Evolutionary algorithms to solve complicated NMR spectra

Abstract

The complexity of 1 H NMR spectra of solutes in partially ordered solvents such as liquid crystals increases rapidly with the number of spins. Spectra of simple solutes with sufficient symmetry and containing not too many spins ͑typically Յ8͒ are readily analyzed. The analysis of larger spin systems is more difficult, and often impossible. In this paper we present the application of a general automated evolutionary algorithm to solve the highly complex proton NMR spectrum of the 12-spin system pentane, a solute that interconverts rapidly among several symmetry-unrelated conformations. The interpretation of the spectral parameters that are obtained from the analysis requires the use of a model to connect relative orientational orders in symmetry-unrelated conformers.

Efficient analysis of highly complex nuclear magnetic resonance spectra of flexible solutes in ordered liquids by using molecular dynamics

“…So far these ranges were decided on by applying the above-mentioned phenomenological models and by incorporating a simple rotational isomeric state (RIS) approach for conformational changes. As is shown, e.g., in experimental studies of n-butane 26 and n-pentane, 21 the ranges for the dipolar couplings obtained in this way provide an adequate starting point for the evolutionary analysis procedure.…”

“…25 In addition, CMA-ES provided the first successful analysis of spectra of n-pentane in the liquid-crystal solvents 1132 and a magic mixture -albeit with starting parameters and ranges that were carefully chosen based on predictions for magic solutes from size and shape model calculations. 21 The CMA-ES method is essentially a brute-force method that relies on recent developments in computer technology which have been geared towards the analysis of complex NMR spectra. In order for the method to reach convergence successfully within acceptable CPU-time, reasonable ranges for the dipolar couplings must be defined beforehand.…”

“…19 and 20) was found to be an invaluable tool for the analysis of NMR spectra of solutes with many spins in anisotropic environments. 21 Evolution strategies such as CMA-ES are optimizers that are inspired by reproduction and natural selection in nature. While classical genetic algorithms aim to find a solution in the parameter space by randomly combining information from a set of trial solutions, the CMA-ES algorithm can sense in which direction the quality of a fit increases.…”

A model-free temperature-dependent conformational study of n-pentane in nematic liquid crystals

“…22,28,29 Sizeand-shape models were used to provide search limits for the n-pentane dipolar couplings at 298.5 K in 1132 which allowed the CMA-ES to extract the fitted parameters. 19 To obtain spectral parameters at an adjacent temperature, one simply uses the previous temperature values as one of the limits (depending on whether one has gone up or down in temperature). The other limit is set so as to have a search range of about 10% of the first limit.…”

“…An earlier analysis of the NMR spectrum of orientationally ordered n-pentane utilized the fact that it is a magic solute and that size-and-shape models could provide a starting point for the spectral analysis. 19 In a later study, 20 molecular dynamics (MD) simulations were employed to successfully predict spectra of n-pentane in the nematic liquid crystal 5CB (4-n-pentyl-4 ′ -cyanobiphenyl). In a recent study on biphenyl in 5CB and 8CB, MD simulations gave good agreement with experimental dipolar couplings, and the biphenyl was found in the simulations to be rather uniformly distributed in the smectic phase of 8CB.…”