Nonunitary projective transcorrelation theory inspired by the F12 ansatz.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• The Jastrow transcorrelation method by Boys-Handy is a standard in quantum chemistry.
• F12 ansatz methods offer improved convergence and accuracy in electronic structure calculations.
• Addressing spin-contamination and cusp conditions is crucial for reliable quantum mechanical simulations.

Purpose of the Study:

• To introduce and investigate an alternative nonunitary transcorrelation method inspired by the F12 ansatz.
• To compare the properties of this new projective transcorrelation with the Jastrow transcorrelation.
• To demonstrate the advantages of the projective transcorrelation in terms of accuracy and computational efficiency.

Main Methods:

• Development of a projective transcorrelation formalism.
• Analysis of the effective Hamiltonian, including its terminating series and spin properties.
• Investigation of the satisfaction of singlet and triplet first-order cusp conditions.
• Application of the method to small molecules and comparison with F12 theory.

Main Results:

• The projective transcorrelation features a series terminating at four-body interactions.
• The method exhibits no spin-contamination in the non-relativistic framework.
• Simultaneous satisfaction of singlet and triplet first-order cusp conditions is achieved.
• Arbitrary pair choices for correlation, including frozen-core approximations, are possible.

Conclusions:

• The projective transcorrelation provides a robust alternative to existing methods.
• The satisfaction of cusp conditions is key to reducing uncertainty in nonunitary transformations.
• This method shows promise for accurate electronic structure calculations in quantum chemistry.