Analysis of 2D THz-Raman spectroscopy using a non-Markovian Brownian oscillator model with nonlinear system-bath interactions.

We explore and describe the roles of inter-molecular vibrations employing a Brownian oscillator (BO) model with linear-linear (LL) and square-linear (SL) system-bath interactions, which we use to analyze two-dimensional (2D) THz-Raman spectra obtained by means of molecular dynamics (MD) simulations. In addition to linear infrared absorption (1D IR), we calculated 2D Raman-THz-THz, THz-Raman-THz, and THz-THz-Raman signals for liquid formamide, water, and methanol using an equilibrium non-equilibrium hybrid MD simulation. The calculated 1D IR and 2D THz-Raman signals are compared with results obtained from the LL+SL BO model applied through use of hierarchal Fokker-Planck equations with non-perturbative and non-Markovian noise. We find that all of the qualitative features of the 2D profiles of the signals obtained from the MD simulations are reproduced with the LL+SL BO model, indicating that this model captures the essential features of the inter-molecular motion. We analyze the fitted 2D profiles in terms of anharmonicity, nonlinear polarizability, and dephasing time. The origins of the echo peaks of the librational motion and the elongated peaks parallel to the probe direction are elucidated using optical Liouville paths.

[1]  R. Kubo,et al.  Time Evolution of a Quantum System in Contact with a Nearly Gaussian-Markoffian Noise Bath , 1989 .

[2]  Y. Tanimura,et al.  Two-dimensional fifth-order Raman spectroscopy of liquid formamide: Experiment and Theory. , 2008, The Journal of chemical physics.

[3]  S. Saito,et al.  Ultrafast intermolecular dynamics of liquid water: a theoretical study on two-dimensional infrared spectroscopy. , 2008, The Journal of chemical physics.

[4]  H. Risken,et al.  The Fokker-Planck Equation: Methods of Solution and Application, 2nd ed. , 1991 .

[5]  P. Wolynes,et al.  The interplay of tunneling, resonance, and dissipation in quantum barrier crossing: A numerical study , 1992 .

[6]  J. G. Snijders,et al.  Close collisions in the two-dimensional Raman response of liquid carbon disulfide , 2003 .

[7]  C. Milne,et al.  Heterodyne detected fifth-order Raman response of liquid CS2: ‘Dutch Cross’ polarization , 2003 .

[8]  Y. Tanimura,et al.  Unified time‐path approach to the effect of anharmonicity on the molecular vibrational spectroscopy in solution , 1996 .

[9]  M. Cho,et al.  An accurate classical simulation of a two-dimensional vibrational spectrum: OD stretch spectrum of a hydrated HOD molecule. , 2014, The journal of physical chemistry. B.

[10]  C. Milne,et al.  Diffractive optics-based six-wave mixing: Heterodyne detection of the full χ(5) tensor of liquid CS2 , 2002 .

[11]  S. Saito,et al.  Off-resonant two-dimensional fifth-order Raman spectroscopy of liquid CS2: Detection of anharmonic dynamics , 2003 .

[12]  Y. Tanimura,et al.  Nonequilibrium molecular dynamics simulations with a backward-forward trajectories sampling for multidimensional infrared spectroscopy of molecular vibrational modes. , 2008, The Journal of chemical physics.

[13]  C. Vega,et al.  A general purpose model for the condensed phases of water: TIP4P/2005. , 2005, The Journal of chemical physics.

[14]  Ma,et al.  Fifth-order raman spectrum of an atomic liquid: simulation and instantaneous-normal-mode calculation , 2000, Physical review letters.

[15]  Y. Tanimura,et al.  Vibrational spectroscopy of a harmonic oscillator system nonlinearly coupled to a heat bath , 2002 .

[16]  Shaul Mukamel,et al.  Coherent multidimensional optical spectroscopy. , 2009, Accounts of chemical research.

[17]  R. Miller,et al.  Fifth-order Raman spectroscopy of liquid benzene: experiment and theory. , 2006, The journal of physical chemistry. B.

[18]  J. Skinner,et al.  Water Dynamics: Vibrational Echo Correlation Spectroscopy and Comparison to Molecular Dynamics Simulations , 2004 .

[19]  Y. Tanimura.  Stochastic Liouville, Langevin, Fokker–Planck, and Master Equation Approaches to Quantum Dissipative Systems , 2006 .

[20]  C. Huiszoon.  Ab initio calculations of multipole moments, polarizabilities and isotropic long range interaction coefficients for dimethylether, methanol, methane, and water , 1986 .

[21]  K. Hermansson,et al.  Structure and predicted near edge x-ray absorption fine structure spectra for the surface of liquid formamide from molecular-dynamics simulation , 2000 .

[22]  B. Ladanyi.  Higher-order interaction-induced effects on depolarized light scattering from fluids of optically anisotropic molecules , 1985 .

[23]  R. Miller,et al.  Fifth-order two-dimensional Raman spectroscopy: A new direct probe of the liquid state , 2003 .

[24]  S. Mukamel,et al.  Two-dimensional femtosecond vibrational spectroscopy of liquids , 1993 .

[25]  S. Mukamel,et al.  Two-dimensional infrared surface spectroscopy for CO on Cu(100): detection of intermolecular coupling of adsorbates. , 2007, The Journal of chemical physics.

[26]  Y. Tanimura.  Fifth-order two-dimensional vibrational spectroscopy of a Morse potential system in condensed phases , 1998 .

[27]  Y. Tanimura,et al.  Real-time and imaginary-time quantum hierarchal Fokker-Planck equations. , 2015, The Journal of chemical physics.

[28]  Y. Tanimura,et al.  Calculating two-dimensional THz-Raman-THz and Raman-THz-THz signals for various molecular liquids: the samplers. , 2014, The Journal of chemical physics.

[29]  Atsunori Sakurai,et al.  Does ℏ play a role in multidimensional spectroscopy? Reduced hierarchy equations of motion approach to molecular vibrations. , 2011, The journal of physical chemistry. A.

[30]  P. Hamm.  2D-Raman-THz spectroscopy: a sensitive test of polarizable water models. , 2014, The Journal of chemical physics.

[31]  Y. Tanimura,et al.  Two-Dimensional Spectroscopy for Harmonic Vibrational Modes with Nonlinear System-Bath Interactions. II. Gaussian-Markovian Case , 2000 .

[32]  S. Saito,et al.  Off-resonant fifth-order nonlinear response of water and CS2: Analysis based on normal modes , 1998 .

[33]  J. R. Carl,et al.  Atom dipole interaction model for molecular polarizability. Application to polyatomic molecules and determination of atom polarizabilities , 1972 .

[34]  Y. Tanimura,et al.  Calculating fifth-order Raman signals for various molecular liquids by equilibrium and nonequilibrium hybrid molecular dynamics simulation algorithms. , 2006, The Journal of chemical physics.

[35]  Y. Tanimura,et al.  Two-time correlation functions of a harmonic system nonbilinearly coupled to a heat bath: Spontaneous Raman spectroscopy , 1997 .

[36]  A. Ishizaki,et al.  Modeling vibrational dephasing and energy relaxation of intramolecular anharmonic modes for multidimensional infrared spectroscopies. , 2006, The Journal of chemical physics.

[37]  Akihito Ishizaki,et al.  Dynamics of a multimode system coupled to multiple heat baths probed by two-dimensional infrared spectroscopy. , 2007, The journal of physical chemistry. A.

[38]  G. Fleming,et al.  Heterodyne-detected fifth-order nonresonant Raman scattering from room temperature CS2. , 2002, Physical review letters.

[39]  S. Saito,et al.  Fifth-order two-dimensional Raman spectroscopy of liquid water, crystalline ice Ih and amorphous ices: sensitivity to anharmonic dynamics and local hydrogen bond network structure. , 2006, The Journal of chemical physics.

[40]  P. Hamm,et al.  Two-dimensional-Raman-terahertz spectroscopy of water: theory. , 2012, The Journal of chemical physics.

[41]  R. Ahlrichs,et al.  A test particle model potential for formamide and molecular dynamics simulations of the liquid , 1987 .

[42]  J. G. Snijders,et al.  Interaction induced effects in the nonlinear Raman response of liquid CS2: A finite field nonequilibrium molecular dynamics approach , 2001 .

[43]  Wilfred F. van Gunsteren,et al.  The effect of force-field parameters on properties of liquids: Parametrization of a simple three-site model for methanol , 2000 .

[44]  A. Ishizaki,et al.  Modeling, calculating, and analyzing multidimensional vibrational spectroscopies. , 2009, Accounts of chemical research.

[45]  P. H. Berens,et al.  Molecular dynamics and spectra. I. Diatomic rotation and vibration , 1981 .

[46]  Y. Tanimura,et al.  Two-dimensional Raman and infrared vibrational spectroscopy for a harmonic oscillator system nonlinearly coupled with a colored noise bath. , 2004, The Journal of chemical physics.

[47]  Wayne B. Bosma,et al.  Simulation of the intermolecular vibrational spectra of liquid water and water clusters , 1993 .

[48]  S. Saito,et al.  Off-resonant fifth-order response function for two-dimensional Raman spectroscopy of liquids CS2 and H2O. , 2002, Physical review letters.

[49]  Note: Inverted time-ordering in two-dimensional-Raman-terahertz spectroscopy of water. , 2012, The Journal of chemical physics.

[50]  J. Skinner,et al.  Hydrogen bonding and Raman, IR, and 2D-IR spectroscopy of dilute HOD in liquid D2O , 2007, Proceedings of the National Academy of Sciences.

[51]  S. Mukamel.  Principles of Nonlinear Optical Spectroscopy , 1995 .

[52]  Gert-Ludwig Ingold,et al.  Quantum Brownian motion: The functional integral approach , 1988 .

[53]  M. Suhm,et al.  Cooperative organic hydrogen bonds: the librational modes of cyclic methanol clusters. , 2006, The Journal of chemical physics.

[54]  Wolynes,et al.  Quantum and classical Fokker-Planck equations for a Gaussian-Markovian noise bath. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[55]  Y. Tanimura,et al.  Interplay of inhomogeneity and anharmonicity in 2D Raman spectroscopy of liquids , 1997 .

[56]  S. Mukamel,et al.  Optical multidimensional coherent spectroscopy , 2013 .