Efficient calculation of NMR isotopic shifts: Difference-dedicated vibrational perturbation theory

Abstract

We present difference-dedicated second-order vibrational perturbation theory (VPT2) as an efficient method for the computation of nuclear magnetic resonance (NMR) isotopic shifts, which reflect the geometry dependence of the NMR property in combination with different vibration patterns of two isotopologues. Conventional calculations of isotopic shifts, e.g., by standard VPT2, require scanning the geometry dependence over the whole molecule, which becomes expensive rapidly as the molecule size increases. In DD-VPT2, this scan can be restricted to a small region around the substitution site. At the heart of DD-VPT2 is a set of localized vibration modes common to the two isotopologues and designed such that the difference between the vibration patterns is caught by a small subset of them (usually fewer than 10). We tested the DD-VPT2 method for a series of molecules with increasing size and found that this method provides results with the same quality as VPT2 and in good agreement with the experiment, with computational savings up to 95% and less numerical instabilities. The method is easy to automatize and straightforward to generalize to other molecular properties.

The Structure of the “Vibration Hole” around an Isotopic Substitution—Implications for the Calculation of Nuclear Magnetic Resonance (NMR) Isotopic Shifts

“…For a single isotopic substitution, the change of the vibration motif is expected to be localized in the region around the substitution site, and for the most common case of a substitution with a heavier isotope, the vibrational amplitude in this region will decrease. This situation resembles the relationship between the electronic energy and the exchange and correlation (XC) hole in electronic-structure theory; therefore, we have coined the term “vibration hole” [ 30 ] for the region where the vibration motif is changed substantially by the isotopic substitution.…”

“…In a recent paper [ 30 ], we presented the difference-dedicated (DD) VPT2 approach, which provides values for NMR isotopic shifts (or isotope effects on other quantities) at VPT2 quality, that is, without any assumptions on the structure of the vibration hole, at a cost comparable to the LMZL or other comparable a priori local methods. As a by-product, which was not addressed in Reference [ 30 ], the DD-VPT2 approach efficiently provides information on the structure of the vibration hole.…”

“…In a recent paper [ 30 ], we presented the difference-dedicated (DD) VPT2 approach, which provides values for NMR isotopic shifts (or isotope effects on other quantities) at VPT2 quality, that is, without any assumptions on the structure of the vibration hole, at a cost comparable to the LMZL or other comparable a priori local methods. As a by-product, which was not addressed in Reference [ 30 ], the DD-VPT2 approach efficiently provides information on the structure of the vibration hole. In the present paper, we will make use of this possibility and investigate the structure and locality of the vibration hole both for the systems investigated in Reference [ 30 ] and for a number of molecules studied recently by Hansen et al [ 20 ] where the substitution site is involved in an intra-molecular hydrogen bond.…”

“…As a by-product, which was not addressed in Reference [ 30 ], the DD-VPT2 approach efficiently provides information on the structure of the vibration hole. In the present paper, we will make use of this possibility and investigate the structure and locality of the vibration hole both for the systems investigated in Reference [ 30 ] and for a number of molecules studied recently by Hansen et al [ 20 ] where the substitution site is involved in an intra-molecular hydrogen bond. The systems under consideration will be studied both with DD-VPT2 and a local VPT2 version (loc-VPT2), which is used as a model a priori local method (see Section 2.2 for details).…”

“…The paper is organized as follows: in Section 2 , the DD-VPT2 and loc-VPT2 methods are described in brief, and the geometry parameters used to describe the vibration hole are defined. Section 3 presents the results of our study—in Section 3.1 , we will reanalyze and complement the results for the cyclic and polycyclic molecules studied in Reference [ 30 ] and in Section 3.2 , those for the halonium complexes investigated in Reference [ 30 ]. Section 3.3 is dedicated to the investigation of the salicyl aldehyde derivatives originally investigated in Reference [ 20 ].…”