Reaction-Level Consistency within the Variational Quantum Eigensolver: Homodesmotic Ring Strain Energies of Cyclic Hydrocarbons

Abstract

Simulation of chemical reactions on quantum computing platforms using quantum classical hybrid algorithms such as the Variational Quantum Eigensolver (VQE) is challenged by the need for a reaction consistent treatment of electron correlation in reaction energy evaluations. In this work, we employ a previously reported symmetry guided active space selection protocol to compute ring strain energies of cyclic hydrocarbons using homodesmotic reaction schemes. The protocol enforces symmetry consistency across all reactants and products by selecting active spaces that yield identical symmetry matched fraction (SMF) values, thereby ensuring balanced correlation treatment at the reaction level. When multiple active spaces satisfy this criterion for a given molecule, larger active spaces often provide improved correlation treatment; however, smaller symmetry consistent active spaces can also yield comparable agreement due to favorable error cancellation within the homodesmotic framework. Using this framework, ring strain energies were evaluated for a series of saturated and unsaturated cyclic hydrocarbons, ranging from cyclopropane to the structurally complex adamantane. The resulting energies achieve chemical accuracy relative to density functional theory (DFT) and remain in close agreement with coupled cluster singles and doubles (CCSD) benchmarks. The systematic performance across increasing molecular complexity highlights the effectiveness of combining homodesmotic reaction design with symmetry-consistent VQE calculations. This approach, which enforces physically grounded consistency across reaction species, demonstrates clear potential for extending reaction based quantum simulations to larger molecular systems and broader classes of chemical reactions.

Figures (10)

• Figure 1: Illustration of ring strain in cyclic hydrocarbons. The top panel shows the bent-bond geometry in cyclopropane, highlighting the deviation from the ideal tetrahedral bond angle and the associated angular strain. The remaining panels depict the representative equilibrium conformations of cyclopropane, cyclobutane (butterfly), cyclopentane (envelope), cyclohexane (chair), and adamantane.
• Figure 2: Illustration of symmetry classification of excitations for cyclopropane in a (2, 2) active space under $C_{2v}$ point group symmetry. (a) Cyclopropane structure with sym. elements indicated. (b) Ground-state electronic config., transforming as the $A_{1}$ irrep. (c) Possible single excitations relative to the ground state: (i) and (ii) excitations transforming as $B_{2}$, and (iii) excitation transforming as $A_{1}$.
• Figure 3: Bar plots comparing ring strain energies (RSEs) of cyclopropane obtained from VQE calculations using different active space selection strategies for Set I and Set II homodesmotic reaction schemes. Panels (a) and (b) correspond to Set I and Set II reactions, respectively, using the smallest symmetry-consistent active spaces, while panels (c) and (d) show results obtained with larger symmetry-consistent active spaces. In each panel, bars (from left to right) represent density functional theory (DFT), coupled-cluster singles and doubles (CCSD), VQE with a uniform (2, 2) active space without symmetry guidance, and VQE with the symmetry-guided active space selection protocol employing a matched SMF value of 33.33 % across all reactants and products.
• Figure 4: Bar plots for cyclobutane
• Figure 5: Bar plots for cyclopentane