ABSTRACT
Sum vibrational frequency spectroscopy, a second order optical process, is interface specific in the dipole approximation. At charged interfaces, there exists a static field, and as a direct consequence, the experimentally detected signal is a combination of enhanced second and static field induced third order contributions. There is significant evidence in the literature of the importance/relative magnitude of this third order contribution, but no previous molecularly detailed approach existed to separately calculate the second and third order contributions. Thus, for the first time, a molecularly detailed time correlation function theory is derived here that allows for the second and third order contributions to sum frequency vibrational spectra to be individually determined. Further, a practical, molecular dynamics based, implementation procedure for the derived correlation functions that describe the third order phenomenon is also presented. This approach includes a novel generalization of point atomic polarizability models to calculate the hyperpolarizability of a molecular system. The full system hyperpolarizability appears in the time correlation functions responsible for third order contributions in the presence of a static field.
Subject(s)
Models, Chemical , Models, Molecular , Optics and Photonics , Static Electricity , Surface Properties , Computer Simulation , Statistics as Topic , Time FactorsABSTRACT
An improved time correlation function (TCF) description of sum frequency generation (SFG) spectroscopy was developed and applied to theoretically describing the spectroscopy of the ambient water/vapor interface. A more general TCF expression than was published previously is presented-it is valid over the entire vibrational spectrum for both the real and imaginary parts of the signal. Computationally, earlier time correlation function approaches were limited to short correlation times that made signal processing challenging. Here, this limitation is overcome, and well-averaged spectra are presented for the three independent polarization conditions that are possible for electronically nonresonant SFG. The theoretical spectra compare quite favorably in shape and relative magnitude to extant experimental results in the O-H stretching region of water for all polarization geometries. The methodological improvements also allow the calculation of intermolecular SFG spectra. While the intermolecular spectrum of bulk water shows relatively little structure, the interfacial spectra (for polarizations that are sensitive to dipole derivatives normal to the interface--SSP and PPP) show a well-defined intermolecular mode at 875 cm(-1) that is comparable in intensity to the rest of the intermolecular structure, and has an intensity that is approximately one-sixth of the magnitude of the intense free O-H stretching peak. Using instantaneous normal mode methods, the resonance is shown to be due to a wagging mode localized on a single water molecule, almost parallel to the interface, with two hydrogens displaced normal to the interface, and the oxygen anchored in the interface. We have also uncovered the origin of another intermolecular mode at 95 cm(-1) for the SSP and PPP spectra, and at 220 cm(-1) for the SPS spectra. These resonances are due to hindered translations perpendicular to the interface for the SSP and PPP spectra, and translations parallel to the interface for the SPS spectra. Further, by examining the real and imaginary parts of the SFG signal, several resonances are shown to be due to a single spectroscopic species while the "donor" O-H region is shown to consist of three distinct species-consistent with an earlier experimental analysis.
ABSTRACT
An improved time correlation function description of sum frequency generation (SFG) spectroscopy was applied to theoretically describe the water/vapor interface. The resulting spectra compare favorably in shape and relative magnitude to extant experimental results in the O-H stretching region of water. Further, the SFG spectra show a well-defined intermolecular mode at 875 cm(-1) that has significant intensity. The resonance is due to a wagging mode localized on a single water molecule. It represents a well-defined population of water molecules at the interface that, along with the free O-H modes, represent the dominant interfacial species.
ABSTRACT
A theory describing the third-order response function R((3))(t(1),t(2),t(3)), which is associated with two-dimensional infrared (2DIR) spectroscopy, has been developed. R((3)) can be written as sums and differences of four distinct quantum mechanical dipole (multi)time correlation functions (TCF's), each with the same classical limit; the combination of TCF's has a leading contribution of order variant Planck's over 2pi (3) and thus there is no obvious classical limit that can be written in terms of a TCF. In order to calculate the response function in a form amenable to classical mechanical simulation techniques, it is rewritten approximately in terms of a single classical TCF, B(R)(t(1),t(2),t(3))=micro(j)(t(2)+t(1))micro(i)(t(3)+t(2)+t(1))micro(k)(t(1))micro(l)(0), where the subscripts denote the Cartesian dipole directions. The response function is then given, in the frequency domain, as the Fourier transform of a classical TCF multiplied by frequency factors. This classical expression can then further be quantum corrected to approximate the true response function, although for low frequency spectroscopy no correction is needed. In the classical limit, R((3)) becomes the sum of multidimensional time derivatives of B(R)(t(1),t(2),t(3)). To construct the theory, the response function's four TCF's are rewritten in terms of a single TCF: first, two TCF's are eliminated from R((3)) using frequency domain detailed balance relationships, and next, two more are removed by relating the remaining TCF's to each other within a harmonic oscillator approximation; the theory invokes a harmonic approximation only in relating the TCF's and applications of theory involve fully anharmonic, atomistically detailed molecular dynamics (MD). Writing the response function as a single TCF thus yields a form amenable to calculation using classical MD methods along with a suitable spectroscopic model. To demonstrate the theory, the response function is obtained for liquid water with emphasis on the OH stretching portion of the spectrum. This approach to evaluating R((3)) can easily be applied to chemically interesting systems currently being explored experimentally by 2DIR and to help understand the information content of the emerging multidimensional spectroscopy.
