EOM-CC Excited-State Gradients and Nonadiabatic Couplings on a Consumer GPU from a Contraction-DAG with Laplace-Transform J/K Kernels

We present a unified, memory-bounded GPU realization of equation-of-motion coupled-cluster (EOM-CC) excited-state gradients and interstate nonadiabatic couplings (NACMEs) on a single 8\,GB consumer GPU.

Both are built from one contraction directed acyclic graph: the EOM-CC relaxation is the reverse-mode transpose of the forward density build rather than a per-state re-derivation, and an atomic-orbital-direct Laplace-transform $J/K$ kernel, made non-symmetric ($J^x(A,B)\neq J^x(B,A)$) by the transition densities, resolves every energy denominator with no four-index molecular-orbital tensor; a two-sided Davidson returns both eigenvectors from one device-resident, spin-pure solve.

The pipeline is \emph{validated end to end at small scale}: gradients and NACMEs match finite differences across four spin multiplicities and full configuration interaction to $<\!10^{-12}$ for two electrons, and the excited-state gradient matches the independent \textsc{Psi4} code to $\le\!4.6\times10^{-7}~E_h/a_0$ from \ce{H2O} to aromatic benzene.

The kernels and the ground-state solve reach chromophores ($\le\!730$ AO) in 8\,GB, and a frozen-natural-virtual compression lets the eigensolver \emph{execute} a complete excited-state gradient and $Q$--$B$ NACME of the chlorophyll-core chromophore \ce{Mg}-porphine (def2-SVP, $439$ AO) on the card.

We present that run as a \emph{capability demonstration} -- executed and translationally invariant to machine zero, but anchored only piece-wise and bounded by a direct convergence study at ${\sim}10^{-2}~E_h/a_0$ -- not a converged spectroscopic result.

The validated small-scale capability and the memory-bounded implementation are the contribution.