Analytic Polarizability and Vibrational Raman Spectra from Constrained Nuclear-Electronic Orbital Density Functional Theory

Accurate and efficient simulation of vibrational Raman spectra for systems with strong anharmonicity and nuclear quantum effects remains challenging. Herein, we apply the recently developed constrained nuclear–electronic orbital (CNEO) framework to simulate Raman spectra. We implement analytic static polarizabilities within CNEO density functional theory (CNEO-DFT) and compute Raman spectra using both CNEO harmonic analysis and CNEO molecular dynamics (CNEO-MD). In the harmonic analysis approach, vibrational frequencies are obtained by diagonalizing the mass-weighted CNEO Hessian, and Raman intensities are derived from the projected derivatives of the polarizability with respect to normal-mode coordinates. In CNEO-MD, both frequency and intensity information are extracted from the Fourier transform of the projected polarizability time derivative autocorrelation function. Applications to formic acid and the mixed water dimer/trimer system show that, compared to conventional DFT, CNEO-DFT achieves substantially improved accuracy, particularly for modes with significant hydrogen motion. Overall, the CNEO framework provides an accurate and efficient approach for simulating vibrational Raman spectra and is especially promising for systems in which hydrogen motion plays a critical role.