SITH: A Quantum-Chemical Framework for Predicting Bond Destabilization in Stretched Molecules

TL;DR

This work tackles the challenge of predicting where mechanical force concentrates energy within a molecule to determine rupture-prone bonds. It introduces SITH, a non-harmonic, quantum-chemical energy-decomposition framework that numerically integrates the work along a constrained stretching path to assign energy changes to individual internal coordinates. Across trialanine, proline, and a dataset of 190 tripeptides, SITH achieves high accuracy relative to DFT, remains robust to ring-structure complications, and reveals amino-acid–specific energy distributions, notably glycine vs. proline in backbone bonds. The method provides interpretable mechanochemical insights and can benchmark classical force fields, with potential to improve rupture predictions in proteins and other polymers under force.

Abstract

Mechanical forces can selectively destabilize chemical bonds of molecular systems, particularly in biological and synthetic polymers. While experimental and theoretical methods have advanced our understanding of mechanochemical processes, predicting where energy concentrates within a molecule remains a significant challenge. To address this, we introduce SITH (Splitting Intramolecular Tension due to stretcHing), a novel method that decomposes the total electronic energy change of a stretched molecule into contributions from individual degrees of freedom -- such as bond lengths, angles, and dihedrals -- using numerical integration of the work-energy theorem. Unlike previous approaches that rely on harmonic approximations, SITH provides high accuracy and robustness to study the distribution of energies of stretched molecules up to a first bond cleavage. Although SITH uses 3N-6 degrees of freedom for the energy decomposition, we show that it can work even for ring structures like prolines. We apply SITH to a dataset of tripeptides and demonstrate that glycine and proline exhibit significantly different energy distributions in their Ca-C backbone bonds under tension: glycine stores more energy, making it more prone to rupture, while proline has the opposite behaviour. These findings reveal intrinsic differences in mechanochemical susceptibility across amino acids, offering more accurate predictions of bond rupture in proteins, and similarly in other (bio)polymers. SITH thus provides a powerful, interpretable tool for understanding energy distribution at the quantum level, with possible implications in mechanochemistry and force field validation.

Figures (13)

• Figure 1: Illustration of SITH stretching and energy distribution. a) stretching process, starting from the optimized configuration (bottom), we increase the end to end distance by a value $\Delta$d and reoptimize with this distance constrained, which is equivalent to a stretching force pulling from the ends. The process is repeated k times, until k+1 produces a rupture (top). b) SITH describes a decomposition of the total energy obtained with DFT in terms of energies of n degrees of freedom ($\Delta E_i$) based on the DFT calculation during the stretching process. The degrees of freedom are distances, angles, and dihedrals that are colored according to the magnitude of the corresponding change of the energy. c) The value of the energy $\Delta E_i$ comes from a numerical integration of the force in the $i$-th degree of freedom, as it changes during the stretching process.
• Figure 2: SITH energy decomposition for tri-alanine. a) Energy stored in each degree of freedom as the stretching increases. The degrees of freedom are grouped in distances, angles, and dihedrals, with background colors indicating the corresponding residue: ACE and NME capping groups and the three alanines (white: atoms of the two adjacent residues are involved). b) Energy stored in the bonds of the central alanine of the tri-peptide (A$_2$). C-N corresponds to the bond between C atom of alanine 1 (A$_1$) and N atom in alanine 2 (A$_2$). c) Total change of energy predicted by SITH and JEDI compared with the expected energy from DFT. d) Root squared energy stored in the C$_\alpha$-C distance according to the prediction by SITH, JEDI, and a harmonic fit to the SITH data. e) Energy stored in the C$_\alpha$-C distance according to SITH (based on quantum chemical calculations) compared to the bond energy predicted by classical force fields Amber99 and GRAPPA.
• Figure 3: SITH energy analysis of proline. a) Set of degrees of freedom used in the analysis. Each set leaves out one bond of the ring to avoid more than $3N - 6$ degrees of freedom, where $N$ is the number of atoms. b) Total change of energy in the stretching predicted by SITH using the different sets and compared with the expected DFT change of energy. c) Energy in the C$_\alpha$-C and the C$_\alpha$-N distances computed by SITH using the 4 sets. d) Energy stored in the dihedral angle N-C$_\alpha$-C-O, which is the degree of freedom that differs the most when using different sets.
• Figure 4: SITH analysis for a dataset of tri-peptides. a) We create a dataset of tripeptides by selecting random sets of three amino acids from the 20 natural amino acids. Here, we show the schematic structure of the amino acids and the associated one-letter code (see Table S1 for a complete description). b) Energy stored in the C$_\alpha$-C of the central amino acid in the peptides as a function of the change of the distance with respect to the equilibrium distance. Each curve corresponds to a different peptide. c) Distribution of energies stored in the C$_\alpha$-C distance for the peptides in the dataset after stretching the bond 0.125Å from the equilibrium distance, shown as a function of the amino acid in the middle. The gray points are energies of the different peptides with the different combinations of amino acids in the first and third positions. The blue dots are the mean values, and the bars are the standard deviations. d) p-values of the energies in the C$_\alpha$-C between every pair of amino acids in the second position of the peptide. The colormap is a divergent scheme where white is the threshold of an accepted p-value of 0.05. Along with the f-statistics test (Fig. S4), we find which distributions statistically differ from the others. In c) and d), glycine and proline are highlighted because their distributions are significantly shifted from the distribution of the other amino acids.
• Figure 5: SITH energy decomposition for penta-alanine in each degree of freedom as the stretching increases (color bar). The degrees of freedom are grouped in distances, angles and diherals, with background colors indicating the corresponding residue (white: atoms of the two adjacent residues are involved).The gray horizontal line shows that the energy stored in the three alanines in the middle is the same, while the two alanines at the extremes are biased by the capping groups.