Size-extensive vibrational self-consistent field method.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Molecular Spectroscopy

Background:

• The vibrational self-consistent field (VSCF) method is a fundamental mean-field approach for solving the vibrational Schrödinger equation.
• VSCF and related methods account for anharmonic effects crucial for accurate vibrational transition frequencies and properties.
• Existing VSCF methods can suffer from nonphysical size dependence and high computational costs.

Purpose of the Study:

• To introduce a diagrammatically size-extensive modification of the VSCF method, termed XVSCF.
• To eliminate nonphysical size dependence inherent in the original VSCF equations.
• To develop a computationally efficient and accurate method for vibrational analysis.

Main Methods:

• Definition and programmable equations for the size-extensive VSCF (XVSCF) method.
• Combination of XVSCF with quartic force fields (QFFs) utilizing quartic force constants.
• Development of diagrams and evaluation rules for the XVSCF energy expression.

Main Results:

• XVSCF eliminates nonphysical size dependence, leading to strictly size-extensive calculations.
• XVSCF exhibits a quadratic scaling with the number of modes when using QFFs, compared to VSCF's quartic scaling.
• XVSCF offers analytical solutions without matrix diagonalization or basis-set expansion, achieving speeds nearly three orders of magnitude faster than VSCF.
• XVSCF results closely approach VSCF results for larger molecules, suggesting VSCF includes unnecessary terms.

Conclusions:

• XVSCF provides a computationally efficient and accurate alternative to VSCF for vibrational analysis.
• The method's size extensivity and speed improvements make it suitable for larger molecular systems.
• XVSCF's simplified potential and analytical solution pave the way for broader applications in computational chemistry.