Controlled Bond Expansion for Density Matrix Renormalization Group Ground State Search at Single-Site Costs.

DMRG ground state search algorithms employing symmetries must be able to expand virtual bond spaces by adding or changing symmetry sectors if these lower the energy. Traditional single-site DMRG does not allow bond expansion; two-site DMRG does, but at much higher computational costs. We present a controlled bond expansion (CBE) algorithm that yields two-site accuracy and convergence per sweep, at single-site costs. Given a matrix product state Ψ defining a variational space, CBE identifies parts of the orthogonal space carrying significant weight in HΨ and expands bonds to include only these. CBE-DMRG uses no mixing parameters and is fully variational. Using CBE-DMRG, we show that the Kondo-Heisenberg model on a width 4 cylinder features two distinct phases differing in their Fermi surface volumes.

Tuning the vibrational coupling of H3O+ by changing its solvation environment.

This study demonstrates how the intermode coupling in the hydronium ion (H3O+) is modulated by the composition of the first solvation shell. A series of rare gas solvated hydronium ions (H3O+Rg3, where Rg = Ne, Ar, Kr, and Xe) is examined via reduced-dimensional anharmonic vibrational (RDAV) ab initio calculations. We considered six key vibrational normal modes, namely: a hindered rotation, two H-O-H bends, and three O-H stretches. Between the O-H stretches and the H-O-H bends, the first is more sensitive to solvation strength. Our calculations revealed that the Fermi resonance between the first overtones of O-H bends and the fundamentals of O-H stretches led to complex spectral features from 3000 to 3500 cm-1. Such an interaction is not only sensitive to the type of rare gas messengers surrounding the H3O+ ion, it also exhibits an anomalous H → D isotope effect. Although it is accepted that visible combination tones (∼1900 cm-1) arise from the complex coupling between the hindered rotation and the H-O-H bends, the origin of their intensities is not yet clearly understood. We found that the intensity of these combination tones could be much stronger than their fundamental H-O-H bends. Within our theoretical framework, we tracked the combination tone's intensity back to the asymmetric O-H stretches. This simple notion of intensity borrowing is confirmed by examining eight complexes (H3O+·Rg3 and D3O+·Rg3) with spectral features awaiting experimental confirmations.

Features in Vibrational Spectra Induced by Ar-Tagging for H3O(+)Arm, m = 0-3.

Understanding the spectral features for solvated hydronium has been hindered due to the strong and complex vibrational couplings that lead to broad bands in the aqueous phase. In this work, utilizing ab initio vibrational calculations, we determine how the vibrational couplings induced by the Ar microsolvation in H3O(+)Arm m = 0-3 affect the observed spectra. With theoretical peak intensities and peak positions, we assign the experimental spectra. We also show that an increase in the number of Ar atoms results in an anticooperative blue shifting in the Ar-tagged OH stretching bands. This change in peak position of the OH stretching fundamental modulates the Fermi resonance with the bending overtone. This is observed as a distinct doublet feature at 3200 cm(-1) with varying intensities for H3O(+)Ar2 and H3O(+)Ar3. The coupling between the in-plane rotation of the hydronium and the bending modes of H3O(+) leads to the existence of a strong association bands around 1900 cm(-1).