The nonlinear optical response of liquids subjected to a series of N femtosecond laser pulses is calculated using a multimode harmonic model for nuclear motions, with nonlinear coupling to the radiation field through the coordinate dependence of the electronic polarizability. Using electronically off‐resonant optical fields, this multidimensional spectroscopy is shown to provide direct information regarding the homogeneous or the inhomogeneous nature of the spectral density obtained from optical birefringence measurements. Complementary information can be obtained using infrared pulses where the multiple time correlation functions of the nuclear dipole moment (rather than the electronic polarizability) are being probed.

http://mukamel.ps.uci.edu/publications/pdfs/247.pdf

Two-dimensional femtosecond vibrational spectroscopy of liquids

The instantaneous normal modes of liquids

We present an instantaneous‐normal‐mode analysis of liquid water at room temperature based on a computer simulated set of liquid configurations and we compare the results to analogous inherent‐structure calculations. The separate translational and rotational contributions to each instantaneous normal mode are first obtained by computing the appropriate projectors from the eigenvectors. The extent of localization of the different kinds of modes is then quantified with the aid of the inverse participation ratio—roughly the reciprocal of the number of degrees of freedom involved in each mode. The instantaneous normal modes also carry along with them an implicit picture of how the topography of the potential surface changes as one moves from point to point in the very‐high dimensional configuration space of a liquid. To help us understand this topography, we use the instantaneous normal modes to compute the predicted heights and locations of the nearest extrema of the potential. The net result is that in liquid water, at least, it is the low frequency modes that seem to reflect the largest‐scale structural transitions. The detailed dynamics of such transitions are probably outside of the instantaneous‐normal‐mode formalism, but we do find that short‐time dynamical quantities, such as the angular velocity autocorrelation functions, are described extraordinarily well by the instantaneous modes.

Instantaneous normal mode analysis of liquid water

Off‐resonant transient birefringence measurements are analyzed using a reduced equation of motion for the ground state density matrix, which is expanded using an effective Hamiltonian. Assuming that the pump field is weak, we express the polarization relevant for the birefringence signal in terms of a convolution of the tensorial polarizability response function with the external fields. The homodyne‐detected birefringence signal is directly compared with the coherent Raman signal. The relationship between off‐resonant birefringence and spontaneous Raman experiments is discussed. By expanding the polarizability in powers of the nuclear coordinates and applying the Brownian oscillator model to the coordinate response function, we separate the birefringence signal into intra‐ and intermolecular coordinate response functions. Off‐resonant transient birefringences of acetonitrile, chloroform, dimethylsulfoxide, and a series of alcohols were measured. The data are transformed to the frequency domain by using a model independent analysis method. The spectra are discussed in the context of various models for the distribution of intermolecular modes (spectral density) in liquids.

/pdf/off-resonant-transient-birefringence-in-liquids-4d6y2tngi8.pdf

Off-resonant transient birefringence in liquids

The vibrational characteristics of liquid dynamics are used to describe the ultrafast relaxations observed in time‐dependent fluorescence Stokes shift [J. Chem. Phys. 95, 4715 (1991)] and heterodyne detected optical Kerr effect measurements on acetonitrile, via a Brownian oscillator model. Introducing a frequency distribution of vibrational modes makes it possible to compare the two experiments. The ultrafast decays observed in the fluorescence Stokes shift and optical Kerr signals are produced by destructive superposition of the high frequency, underdamped modes.

/pdf/ultrafast-solvent-dynamics-connection-between-time-resolved-49qnzllrd2.pdf

Ultrafast solvent dynamics: Connection between time resolved fluorescence and optical Kerr measurements

Recent theoretical developments have shown how such examples of excitation properties as the electronic band structure and the set of vibrational normal modes of a liquid can be studied by traditional classical‐liquid‐theory methods. In this paper, we add another example to this collection: the set of polarization modes of a liquid. The basic notion is that in any polarizable but nonpolar fluid, the dynamics of the instantaneous dipoles can be represented as a linear combination of harmonic contributions from independent, microscopically defined, polarization modes. We note first how many of the properties one would like to know about the liquid—its full dielectric behavior, its optical absorption spectrum, its effect on the absorption spectrum of a solute, and even how the net polarization of the liquid fluctuates with time—are available from these polarization modes. We then point out how the requisite information about the modes can be ascertained by the same liquid theory methods used to treat p‐orbit...

The spectrum of polarization fluctuations in an atomic liquid

One can make significant inroads into the problems of identifying the collective linear excitations (band structure) of liquids using what have been called ‘‘single‐site’’ theories. In the context of liquid‐theory methods for band structure, such theories arise from linear liquid theories such as the mean spherical approximation. However, at low densities, and when certain levels of eigenvector information are required, these theories are manifestly inadequate. We show here how a nonlinear theory for band structure in liquids can be constructed based on the EXP liquid theory. When tested against simulations of electronic s bands, the predictions are found to be quantitatively accurate in both low‐density fluids and in impurity‐band situations with uncorrelated dopants. Beyond its ramifications for band structure, the calculation presented here is also of some technical interest as an example of a nonlinear treatment of fluctuating internal degrees of freedom in liquids.

Nonlinear aspects of band structure in liquids. I. Neat liquids

Formally, the problem of calculating the single‐electron energy levels for a liquid requires that one diagonalize a 1023×1023 matrix, but previous work has made it clear that precisely the same information is available from the solution of a simple classical liquid problem. We extend our previous applications of this idea in several ways here: (1) the mean spherical approximation (MSA) for liquids is used to provide an explicit route to the density of states for a band resulting from a basis of p orbitals, (2) the previous MSA solution for s bands and the new MSA solution for p bands are both generalized to allow for nonorthogonality in the basis, and (3) numerical procedures are described for solving the integral equations resulting from these MSA theories. These developments mean that it is now computationally feasible to find the band structure of almost any simple liquid within a tight‐binding model. We illustrate this point by computing the s and p bands expected from a hard‐sphere liquid with a minimal basis of hydrogenic orbitals on each atom.

Liquid theory for band structure in a liquid. III, The mean spherical approximation for p bands and the numerical solution of the mean spherical approximation for both s and p bands

If a set of solvent molecules are sufficiently weakly interacting, then their net effect on a solute is simply the sum of their individual effects. The shift and broadening of any solute quantum state would then be determined solely by the statistics of this sum (the local field at the solute). However, when the solvent–solvent interaction is comparable to that felt by the solute, the problem of ascertaining solvent effects on solute states becomes one of understanding how a band of collective solvent states couples to a solute. In this paper we show that a nonlinear liquid theory for band structure can be used to understand phenomena such as inhomogeneous broadening from precisely this solvent–band perspective. Inhomogeneous broadening in this language arises from configuration‐to‐configuration fluctuations in the solvent’s Green’s function, the size of which one can now evaluate.

Zhe Chen

Papers

The spectrum of polarization fluctuations in an atomic liquid

Nonlinear aspects of band structure in liquids. I. Neat liquids

Liquid theory for band structure in a liquid. III, The mean spherical approximation for p bands and the numerical solution of the mean spherical approximation for both s and p bands

Nonlinear aspects of band structure in liquids. II. Solute spectra