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The Interplay of Pauli Repulsion, Electrostatics, and Field Inhomogeneity for Blueshifting and Redshifting Vibrational Probe Molecules

R. Allen LaCour, Ruoqi Zhao, Teresa Head-Gordon

TL;DR

This work investigates why vibrational frequencies of molecular probes blueshift or redshift in intermolecular environments by dissecting contributions from Pauli repulsion and electrostatics, and by assessing how field inhomogeneity modulates these effects. Using absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA) and a controlled inhomogeneous-field model, the authors show that Pauli repulsion consistently blueshifts stretching modes, while electrostatics redshift probes only when sufficiently strong to overcome Pauli; field gradients can either reinforce or oppose the homogeneous-field shift, depending on probe properties. The results explain variable probe responses across different reporters and offer guidance for selecting and interpreting vibrational probes in complex media, including recommendations that CO stretches may be optimal for reporting on intermolecular fields. These insights enhance the interpretability of vibrational Stark shifts in interfaces, solvation, and biomolecular contexts by clarifying which interactions govern observed frequency changes.

Abstract

Many molecules' vibrational frequencies are sensitive to intermolecular electric fields, enabling them to probe the field in complex molecular environments. However, it is often unclear whether the probe is responding to the local electric field or other types of intermolecular interactions, inhibiting interpretation of the frequency and effectiveness as probes. This is especially true of molecules whose vibrational frequencies blueshift instead of the more typical redshift in hydrogen bonding configurations. Here we computationally investigate the causes of redshifting versus blueshifting over a range of vibrational reporters. First, we apply adiabatic energy decomposition analysis to a paradigmatic set of probes, finding that redshifting only occurs when electrostatic interactions are strong enough to overcome the dominant and large blueshifting contribution of Pauli repulsion. Furthermore, we demonstrate that field inhomogeneity can further shift the frequency of many probes substantially to either reinforce or counteract the shift expected from a homogeneous field. We find that redshifting is reinforced by electric field inhomogeneity, otherwise field inhomogeneity further weakens the electrostatic contribution relative to Pauli repulsion, leading to blueshifting. Further calculations indicate that the probe's response to field inhomogeneity can be understood by considering the mass of the atoms involved in the stretching mode and sign of the electric field. In explaining the interplay of different intermolecular interactions and field inhomogeneity for many probes, our results should enable the use and interpretation of spectroscopic probes and their connection to electric fields in more complex systems.

The Interplay of Pauli Repulsion, Electrostatics, and Field Inhomogeneity for Blueshifting and Redshifting Vibrational Probe Molecules

TL;DR

This work investigates why vibrational frequencies of molecular probes blueshift or redshift in intermolecular environments by dissecting contributions from Pauli repulsion and electrostatics, and by assessing how field inhomogeneity modulates these effects. Using absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA) and a controlled inhomogeneous-field model, the authors show that Pauli repulsion consistently blueshifts stretching modes, while electrostatics redshift probes only when sufficiently strong to overcome Pauli; field gradients can either reinforce or oppose the homogeneous-field shift, depending on probe properties. The results explain variable probe responses across different reporters and offer guidance for selecting and interpreting vibrational probes in complex media, including recommendations that CO stretches may be optimal for reporting on intermolecular fields. These insights enhance the interpretability of vibrational Stark shifts in interfaces, solvation, and biomolecular contexts by clarifying which interactions govern observed frequency changes.

Abstract

Many molecules' vibrational frequencies are sensitive to intermolecular electric fields, enabling them to probe the field in complex molecular environments. However, it is often unclear whether the probe is responding to the local electric field or other types of intermolecular interactions, inhibiting interpretation of the frequency and effectiveness as probes. This is especially true of molecules whose vibrational frequencies blueshift instead of the more typical redshift in hydrogen bonding configurations. Here we computationally investigate the causes of redshifting versus blueshifting over a range of vibrational reporters. First, we apply adiabatic energy decomposition analysis to a paradigmatic set of probes, finding that redshifting only occurs when electrostatic interactions are strong enough to overcome the dominant and large blueshifting contribution of Pauli repulsion. Furthermore, we demonstrate that field inhomogeneity can further shift the frequency of many probes substantially to either reinforce or counteract the shift expected from a homogeneous field. We find that redshifting is reinforced by electric field inhomogeneity, otherwise field inhomogeneity further weakens the electrostatic contribution relative to Pauli repulsion, leading to blueshifting. Further calculations indicate that the probe's response to field inhomogeneity can be understood by considering the mass of the atoms involved in the stretching mode and sign of the electric field. In explaining the interplay of different intermolecular interactions and field inhomogeneity for many probes, our results should enable the use and interpretation of spectroscopic probes and their connection to electric fields in more complex systems.
Paper Structure (7 sections, 3 equations, 4 figures)

This paper contains 7 sections, 3 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. Results
  4. Energy Decomposition Analysis
  5. Inhomogeneous Field from a Point Charge
  6. Additional Features of an Inhomogeneous Field on Vibrational Shifts
  7. Discussion and Conclusions

Figures (4)

  • Figure 1: The electric field produced by point charges. Illustration of the interaction of (a) H$_2$O and (b) acetonitrile with point charges. Both molecules prefer to align their dipoles with the field. For H$_2$O, this corresponds to the H pointing towards a negative charge. For acetonitrile, this corresponds to the N points towards a positive charge. In b) we also illustrate the coordinate system used throughout the text, in which the midpoint of the probe stretch is at $x=0$ and the point charge is $D$ distance away. In c) we show how the field experienced by the probe depends upon the position of a positive point charge. We specifically show the $x$-components of the field (the other components are zero) relative to a homogenous field with same magnitude at the bond midpoint. As the point charge approaches the probe, the spatial variation, or inhomogeneity, of the field increases.
  • Figure 2: Energy decomposition analysis for probes interacting with water. In each panel, we use EDA to analyze the different contributions to the probe frequencies. The dashed line marked "Total" indicates the overall force on the stretching mode, while other lines represent the contributions from specific intermolecular interactions. Positive forces contract the bond and induce blueshifting, while negative forces expand it to induce redshifting. $\Delta d_{equil}$ is the distance between the terminal atom of the probe's stretching mode and nearest molecule of the water relative to their distance at equilibrium. Redshifting probes in hydrogen-bonding with a water moleculezheng2025beyond (a) HOH, (b) HCCH, and (c) (CH$_3$)$_2$CO. Probes (d) F$_3$CH, (e) CH$_3$CN, (f) CH$_3$NC that blueshifthobza2000bluemaj2016isonitrile in H-bond configurations.
  • Figure 3: The frequency response of probes to the electric field generated by point charges. Each panel shows the relationship between the stretching frequency ($\omega$) and the electric field ($\boldsymbol{E}$) experienced at the midpoint of the stretch. The sign of the point charge was chosen based upon whether the probe prefers to interact with atoms carrying partial negative (a, b, d, e, h) or partial positive (c, f, g) charges. The specific molecules examined are given in the bottom-left corner of each panel; the relevant stretching mode is between the last two atoms given. The distance ($D$) is the distance between the point charge and the midpoint of the bond. Smaller $D$ indicate greater field inhomogeneity.
  • Figure 4: The response of homonuclear diatoms to field inhomogeneity. The homonuclear probe molecules have no dipole moment, thus we report the component of the electric field in the $x$ direction without projecting it along the bond dipole. We show the frequency response of (a) HH, (b) FF, (c) OO, and (d) NN to the field generated by a point charge. Positive and negative fields were generated by negative and positive point charges, respectively. In (e), we examine the derivatives of the quadrupole with respect to directions parallel to and perpendicular to the bond axis for all probes examined in this study. We add the dashed lines to highlight which quadrant the values falls into.