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Lombardi and co-workers have invoked the Herzberg-Teller intensity borrowing concept as used by Tang and Albrecht in their calculation of the contribution of the charge-transfer mechanism to SERS. In the analysis here, based on Eq., this is unnecessary. This concept was introduced in order to explain the appearance of molecular spectral features that are forbidden by symmetry in the Born-Oppenheimer (BO) approximation. However, the zero-order description of the molecule-metal system is not done in the adiabatic BO, but on the "diabatic" level in which the BO picture is applied to the uncoupled molecule and metal systems, leaving their electronic coupling as a perturbative correction in the Hamiltonian. In this representation there is no need to invoke intensity borrowing in a discussion of photon induced charge-transfer transitions between metal(s) and molecule. The actual coupling needs of course to be estimated, and in the present work, we have based our estimate on a model proposed by Persson (Ref.) as discussed at the end of Sec..
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We use the term normal Raman scattering for the process that starts and ends in the molecular ground state, while inverse Raman starts and ends with the molecule in the excited state. The term normal in the present paper is unrelated to the normal used to distinguish from "resonant."
-
We use the term normal Raman scattering for the process that starts and ends in the molecular ground state, while inverse Raman starts and ends with the molecule in the excited state. The term normal in the present paper is unrelated to the normal used to distinguish from "resonant."
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Note that the electron-hole contribution to damping rates in the single electron GFs, as taken into account in Refs. 27 and 28, is dropped here for simplicity. In the present consideration we focus on the effect of damping due to electron-hole excitations on the two-particle Green functions, since it is this process which directly influences the Raman signal. The latter enters via the ansatz, Eq., employed in the calculation of excitation operators correlation function.
-
Note that the electron-hole contribution to damping rates in the single electron GFs, as taken into account in Refs. 27 and 28, is dropped here for simplicity. In the present consideration we focus on the effect of damping due to electron-hole excitations on the two-particle Green functions, since it is this process which directly influences the Raman signal. The latter enters via the ansatz, Eq., employed in the calculation of excitation operators correlation function.
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Due to the assumed weak coupling between the molecular vibration and the thermal bath, the vibrational state density is almost a delta function. Hence the actual character of the distribution is not important, since the vibration population is defined by one point N (ω).
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Due to the assumed weak coupling between the molecular vibration and the thermal bath, the vibrational state density is almost a delta function. Hence the actual character of the distribution is not important, since the vibration population is defined by one point N (ω).
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In principle, the same ansatz can be used to include damping due to coupling to the laser field; however, we disregard it due to the weak electron-photon coupling assumed.
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In principle, the same ansatz can be used to include damping due to coupling to the laser field; however, we disregard it due to the weak electron-photon coupling assumed.
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Equations are obtained by separating the polarization correlation functions into products of correlation functions involving d operators associated with the individual levels (this can be done when these levels do not mix by their interactions with the leads), then applying Wick's theorem to represent these correlation functions as sums of products of single electron GFs for the corresponding levels. The assumption of no level mixing can be relaxed at the price of getting more complex expressions that involve also mixed single electron GFs G 12 >,<
-
Equations are obtained by separating the polarization correlation functions into products of correlation functions involving d operators associated with the individual levels (this can be done when these levels do not mix by their interactions with the leads), then applying Wick's theorem to represent these correlation functions as sums of products of single electron GFs for the corresponding levels. The assumption of no level mixing can be relaxed at the price of getting more complex expressions that involve also mixed single electron GFs G 12 >,<.
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52
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65249092279
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In Eqs. two energy variables are used for each molecular electronic level. Ej (k) represents the energy variable j associated with level k.
-
In Eqs. two energy variables are used for each molecular electronic level. Ej (k) represents the energy variable j associated with level k.
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53
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65249154539
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Because each term in Eq. contains a product of two functions S, the substitution of 2 (K) by C2 (K) corresponds to multiplying the state to state flux by ρ R (i) ρ R (f) ≃ ρ R2, in analogy to Eq..
-
Because each term in Eq. contains a product of two functions S, the substitution of 2 (K) by C2 (K) corresponds to multiplying the state to state flux by ρ R (i) ρ R (f) ≃ ρ R2, in analogy to Eq..
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This result was obtained using the order of magnitude estimate based on Eq., taking R the same molecular radiative rate used to estimate the Raman intensity associated with the molecular process. Note, however, that R in Eq. is the radiative rate associated with a transition dipole of magnitude (e is the electron charge and d molecule-metal distance) that may be considerably larger than a typical molecular radiative rate.
-
This result was obtained using the order of magnitude estimate based on Eq., taking R the same molecular radiative rate used to estimate the Raman intensity associated with the molecular process. Note, however, that R in Eq. is the radiative rate associated with a transition dipole of magnitude (e is the electron charge and d molecule-metal distance) that may be considerably larger than a typical molecular radiative rate.
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