A molecular spectroscopic view of surface plasmon enhanced resonance Raman scattering

The enhancement of resonance Raman scattering by coupling to the plasmon resonance of a metal nanoparticle is developed by treating the molecule-metal interaction as transition dipole coupling between the molecular electronic transition and the much stronger optical transition of the nanoparticle. A density matrix treatment accounts for coupling of both transitions to the electromagnetic field, near-resonant energy transfer between the molecule-excited and nanoparticle-excited states, and dephasing processes. This fully quantum mechanical approach reproduces the interference effects observed in extinction spectra of J-aggregated dyes adsorbed to metal nanoparticles and makes testable predictions for surface-enhanced resonance Raman excitation profiles.     

Solute-solvent intermolecular vibronic coupling as manifested by the molecular near-field effect in resonance hyper-Raman scattering

Vibronic coupling within the excited electronic manifold of the solute all-trans-β-carotene through the vibrational motions of the solvent cyclohexane is shown to manifest as the "molecular near-field effect," in which the solvent hyper-Raman bands are subject to marked intensity enhancements under the presence of all-trans-β-carotene. The resonance hyper-Raman excitation profiles of the enhanced solvent bands exhibit similar peaks to those of the solute bands in the wavenumber region of 21,700-25,000 cm(-1) (10,850-12,500 cm(-1) in the hyper-Raman exciting wavenumber), where the solute all-trans-β-carotene shows a strong absorption assigned to the 1A(g) → 1B(u) transition. This fact indicates that the solvent hyper-Raman bands gain their intensities through resonances with the electronic states of the solute. The observed excitation profiles are quantitatively analyzed and are successfully accounted for by an extended vibronic theory of resonance hyper-Raman scattering that incorporates the vibronic coupling within the excited electronic manifold of all-trans-β-carotene through the vibrational motions of cyclohexane. It is shown that the major resonance arises from the B-term (vibronic) coupling between the first excited vibrational level (v = 1) of the 1B(u) state and the ground vibrational level (v = 0) of a nearby A(g) state through ungerade vibrational modes of both the solute and the solvent molecules. The inversion symmetry of the solute all-trans-β-carotene is preserved, suggesting the weak perturbative nature of the solute-solvent interaction in the molecular near-field effect. The present study introduces a new concept, "intermolecular vibronic coupling," which may provide an experimentally accessible∕theoretically tractable model for understanding weak solute-solvent interactions in liquid.     

Theory of raman scattering from molecules. Summation over vibrational states

Upper and lower bounds of the vibrational sums involved in the polanzability tensor are derived. The lower bound leads to a simplified formula applicable to resonance Raman scattering in both weak and strong coupling cases. A new expansion of the vibrational sum is introduced and useful expressions for excitation profiles are obtained.     

The theory of surface-enhanced Raman scattering

By considering the molecule and metal to form a conjoined system, we derive an expression for the observed Raman spectrum in surface-enhanced Raman scattering. The metal levels are considered to consist of a continuum with levels filled up to the Fermi level, and empty above, while the molecule has discrete levels filled up to the highest occupied orbital, and empty above that. It is presumed that the Fermi level of the metal lies between the highest filled and the lowest unfilled level of the molecule. The molecule levels are then coupled to the metal continuum both in the filled and unfilled levels, and using the solutions to this problem provided by Fano, we derive an expression for the transition amplitude between the ground stationary state and some excited stationary state of the molecule-metal system. It is shown that three resonances contribute to the overall enhancement; namely, the surface plasmon resonance, the molecular resonances, as well as charge-transfer resonances between the molecule and metal. Furthermore, these resonances are linked by terms in the numerator, which result in SERS selection rules. These linked resonances cannot be separated, accounting for many of the observed SERS phenomena. The molecule-metal coupling is interpreted in terms of a deformation potential which is compared to the Herzberg-Teller vibronic coupling constant. We show that one term in the sum involves coupling between the surface plasmon transition dipole and the molecular transition dipole. They are coupled through the deformation potential connecting to charge-transfer states. Another term is shown to involve coupling between the charge-transfer transition and the molecular transition dipoles. These are coupled by the deformation potential connecting to plasmon resonance states. By applying the selection rules to the cases of dimer and trimer nanoparticles we show that the SERS spectrum can vary considerably with excitation wavelength, depending on which plasmon and/or charge-transfer resonance is excited.     

Time-dependent picture of the charge-transfer contributions to surface enhanced Raman spectroscopy

We reexamine the Herzberg-Teller theory of charge-transfer contributions to the theory of surface enhanced Raman scattering (SERS). In previous work, the Kramers-Heisenberg-Dirac framework was utilized to explain many of the observed features in SERS. However, recent experimental and theoretical developments suggest that we revise the theory to take advantage of the time-dependent picture of Raman scattering. Results are obtained for molecular adsorption on nanoparticles in both the strong confinement limit and the weak confinement limit. We show that the Herzberg-Teller contributions to the charge-transfer effect in SERS display a resonance at the molecule-to-metal or metal-to-molecule transition while retaining the selection rules associated with normal Raman spectroscopy (i.e., harmonic oscillator, as opposed to Franck-Condon overlaps). The charge-transfer contribution to the enhancement factor scales as Gamma(-4), where Gamma is the homogeneous linewidth of the charge-transfer transition, and thus is extremely sensitive to the magnitude of this parameter. We show that the Herzberg-Teller coupling term may be associated with the polaron-coupling constant of the surface phonon-electron interaction. A time-dependent expression for the Raman amplitude is developed, and we discuss the implications of these results for both metal and semiconductor nanoparticle surfaces.     

Hyper-Rayleigh and hyper-Raman scatterings with intermediate and two-photon resonances

The normally weak process of hyper-Raman scattering can be greatly enhanced when the excitation is two photon resonant with an electronic transition that is both one and two photon allowed. It might be expected to be further enhanced when a one-photon allowed transition provides an intermediate state resonance in the two-photon excitation step. The theory of this triply resonant process is developed for organic nonlinear chromophores. Experimental results are obtained for one donor-acceptor substituted push-pull chromophore in which the energy of the strongly allowed lowest-lying one-photon state may be tuned by varying the solvent without substantially affecting the two-photon resonant transition. Surprisingly, bringing the one-photon allowed state into resonance does not significantly increase the hyper-Rayleigh or hyper-Raman hyperpolarizabilities. Analysis of the resonance Raman, hyper-Rayleigh, and hyper-Raman profiles suggests that the triply resonant path does not make the dominant contribution to the hyperpolarizability in this system.     

Exciton dynamics in molecular crystals from line shape analysis. Spectral moment analysis of the origin region of the 4000 Å transition of crystal anthracene

A spectral moment analysis of the line shape function ω?₂(ω) in the region of the (0—0) band of the 4000 ŹB_2u ← ¹A_g transition in crystal anthracene at various temperatures is performed. The data are compared with the predictions of three coupling models, viz., weak exciton—photon with weak exciton—phonon coupling, strong exciton—photon with weak exciton—phonon coupling, weak exciton—photon with strong exciton—phonon coupling. The terms contributing to each spectral moment for each model are rendered explicit. The experimental data indicate that the exciton—intermolecular phonon coupling is primarily weak. The exciton interacts with optical phonons of about 90 cm^-1 frequency with a coupling strength of about 140 cm^-1 , a value near that predicted by a weak coupling model. The coupling strength is nearly the same irrespective of whether the exciton is created by b- or a-polarized light probably indicative of the importance of higher multipole contributions to the coupling although the existence of strong interband scattering could affect that suggestion. The coupling parameters g_op and g_ac are about 10^-1 and 10^-4 respectively.     

Li2 Autler-Townes分裂的实验观察

用光学-光学双共振激光光谱研究了 7Li2A 1Σ+u态的Autler-Townes (A-T) 分裂.一个强的耦合场 (泵浦激光)激发 7Li2A 1Σ+u v′, J′← X 1Σ+g v″, J″跃迁,诱发A 1Σ+u v′, J′能级和 X 1Σ+gv″, J″能级的A-T分裂.另一个探测激光从A 1Σ+u v′,J′能级进一步激发到4 1Σ+g态.扫描探测激光,监测4 1Σ+g态碰撞诱导紫色荧光,从而探测A 1Σ+u v′, J′能级的A-T分裂.当耦合场频率偏离共振时,激发光谱线出现双重分裂.在该实验条件下,分裂大小和泵浦激光频率偏离共振频率的失谐量成正比. 研究了A-T分裂的两条线的相对强度与泵浦、探测光的强度及缓冲气体压力的关系.     

Comment on the applicability of Urbach's rule to molecular crystals

The extent to which the absorption profile below the first exciton band can be predicted without recourse to resonance transfer and strong exciton—phonon coupling is evaluated for a crystal transition derived from a moderately intense free molecule transition. It is argued, on the basis of a simple model, that Urbach rule behavior can arise from the same class of weak exciton—phonon interactions that determine hot band absorption shapes.     

Ab initio study of low-lying triplet states of the lithium dimer

Observation of Bose-Einstein condensation in Li27 initiated the interest in the scattering length of two ground state lithium atoms when they approach each other as a radical pair triplet aSigmau+3 state. But some properties of this state are still unknown. In present work, a number of low-lying triplet states of lithium molecule are calculated by multi-configuration self-consistent field (MCSCF) and response techniques with account of spin-orbit coupling, spin-spin coupling and some other magnetic perturbations. The singlet-triplet transition probabilities to the ground state are also presented. Most results are connected with the weakly bound lowest triplet a3Sigmau+ state, whose radiative lifetime and spin-splitting are unknown so far in spite of its great importance in Bose-Einstein condensation. Calculations indicate that this state has a very small spin-splitting, lambdass=-0.01 cm-1, which is negligible in comparison with the line-width in experimental Fourier transform spectra published so far. Similar splitting is obtained for the upper state of the 1(3)Sigmag+--a3Sigmau+ transition. This is in agreement with experimental rovibronic analysis of the 1(3)Sigmag+--a3Sigmau+ band system in which the triplet structure was not resolved. The radiative lifetime of the a3Sigmau+ state is predicted to exceed 10 h.     

Collinear collisions in a double-morse well

We discuss the fraction of chaotic trajectories in a bound system near the dissociation limit, and the fraction of apparent chaos in scattering trajectories above that energy. Both depend in an oscillatory manner on the coupling parameter δ = m/(m + M), which means that not the coupling as such is responsible for more or less chaos. Rather, two different kinds of resonance condition determine what counts as chaos in the bound and scattering cases. The second resonance condition, determining more or less easy passage through the well for scattering trajectories, determines also the average lifetime and the RRKM-ness of unimolecular complex decay. They depend also in an oscillatory way on the mass ratio.     

Multimodal coupling of optical transitions and plasmonic oscillations in rhodamine B modified gold nanoparticles

The optical properties of a photoluminescent dye rhodamine B (RhB) interacting with gold nanoparticles (AuNP) have been investigated using plasmonic absorbance, fluorescence, and resonance elastic light scattering (RELS) spectroscopy. We have found that these interactions result in a multimodal coupling that influence optical transitions in RhB. In absorbance measurements, we have observed for the first time the coupling resulting in strong screening of RhB π-π* transitions, likely caused by a contact adsorption of RhB on a conductive surface of AuNP. The nanoparticles quench also very efficiently the RhB fluorescence. We have determined that the static quenching mechanism with a non-F?rster fluorescence resonance energy transfer (FRET) from RhB molecules to AuNP is involved. The Stern-Volmer dependence F(0)/F = f(Q) shows an upward deviation from linearity, attributed to the ultra-high quenching efficiency of AuNP leading to the new extended Stern-Volmer model. A sharp RELS peak of RhB alone (λ(max) = 566 nm) has been observed for the first time and attributed to the resonance fluorescence and enhanced scattering. This peak is completely quenched in the presence of AuNP(22nm). Our quantum mechanical calculations confirm that the distance between AuNP surface and conjugated π-electron system in RhB is well within the range of plasmonic fields extending from AuNP. The optical transition coupling to plasmonic oscillations and the efficient energy transfer due to the interactions of fluorescent dyes with nanoparticles are important for biophysical studies of life processes and applications in nanomedicine.     

Vibronic coupling simulations for linear and nonlinear optical processes: theory

A comprehensive vibronic coupling model based on the time-dependent wavepacket approach is derived to simulate linear optical processes, such as one-photon absorbance and resonance Raman scattering, and nonlinear optical processes, such as two-photon absorbance and resonance hyper-Raman scattering. This approach is particularly well suited for combination with first-principles calculations. Expressions for the Franck-Condon terms, and non-Condon effects via the Herzberg-Teller coupling approach in the independent-mode displaced harmonic oscillator model are presented. The significance of each contribution to the different spectral types is discussed briefly.     

Reduced dimensionality spin-orbit dynamics of CH3 + HCl ⇌ CH4 + Cl on ab initio surfaces

A reduced dimensionality quantum scattering method is extended to the study of spin-orbit nonadiabatic transitions in the CH(3) + HCl ? CH(4) + Cl((2)P(J)) reaction. Three two-dimensional potential energy surfaces are developed by fitting a 29 parameter double-Morse function to CCSD(T)/IB//MP2/cc-pV(T+d)Z-dk ab initio data; interaction between surfaces is described by geometry-dependent spin-orbit coupling functions fit to MCSCF/cc-pV(T+d)Z-dk ab initio data. Spectator modes are treated adiabatically via inclusion of curvilinear projected frequencies. The total scattering wave function is expanded in a vibronic basis set and close-coupled equations are solved via R-matrix propagation. Ground state thermal rate constants for forward and reverse reactions agree well with experiment. Multi-surface reaction probabilities, integral cross sections, and initial-state selected branching ratios all highlight the importance of vibrational energy in mediating nonadiabatic transition. Electronically excited state dynamics are seen to play a small but significant role as consistent with experimental conclusions.     

Vibrational dephasing and resonance energy transfer in molecular liquids

The influence of vibrational band-broadening mechanisms (pure dephasing, resonance transfer, depopulation processes) on the vibrational correlation functions of dense fluids is discussed. The coupling between the vibrational and the rotational-translational subsystems is assumed to be weak. It is found that even for weak coupling the homogeneously broadened linewidth (the inverse dephasing time τ^?1) cannot be represented as a sum of widths related to the individual mechanisms. Using an exponential repulsive interaction potential, we obtain numerical estimates for the dephasing time of the 1 ← 0 transition of liquid nitrogen, which agree very well with experimental observations. It turns out that the most significant contribution for τ arises from the weak anharmonicities of the molecular oscillator.     

On the origin of the forward peak and backward oscillations in the F + H(2)(v = 0) --> HF(v' = 2) + H reaction

We present a semiclassical complex angular momentum (CAM) analysis of the forward scattering peak which occurs at a translational collision energy around 32 meV in the quantum mechanical calculations for the F + H(2)(v = 0, j = 0) --> HF(v' = 2, j' = 0) + H reaction on the Stark-Werner potential energy surface. The semiclassical CAM theory is modified to cover the forward and backward scattering angles. The peak is shown to result from constructive/destructive interference of the two Regge states associated with two resonances, one in the transition state region and the other in the exit channel van der Waals well. In addition, we demonstrate that the oscillations in the energy dependence of the backward differential cross section are caused by the interference between the direct backward scattering and the decay of the two resonance complexes returning to the backward direction after one full rotation.     

Accidental vibrational degeneracy in vibrational excited states observed with ultrafast two-dimensional IR vibrational echo spectroscopy

The coupling between the OD stretch v=2 level and benzene-ring modes in 2-methoxyphenol-OD (hydroxyl H replaced by D) is observed with ultrafast two-dimensional (2D) IR vibrational echo spectroscopy. Because of this coupling, the 1-2 transition peak in the 2D spectrum is split into a doublet with peaks of approximately equal amplitudes. Several molecules and solvents were used to study this phenomenon. Near-IR (NIR) spectroscopy measurements and density-functional theory calculations (B3LYP6-31+G(d,p) level) were also applied. Experimental results and calculations show that the OD stretch 1-2 transition is coupled to a combination band related to the benzene-ring motions. A simple quantum-mechanical model indicates that the combination band has a frequency of 5172 and 5176.5 cm(-1) in CCl4 and hexane, respectively. The transition between this combination band and the ground state is too weak to detect by NIR. The transition between this band and the OD stretch first excited state is also so weak that most of the intensity of the doublet comes from the oscillator strength produced by coupling to the OD stretch. The model gives the coupling strengths as 6.5 and 7 cm(-1) in CCl4 and hexane, respectively.     

An application of the dynamical Lie algebraic method to energy transfer of the collinear scattering system AB+CD

The dynamical Lie algebraic method has been applied to treat the V–V and T–V energy transfers in the collinear scattering system AB+CD. The expression for the vibrational transition probability, which contains the main dynamical parameters, is given analytically. By using this expression we probe into the V–V resonance and T–V resonance phenomena appearing in the process of energy transfer. We find that the transition probability of V–V resonance is in good agreement with that obtained using the resonant exchange hypothesis. Then the reliability of the resonant exchange hypothesis is confirmed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Vibronic coupling simulations for linear and nonlinear optical processes: simulation results

A vibronic coupling model based on time-dependent wavepacket approach is applied to simulate linear optical processes, such as one-photon absorbance and resonance Raman scattering, and nonlinear optical processes, such as two-photon absorbance and resonance hyper-Raman scattering, on a series of small molecules. Simulations employing both the long-range corrected approach in density functional theory and coupled cluster are compared and also examined based on available experimental data. Although many of the small molecules are prone to anharmonicity in their potential energy surfaces, the harmonic approach performs adequately. A detailed discussion of the non-Condon effects is illustrated by the molecules presented in this work. Linear and nonlinear Raman scattering simulations allow for the quantification of interference between the Franck-Condon and Herzberg-Teller terms for different molecules.     

Exciton coupling of tetra(p-hydroxyphenyl)porphyrin controlled by substituents of counterions in Triton X-100 micellar solution

The interactions of nonionic meso-tetra(p-hydroxyphenyl)porphyrin (THPP) with CX3COOH (X = F, Cl, Br) in Triton X-100 (TX) micellar solution have been investigated by optical absorption, resonance light-scattering, and fluorescence spectroscopies. The double red-shifted absorption bands and strong resonance light scattering (RLS) signal imply that the assemblies induced by trihalo acetic acids belong to J-aggregates. The fluorescence of porphyrin is quenched due to the aggregate formation. The kinetics of assemblies trigged by CBr3COOH is studied via stopped-flow techniques. No characteristics of autocatalyzed reactions are observed, and there is only a log phase. The nature of the exciton coupling of transition dipole moment can be systematically changed by the haloid substituents of the organic counteranion.