Interfacial water structures have been studied intensively by probing the O–H stretch mode of water molecules using sum-frequency generation (SFG) spectroscopy. This surface-specific technique is finding increasingly widespread use, and accordingly, computational approaches to calculate SFG spectra using molecular dynamics (MD) trajectories of interfacial water molecules have been developed and employed to correlate specific spectral signatures with distinct interfacial water structures. Such simulations typically require relatively long (several nanoseconds) MD trajectories to allow reliable calculation of the SFG response functions through the dipole moment-polarizability time correlation function. These long trajectories limit the use of computationally expensive MD techniques such as ab initio MD and centroid MD simulations. Here, we present an efficient algorithm determining the SFG response from the surface-specific velocity-velocity correlation function (ssVVCF). This ssVVCF formalism allows us to calculate SFG spectra using a MD trajectory of only ∼100 ps, resulting in the substantial reduction of the computational costs, by almost an order of magnitude. We demonstrate that the O–H stretch SFG spectra at the water-air interface calculated by using the ssVVCF formalism well reproduce those calculated by using the dipole moment-polarizability time correlation function. Furthermore, we applied this ssVVCF technique for computing the SFG spectra from the ab initio MD trajectories with various density functionals. We report that the SFG responses computed from both ab initio MD simulations and MD simulations with an ab initio based force field model do not show a positive feature in its imaginary component at 3100 cm−1.
T.O. and T.H. thank to the Grant-in-Aid for Scientific Research on Innovative Area, “The Function of Soft Molecular Systems” from JSPS. Y.N. acknowledges the financial support from the German Science Foundation through the project of No. TRR146. The simulations were performed by using the computational facilities in Institute of Solid State Physics, the University of Tokyo, Institute of Molecular Science, and Rechenzentrum Garching of the Max-Planck Society.
I. INTRODUCTION II. EFFICIENT ALGORITHM FOR CALCULATING SFG SPECTRA A. IR response function via VVAF B. SFG response function via ssVVAF C. Intra-/intermolecular coupling in ssVVCF D. Non-Condon effects III. SIMULATION PROTOCOLS A. Force field MD simulation B. AIMD simulation IV. RESULTS AND DISCUSSIONS A. Accuracy of SFG spectrum based on ssVVCF formalism B. Effects of intermolecular couplings C. Efficiency of SFG spectrum calculation with ssVVCF D. SFG spectra with AIMD trajectories V. CONCLUDING REMARKS