首次实现双杂化激发态梯度与非绝热耦合，可在消费级显卡上高效运行。
Density-Functional Excited-State Gradients and Nonadiabatic Couplings on a Consumer GPU from a Contraction-DAG
- 基于收缩图谱的反向模式计算，统一求解激发态梯度与非绝热耦合。
- 双杂化方法将垂直激发能误差降至0.47 eV，消除0.53 eV过激偏差。
- 仅需8GB显存的消费级显卡即可完成高精度计算，适合分子动力学研究者。
非绝热动力学需要在每个核构型下获取激发态梯度和态间非绝热耦合矩阵元（NACME），而双杂化泛函的耦合至今无法解析计算。本文首次推导出双杂化激发态的解析导数NACME，基于孔-孔与粒子-粒子的Tamm-Dancoff近似（\hhTDA/\ppTDA）梯度与耦合，通过一个非对称原子轨道直接$J/K$核闭合的单个反向模式转置收缩图实现。该方法使双杂化激发能的垂直激发平均绝对偏差从纯\hhTDA的0.86 eV降低至0.47 eV，消除+0.53→+0.05 eV的过激偏倚，改善了十种状态中的七种，但对离子型$ππ^*$态过度修正——符合微扰双激发的预期失效，未做裁剪。所有耦合均经独立的*字面多电子波函数重叠*基准验证，精度达~10⁻⁴，且在氨气$n\rightarrowσ^*$共价锥形交叉点物理意义明确；\hhTDA/\ppTDA流形恢复$F\!-\!2$缝，而绝热线性响应TDDFT因构造原因给出$τ\equiv0$。梯度、NACME及双杂化耦合均通过共享的乔列斯基分解$J/K$引擎在8 GB显存的消费级RTX 4060上设备端原位运行，采用轮廓引导的~10²×启动压缩，保持双精度比特一致性，将原本需数据中心硬件的关联激发态导数能力部署于普通台式机。
原文摘要 · Abstract (English)
Nonadiabatic dynamics needs an excited-state gradient and an interstate nonadiabatic coupling matrix element (NACME) at every nuclear geometry, and a double-hybrid functional's accuracy has been unavailable for the coupling. We report the first analytic derivative NACME for a double-hybrid excited state---deferred in the original hh-TDA method and supplied for hybrids only by Yu \emph{et al.}---derived, with the hole-hole and particle-particle Tamm--Dancoff (\hhTDA/\ppTDA) gradients and NACMEs, as a single reverse-mode transpose of one contraction graph closed under a non-symmetric atomic-orbital-direct $J/K$ kernel. Its double-hybrid excitation energy lowers the vertical-excitation mean absolute deviation from bare-\hhTDA\ $0.86$ to $0.47$~eV and removes the $+0.53\!\rightarrow\!+0.05$~eV over-excitation bias, improving seven of ten states while over-correcting the ionic $ππ^*$ states---the expected perturbative-doubles failure, reported not trimmed. Every coupling is validated to $\sim\!10^{-4}$ against an independent \emph{literal many-electron wavefunction-overlap} oracle that shares no code path with the method, and is physically meaningful at the ammonia $n\!\rightarrow\!σ^*$ \emph{covalent} conical intersection, where the \hhTDA/\ppTDA manifolds recover the $F\!-\!2$ seam and adiabatic linear-response TDDFT gives $τ\!\equiv\!0$ by construction. Gradients, NACMEs, and the double-hybrid coupling all run device-resident and AO-direct through one shared Cholesky-decomposed $J/K$ engine within the 8\,GB of a consumer RTX~4060 (a profile-guided $\sim\!10^2\times$ launch collapse preserving double-precision bit-identity)---placing on a commodity desktop card a correlated excited-state derivative capability that has until now required datacenter hardware.
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