NonSingletCI Class, AP1roGSDGeneralizedSen-o Wfn

[q-pratz-chem]

Overview

This PR introduces the following key features and fixes:

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1. NonSingletCI Class

A new NonSingletCI class derived from the GenCIWfn class is added to construct wavefunctions comprising configurations with unequal alpha and beta spin orbitals. Key highlights include:

• Error Fix: Resolves incorrect indexing of k in updating nword in genciwfn.cpp, addressing an issue reported in PR #82 Update genciwfn.cpp #91.
• Overwritten Methods:
  • fill_hartreefock_det: Constructs a single-bitstring representation of all spin orbitals (occupied, virtual, alpha, and beta).
    • Example: For 6 basis functions (12 spin orbitals) and 4 electrons, the Hartree-Fock bitstring is 000011000011, where the left (right) half represents beta (alpha) spin orbitals.
    • Note: Bitstrings are typically read from right to left, as the least significant bit is on the right. In the GenCI wavefunction, the bitstring is indexed as [2n-1, 2n-2, ..., 2, 1, 0], where n is the number of spatial orbitals. The spin orbitals are ordered from 0 to 2n-1 as [φ(α,0), ..., φ(α,n-1), φ(β,n+0), ..., φ(β,2n-1)].
  • add_excited_det: Adds configurations based on a specified excitation order and reference configuration.
    • Current Features: Supports two excitation types: paired doubles and non-spin-preserving singles. This aligns with the geminal function under implementation, generating combinations of non-spin-preserving singles and paired doubles to create new configurations.
• Sparse Matrix Support: Introduces a new add_row function in sparseop.cpp tailored for NonSingletCI to include matrix elements and a new `update' function.

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2. Geminal Wavefunction (AP1roGSDGeneralizedSen-o)

Implements a new geminal wavefunction consisting of:

• AP1roG (pCCD): Paired doubles.
• Singles ('Sen-o'): Excites a single electron from doubly occupied spin-orbital pairs under the non-spin-preserving condition ('Generalized').

Implementation Details:

• C++ Implementation:
  • Added in the ap1rogen.cpp file, based on the NonSingletCI class.
  • Introduces a new storage structure DetExcParamIndx for efficient management of bitstring representations (determinants) and their associated parameter indices (singles and doubles).
• Ryser’s Algorithm:
  • Used for calculating permanents to implement overlaps and derivatives efficiently.
• Testing Progress:
  • Basic testing is in progress using Pytest.
  • Note: The diff_ridders function from derivcheck.py (which requires installation via pip install derivcheck) currently fails due to an assertion error when comparing numerical and analytical derivatives.

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This PR lays the groundwork for future development and testing, particularly in the context of advanced geminal wavefunctions and their application.