nonlinear. At equilibrium, the O–H bond of water makes an angle of 11.5° with the a axis of the complex; the C 2v axis of water is 64° from the a axis of the complex. The hydrogen bond length is about 2.41 Å. The barrier to exchange of the bound and free hydrogens is determined as 210(20) cm− 1 (600 cal/mol) from the dipole moment differences between the symmetric and antisymmetric states. The tunneling proceeds through a saddle point, with C 2v structure, with the hydrogen directed towards the CO subunit. The equilibrium tilt away from a linear hydrogen bond is in the direction opposite to the tunneling path.
The dynamics of binary mixtures of nonpolymeric viscoelastic liquids as studied by quasielastic light scattering92(1990); http://dx.doi.org/10.1063/1.458251View Description Hide Description
In this paper we report quasielastic light‐scattering experiments of the compatible binary mixture of simple viscoelastic liquids made up of o‐terphenyl as one component and newly synthesized model materials, 1,1‐di(paramethoxyphenyl)‐cyclo‐hexan and 1,1‐di(paramethoxyphenyl, metamethyl)‐cyclohexan, as the other components. The measurements were done in a wide temperature range above T g (≂T g +100 K) of the mixtures and in a volume fraction range up to φ=0, 5 of bis‐cresol‐cyclohexane‐dimethylether and bis‐phenol‐cyclohexane‐dimethylether. We have found that the measured dynamics is governed by three effects: At short times we observe the dynamics of the density fluctuations of the system characterized by a broad distribution of relaxation times, which can be scaled to a masterplot taking the T g of the mixtures into account. At longer times we observe two translational diffusion processes whose decay is single exponential with a characteristic time proportional to q −2, q being the scattering vector. The faster one is attributed to the interdiffusion coefficient of the system. The second, slower mode is related to the motion of dynamic clusters which have their origin in a spatial inhomogeneity of the samples. The mean cluster diameter is about 1000 Å, thus in any case the occurrence of the slow mode is accompanied by a strong increase of the elastically scattered intensity towards small scattering angles. This mode also appears in pure components. We relate its intensity to the fluctuations of an order parameter, usually introduced to describe the glassy state.
Hyperfine structure of the MnH X 7Σ+ state: A large gas‐to‐matrix shift in the Fermi contact interaction92(1990); http://dx.doi.org/10.1063/1.458252View Description Hide Description
Sub‐Doppler spectra of the A 7Π–X 7Σ+ (0,0) band of gas phase MnH near 5680 Å were recorded by intermodulated fluorescence spectroscopy. The spectra reveal hyperfine splittings arising from both the 5 5Mn and 1H nuclear spins. Internal hyperfine perturbations have been observed between the different spin components of the ground state at low N‘. From a preliminary analysis of several rotational lines originating from the isolated and unperturbed F 1(J‘=3) spin component of the X 7Σ+(N‘=0) level, the 5 5Mn Fermi contact interaction in the ground state has been measured as b F =A iso =276(1) MHz. This value is 11% smaller than the value obtained by Weltner e t a l. from an electron‐nuclear double resonance(ENDOR) study of MnH in an argon matrix at 4 K. This unprecedented gas‐to‐matrix shift in the Fermi contact parameter is discussed.
92(1990); http://dx.doi.org/10.1063/1.458253View Description Hide Description
Two‐photon pure rotational transitions in the symmetric top CF3CCH have been observed with a pulsed beam Fourier transform crossed‐cavity spectrometer modified to allow the application of a static Stark field. Transient one‐photon emission signals at ν0=17 267 MHz for transitions between the levels (J=3,K,M) and (2,K,M) are generated for K M≠0 by the application of intense pulses at ν0/2. It has been demonstrated that the two‐photon transitions occur within an effectively isolated two‐level system as a result of the first order acStark effect. Quantitative studies of the intensities as a function of pulse length and power show that the two‐photon transition probability in the microwave region is well represented by the theoretical model used by Meerts, Ozier, and Hougen [J. Chem. Phys. 9 0, 4681 (1989)] to treat multiphoton transitions in a two‐level system whose one‐photon frequency is ≲1 MHz. A description is given of the spectrometer with emphasis on the modifications made for two‐photon studies.
State‐to‐state rotational energy transfer measurements in silane by infrared double resonance with a tunable diode laser92(1990); http://dx.doi.org/10.1063/1.458254View Description Hide Description
Infrared double resonancespectroscopy has been used to study state‐resolved rotational and vibrational energy transfer in vibrationally excited SiH4. Completely specified rotational levels (v,J,C n ) are populated by CO2 laser radiation. Subsequent energy transfer is followed by diode laser transient absorption. The total relaxation efficiencies of the initially populated levels for self‐collisions and collisions with Ar and CH4 follow the ordering σ(F 2)>σ(A 2)>σ(E) and are slightly larger than the Lennard‐Jones cross sections. State‐to‐state rotational energy transfer in the ν4 vibration of SiH4 is extremely state specific. In addition to a differentiation between the A, E, and F symmetry levels, there is a selectivity with respect to the fine‐structure levels within each rotational state. A preference for transfer to other levels of the same Coriolis sublevel of ν4 was found. This can be phrased as a Δ(J−R)=0 propensity rule. Principal pathways, only one per J per symmetry, are identified. Within each rotational level, the principal‐pathway final states are closely spaced; this effect is related to the clustering of the rovibrational levels of the dyad. Large changes in J are possible in a single collision between silane molecules. A kinetic master equation has been used to model energy flow among rotational levels in silane, from which state‐to‐state energy transfer parameters could be extracted. Collision‐assisted absorption of two CO2photons into the triad has also been detected. A simple modification of the kinetic analysis allows us to obtain an estimate for the relaxation rate out of the triad levels. These laser pumping and relaxation processes determine the efficiency with which high vibrational levels of silane may be populated by infrared multiple photon excitation.
One‐ and two‐dimensional 31P cross‐polarization magic‐angle‐spinning nuclear magnetic resonance studies on two‐spin systems with homonuclear dipolar coupling and J coupling92(1990); http://dx.doi.org/10.1063/1.458255View Description Hide Description
The effect of dipolar interactions on the solid state 31P cross‐polarization magic‐angle‐spinning (CP‐MAS) nuclear magnetic resonance(NMR) line shapes for the coupled two‐spin systems, sodium pyrophosphate decahydrate, Na4P2O7⋅10H2O, and tetraphenyl diphosphine‐1‐oxide, (C6H5)2PP(O)(C6H5)2, has been investigated. The one‐dimensional (1D)CP‐MAS spectra of Na4P2O7⋅10H2O shows spinning frequency dependent sideband splittings. A theory was developed to permit the calculation of the MAS NMR line shapes of the dipolar and J‐coupled two‐spin systems. An exact solution of the periodic Hamiltonian was obtained by the use of Floquet Hamiltonian theory. The experimental spectra of Na4P2O7⋅10H2O are well reproduced by the theoretical ones calculated from the present theory, in which the homonuclear dipolar interaction between the two 31P nuclei in the P2O7 4 − group was taken into consideration. Our Hamiltonian also leads to calculated spectra which are in good agreement with the experimental observations even at low rotor spinning speeds. The two‐dimensional J‐resolved experiments, with rotationally synchronized acquisition in the t 1 dimension, were performed for both Na4P2O7⋅10H2O and (C6H5)2PP(O)(C6H5)2. These experiments were found to be useful in distinguishing between the different mechanisms of the rotational sideband splitting of 1D spectra, as well as the dipolar interactions between spins with the same isotropic chemical shift, but different orientations of chemical shifttensors. These studies also allowed the identification of splittings caused by homonuclear J‐coupled interactions, because the resolution of the 2D J‐resolved spectra was greater than that of the 1D spectra.
92(1990); http://dx.doi.org/10.1063/1.458256View Description Hide Description
The electron–electron coincidence technique has been used to measure the spectrum of autoionizing (Auger) electrons that are emitted following excitation of a core electron in O2 to the half‐filled 1π g orbital. The spectrum is dominated by transitions to doublet states, with very little intensity in quartet peaks. The kinetic energyspectrum calculated with inclusion of the effects of vibrational overlap in excitation and deexcitation as well as the effects of lifetime‐vibrational interference agrees well with experiment. Comparison of the spectrum with the normal Auger spectrum shows significant similarities between the major features of each.
Two‐photon double resonance spectroscopy of bacteriorhodopsin. Assignment of the electronic and dipolar properties of the low‐lying 1 A *− g ‐like and 1 B *+ u ‐like π, π* states92(1990); http://dx.doi.org/10.1063/1.458206View Description Hide Description
The electronic and dipolar properties of the all‐t r a n s retinyl polyene in light‐adapted bacteriorhodopsin are examined by using two‐photon double resonancespectroscopy to assign the Franck–Condon maxima, the absolute two‐photon absorptivities and the change in dipole moments upon excitation of the low‐lying ‘‘forbidden’’ 1 A *− g ‐like and ‘‘allowed’’ 1 B *+ u ‐like π, π* excited singlet states. The second‐order hyperpolarizability is also determined. The two‐photon double resonancespectrum, collected with laser excitation from 820–1200 nm in 10 nm steps, displays two maxima, an intense band at ∼18 000 cm− 1 assigned to the 1 B *+ u ‐like π, π* excited singlet state and a weaker shoulder at ∼21 000 cm− 1 assigned to the 1 A *− g ‐like π, π* excited singlet state. Thus, the 1 A *− g ‐like state is 3500±500 cm− 1 above the 1 B *+ u ‐like state, which is indicative of a protonated Schiff base chromophore.
A log‐normal fit of the two‐photon spectrum indicates that the maximum two‐photon absorptivity of the 1 B *+ u ‐like state is 290±50 GM whereas the maximum two‐photon absorptivity of the 1 A *− g ‐like state is less than half this value, 120±90 GM. The ‘‘1 B *+ u ’’ state exhibits an absorptivity that is dominated by initial and final state contributions to the two‐photon tensor, and this observation allows an accurate assignment of the change in dipole moment upon excitation yielding Δμ s o =13.5±0.8 D. A similar analysis of the ‘‘1 A *− g ’’ state predicts that the change in dipole moment upon excitation into the latter state is slightly smaller (Δμ s o =9.1±4.8 D). We demonstrate that the second‐order hyperpolarizability of a molecule can be determined directly from the two‐photon absorptivity of the low‐lying charge transfer state and other spectroscopic parameters, all but one of which can be determined directly from experiment. Our analysis of light adapted bacteriorhodopsin indicates that β=β x x x +(1/3)[β x y y +2β y y x +β x z z +2β z z x ] =(2250±240)×10− 3 0cm5/esu for a laser wavelength of 1.06μ assuming that the homogeneous linewidth is 250 cm− 1. Preliminary analyses of the two‐photon data indicate that the chromophore in bacteriorhodopsin is a protonated Schiff base chromophore in a very ionic, and possibly charged, binding site. The two‐photon data are not consistent with charged species near the β‐ionylidene ring, but are consistent with polar species near the β‐ionylidene ring. Direct hydrogen bonding of a negative counterion with the imine proton is not supported by the two‐photon data.
Localized chaos and partial assignability of dynamical constants of motion in the transition to molecular chaos92(1990); http://dx.doi.org/10.1063/1.458207View Description Hide Description
The implications of approximate dynamical constants of motion for statistical analysis of highly excited vibrational spectra are investigated. The existence of approximate dynamical constants is related to localized chaos and partial assignability of a ‘‘chaotic spectrum.’’ Approximate dynamical constants are discussed in a dynamical symmetry breaking formulation of the transition from periodic to quasiperiodic motion, and from quasiperiodic to chaotic motion. Level repulsion, leading to a Wigner distribution in the case of a strongly chaotic system, is shown to originate in dynamical symmetry breaking via the noncrossing rule that states of the same symmetry do not cross. It is argued that quantum numbers for dynamical constants must be correctly assigned to detect localized chaos in statistical spectroscopy. Two possible kinds of approximate constants, for a ‘‘total polyad number’’ and a bend normal mode, are discussed in relation to two coupling schemes that could govern the transition to chaos in H2O.