A truncated Davidson method for the efficient "chemically accurate" calculation of full configuration interaction...

Area of Science:

• Quantum Chemistry
• Computational Chemistry

Background:

• Full configuration interaction (CI) is computationally expensive due to large matrix diagonalization.
• Modern selective CI methods also face challenges with this diagonalization step.

Purpose of the Study:

• To develop a new method for calculating "chemically accurate" electronic wavefunctions and energies.
• To circumvent the computational bottleneck of large matrix diagonalization in CI procedures.

Main Methods:

• A truncated full configuration interaction (CI) procedure is developed.
• The method utilizes a direct Davidson approach, applying the electronic Hamiltonian operator in second quantization.
• Only a small portion of the resultant expansion vector is computed in each iteration, with the vector size doubling iteratively.

Main Results:

• A small set of truncated expansion vectors (10-30) is incrementally constructed.
• Diagonalization within this small subspace yields variational convergence to the approximate full CI limit.
• Chemical accuracy (1.6 mhartree) is achieved efficiently for large Hilbert spaces (10^18) and wavefunctions (10^8 determinants).

Conclusions:

• The truncated Davidson methodology provides an efficient alternative to standard CI and complete-active space methods.
• This approach is suitable when only a few chemically significant digits of accuracy are required.
• The method is effective for problems with large Hilbert spaces and wavefunctions.