Mode-Selective Dual-Level Vibrational Perturbation Theory Assisted by Machine Learning for Rotational and Vibrational Spectra of Benzoic Acid and Aspirin.

The rigid-rotor/harmonic-oscillator model is often insufficient for unbiased comparison with high-resolution microwave data and infrared measurements of medium-sized molecules, but direct high-level anharmonic force fields are rarely affordable for targets with many tens of normal modes. Here, we examine a pragmatic quartic force field/second-order vibrational perturbation theory (QFF/VPT2) route, in which different electronic structure levels are used for different layers of the calculation. In the L1//L0 implementation, a low level (L0) supplies the cubic and semidiagonal quartic force constants, whereas a high level (L1) supplies the equilibrium geometry and either the complete or a mode-selected harmonic reference. In this protocol, an already available machine-learning (ML)-derived QFF can be upgraded selectively with new high-level harmonic information, and the lower-level anharmonic layer does not need to be rebuilt or retrained. Thus, all harmonic terms, or only selected ones, can be promoted to L1, provided that the correspondence between the L0 and L1 coordinates is controlled. The approach is tested on benzoic acid and on the two observed conformers of aspirin, where the molecules are large enough that analytical high-order derivatives and full high-level QFFs are not routine options. Microwave and infrared (IR) observables are used together because they test different parts of the model: rotational constants probe the equilibrium geometry and vibrational averaging, whereas IR spectra probe the anharmonic force field and intensity patterns. Benzoic acid shows that L1//L0 and L1//L1 are equivalent within about 10 reciprocal centimeters for the present spectroscopic purpose and identifies modes with large OH stretching content as the relevant targets for L1 harmonic repair. Aspirin preserves the same pattern, despite its larger size and conformational flexibility. For the diagnostic OH stretch of aspirin I, direct finite differences and a preexisting permutationally invariant polynomial machine-learned potential give identical L0//L0 and L1//L0 VPT2 fundamentals. The combined microwave/IR analysis therefore supports a controlled, mode-selective high-level correction of low-level or machine-learned anharmonic layers while also clarifying the limits of the strategy when a high-quality machine-learned potential is not already available.