Active-Space Quantum Simulation of N$_2$ Hydrogenation at a Ru Single-Atom Site on Ru(0001)
Selective activation of dinitrogen (N$_2$) under mild conditions is difficult: N$\equiv$N is one of the strongest bonds in chemistry, and most heterogeneous catalysts capable of breaking it require high temperature and pressure. Atomically dispersed transition-metal sites offer a computationally tractable route to studying the strongly correlated intermediates involved. We connect periodic DFT calculations with correlated active-space calculations on a finite, non-periodic surface fragment, demonstrating the workflow for the hydrogenation step RuH$_2$(N$_2$)* $\rightarrow$ RuH(NNH)* at an isolated Ru$_1$ site on Ru(0001). A first-shell fragment is extracted from the periodically relaxed structure, an active space is selected with Active Atomic Valence Space (AVAS) around the Ru-N/N-H bond reorganization, and natural-orbital truncation reduces its cost while retaining the relevant correlated degrees of freedom. The reduced Hamiltonian is mapped to qubits with the Jordan-Wigner transformation and solved with the adaptive derivative-assembled pseudo-Trotter variational quantum eigensolver (ADAPT-VQE). Dynamic correlation beyond the active space is examined with strongly contracted NEVPT2 and DSRG-MRPT2. AVAS gives a 22-qubit active space, which natural-orbital truncation compresses to 16 qubits, reproducing the untruncated CASCI state energies to within 0.21 kcal/mol (reaction-energy error 0.2 kcal/mol). Statevector ADAPT-VQE in this reduced space converges for both reaction states under a fixed pool-gradient stopping criterion. NEVPT2 yields anomalously large, state-imbalanced corrections for the finite Ru fragment, while DSRG-MRPT2 retains an endothermic reaction energy at its default flow parameter, although its magnitude depends strongly on that parameter.