Editor's note: Chemical bonding group from Xiamen University has developed a hybrid density functional valence bond (VB) method with multistate treatment, namely λ-DFVB(MS). This method introduces dynamic correlation into the VB theory through density functional theory (DFT), while considering the interaction between electronic states, and therefore can provide high-precision potential energy surfaces for both adiabatic and diabatic states near the conical intersection region. The accuracy of the adiabatic potential energy surface computed with λ-DFVB(MS) is comparable to XMS-CASPT2, which is a molecular orbital method with high accuracy.

The conical intersection region of a molecule is a typical strongly correlated system. To describe strongly correlated systems effectively, it is necessary to consider both static and dynamic correlations. Moreover, in order to accurately describe the conical intersection regions, it is essential to not only fully consider electronic correlations but also take into account the interaction between electronic states.

This article presents a multistate DFT method based on VB wave function, namely λ-DFVB(MS). The method first uses the valence-bond-based compression approach for the diabatization (VBCAD) method to construct the VB diabatic states. Then, based on the density and unpaired density of the diabatic states, the dynamic correlation is introduced into the VB calculation through DFT, and an effective Hamiltonian matrix based on the VB diabatic states is constructed . Finally, by diagonalizing the effective Hamiltonian matrix, the interaction between electronic states is introduced.

This article tests the performance of the λ-DFVB(MS) method using several classical examples. The test results indicate that the accuracy of the λ-DFVB(MS) method is comparable to  XMS-CASPT2 method. In fact, for observable quantities such as the bond dissociation energy of ground state, the excitation energy at the dissociation limit, and the bond length at avoided crossing points for the LiF molecule, the computed results from λ-DFVB(MS) are even closer to the experimental values than those from XMS-CASPT2.

One important character of VB theory is that its wave function can be compactly expressed as the linear combination of only several important VB structures. To test this feature in λ-DFVB(MS) method, 12 VB structures were selected for describing the ground and the first excited states of methylamine (CH3NH2) molecule. Block-localized orbitals were employed, and the potential energy surfaces of N-H bond dissociation were computed using λ-DFVB(MS) method. The results show that even only a subset of VB structures in the active space is included, the computed results from λ-DFVB(MS) remain close to those from XMS-CASPT2. This demonstrates that the λ-DFVB(MS) method can be utilized for accurate potential energy surface calculations while retaining the compact and intuitive nature of the VB wave function, making it a promising approach for both electronic structure and dynamics computations. 

Paper:

Hybrid Density Functional Valence Bond Method with Multistate Treatment

Xun Wu, Chan Cao, Chen Zhou*, and Wei Wu*