[论文解读] Tailoring CIPSI expansions for QMC calculations of electronic excitations: the case study of thiophene

Monika Dash, Saverio Moroni+2 more|arXiv (Cornell University)|Mar 1, 2021

Advanced Chemical Physics Studies参考文献 49被引用 26

一句话总结

该论文提出一种修改的 CIPSI 选择方案，为同一对称性的多态态建立 iso-PT2 CIPSI 展开，并将其应用于 QMC 的噻吩，在相对紧凑的行列式空间中获得准确的激发态能量和结构。

ABSTRACT

The perturbatively selected configuration interaction scheme (CIPSI) is particularly effective in constructing determinantal expansions for quantum Monte Carlo (QMC) simulations with Jastrow-Slater wave functions: fast and smooth convergence of ground-state properties, as well as balanced descriptions of ground- and excited-states of different symmetries have been reported. In particular, accurate excitation energies have been obtained by the pivotal requirement of using CIPSI expansions with similar second-order perturbation corrections for each state, that is, similar estimated errors with respect to the full configuration interaction limit. Here we elaborate on the CIPSI selection criterion for excited states of the same symmetry as the ground state, generating expansions from a common orbital set. Using these expansions in QMC as determinantal components of Jastrow-Slater wave functions, we compute the lowest, bright excited state of thiophene, which is challenging due to its significant multireference character. The resulting vertical excitation energies are within 0.05~eV of the best theoretical estimates, already with expansions of only a few thousand determinants. Furthermore, we relax the ground- and excited-state structures following the corresponding root in variational Monte Carlo and obtain bond lengths which are accurate to better than 0.01~\\AA. Therefore, while the full treatment at the CIPSI level of this system would be quite demanding, in QMC we can compute high-quality excitation energies and excited-state structural parameters building on affordable CIPSI expansions with relatively few, well chosen determinants.

研究动机与目标

• Motivate balanced electronic-state descriptions for photoinduced processes.
• Develop and test a modified CIPSI selection criterion to generate iso-PT2 expansions for states of the same symmetry.
• Demonstrate that Jastrow-Slater QMC with these expansions yields accurate vertical excitation energies and structures for thiophene.
• Assess how the approach performs across basis sets and orbital choices.
• Provide guidelines for achieving balanced excited-state descriptions in QMC with compact CIPSI expansions.

提出的方法

• Use Jastrow-Slater wave functions with CIPSI-determined determinant expansions.
• Introduce a state-average weighting in CIPSI selection to achieve similar PT2 corrections and CI variances across states of the same symmetry.
• Optimize non-linear (Jastrow/orbital) parameters via state-average energy minimization and solve for linear coefficients with a Davidson-like approach.
• Construct CIPSI expansions from a common orbital set for ground and excited states to ensure orthogonality and balance.
• Perform VMC and DMC calculations with pseudopotentials and diffuse basis sets (BFD) to obtain vertical excitation energies.
• Compare QMC results to CC3 and CASPT2 references and explore geometry optimizations along the root path.

实验结果

研究问题

• RQ1 Can CIPSI selections be modified to produce nearly iso-PT2 expansions for multiple states of the same symmetry?
• RQ2 Do iso-PT2 balanced CIPSI expansions yield accurate QMC vertical excitation energies and excited-state geometries for a challenging multireference state like thiophene?
• RQ3 How do basis set choice and orbital set affect the balance and accuracy of QMC results using the modified CIPSI scheme?
• RQ4 What is the impact of balanced CIPSI expansions on ground- and excited-state energies and structures in VMC/DMC?
• RQ5 Is a simple state-average weighting robust across basis sets for achieving balanced descriptions?

主要发现

• The modified CIPSI selection, using state-average weights in the threshold, yields nearly iso-PT2 expansions for ground and excited states of thiophene.
• In QMC, Jastrow-Slater wave functions built from these balanced expansions give vertical excitation energies within about 0.05 eV of the best theoretical estimates with only several thousand determinants.
• VMC and DMC excitation energies converge to near CC3 reference values; DMC results are within 0.05(2) eV of the theoretical best estimate for aug-cc-pVDZ/aug-cc-pVTZ bases.
• Ground- and excited-state geometries optimized in VMC are accurate to better than 0.01 Å for bond lengths and about 1 degree for bond angles, relative to CASPT2/CC benchmarks.
• The iso-PT2 approach slows ground-state convergence and speeds up the excited-state convergence, yielding a more balanced description than the original cmax scheme.
• The method remains effective across basis sets, with weights around 0.4/0.6 (ground/excited) providing balanced PT2 and CI-variance matching.