Orbital Optimization of Large Active Spaces via AI-Accelerators

Abstract

We present an efficient orbital optimization procedure that combines the highly GPU accelerated, spin-adapted density matrix renormalization group (DMRG) method with the complete active space self-consistent field (CAS-SCF) approach for quantum chemistry implemented in the ORCA program package. Leveraging the computational power of the latest generation of Nvidia GPU hardware, we perform CAS-SCF based orbital optimizations for unprecedented CAS sizes of up to 82 electrons in 82 orbitals [CAS(82,82)] in molecular systems comprising active space sizes of hundreds of electrons in thousands of orbitals. For both the NVIDIA DGX-A100 and DGX-H100 hardware, we provide a detailed scaling and error analysis of our DMRG-SCF approach for benchmark systems consisting of polycyclic aromatic hydrocarbons and iron-sulfur complexes of varying sizes. Our efforts demonstrate for the first time that highly accurate DMRG calculations at large bond dimensions are critical for obtaining reliably converged CAS-SCF energies. For the more challenging iron-sulfur benchmark systems, we furthermore find the optimized orbitals of a converged CAS-SCF calculation to depend more sensitively on the DMRG parameters than those for the polycyclic aromatic hydrocarbons. The ability to obtain converged CAS-SCF energies and orbitals for active spaces of such large sizes within days reduces the challenges of including the appropriate orbitals into the CAS or selecting the correct minimal CAS, and may open up entirely new avenues for tackling strongly correlated molecular systems.

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Smallest molecules of the PAH series for ring numbers n = 1, 2, and 3.

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Fe₂S₂ cluster series for n = 1, 2, and 3.

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(left) Convergence of ground state energy, E ₀, shifted by 1146 for the heptacene on a CAS­(30,30) as a function of the DMRG-SCF macro iterations for various fixed U(1) D̃ _opt values and (right) via the spin adapted workflow for various fixed SU(2) bond dimensions, D _opt. Data points shown by open circle symbols were obtained via the DBSS procedure by setting D̃ _opt,min = 2048 and D _opt,min = 1024, ε_TR = 10^–4 and maximum number of DMRG sweeps to ten. In the SCF module we set ε_ECT = 10^–7 and ε_OGC = 10^–3. Symbols X together with horizontal dotted lines stand for post DMRG-SCF energy values obtained for various D values using the basis optimized with D _opt = 128. The inset shows the 1/D scaling of the shifted ground state energy, using the original nonoptimized and the optimized basis with D _opt = 128, i.e. E ₀(D) and E ₀(D _opt, D), respectively.

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(left) Occupation number, N _occ, obtained by the first and last DMRG-SCF macro iteration for D _opt = 2048 and (right) the difference between the obtained N _occ profile via the first and last DMRG-SCF macro iteration for various D _opt values. In the SCF module the convergence on energy was set to 10^–7 and the gradient to 10^–3.

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(Left panel) Similar to Figure (right), but for the dodecacene on a CAS­(50,50) and (right panel) for the Icosacene on a CAS­(82,82).

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(left) Convergence profiles of the DMRG-SCF method for the Fe₁S₄ cluster for various bond dimension values and for three different active spaces. Symbols X together with horizontal dotted lines stand for post DMRG-SCF energy values obtained for the D values shown in the legend, but using the basis optimized with D _opt = 256. (right) occupation number distribution of active space orbitals calculated by the first and last DMRG-SCF iterations.

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Similar to Figure but for the Fe₂S₆H₄ ^–2 cluster corresponding to one Fe₂S₂ motif, parametrized with n = 1. Symbols filled circle together with horizontal dotted lines stand for post DMRG- SCF energy values obtained for various D = {256, 512, 1024, 2048} values using the basis optimized with D _opt = 256.

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Similar to Figure but for the Fe₃S₈H₄ ^3– cluster corresponding to two Fe₂S₂ motifs parametrized with n = 3. Symbols X together with horizontal dotted lines stand for post DMRG-SCF energy values obtained for various D values using the basis optimized with D _opt = 512.