Efficient construction of nonorthogonal localized molecular orbitals in large systems.

Localized molecular orbitals (LMOs) are much more compact representations of electronic degrees of freedom than canonical molecular orbitals (CMOs). The most compact representation is provided by nonorthogonal localized molecular orbitals (NOLMOs), which are linearly independent but are not orthogonal. Both LMOs and NOLMOs are thus useful for linear-scaling calculations of electronic structures for large systems. Recently, NOLMOs have been successfully applied to linear-scaling calculations with density functional theory (DFT) and to reformulating time-dependent density functional theory (TDDFT) for calculations of excited states and spectroscopy. However, a challenge remains as NOLMO construction from CMOs is still inefficient for large systems. In this work, we develop an efficient method to accelerate the NOLMO construction by using predefined centroids of the NOLMO and thereby removing the nonlinear equality constraints in the original method ( J. Chem. Phys. 2004 , 120 , 9458 and J. Chem. Phys. 2000 , 112 , 4 ). Thus, NOLMO construction becomes an unconstrained optimization. Its efficiency is demonstrated for the selected saturated and conjugated molecules. Our method for fast NOLMO construction should lead to efficient DFT and NOLMO-TDDFT applications to large systems.

Reformulating time-dependent density functional theory with non-orthogonal localized molecular orbitals.

Time-dependent density functional theory (TDDFT) has broad application in the study of electronic response, excitation and transport. To extend such application to large and complex systems, we develop a reformulation of TDDFT equations in terms of non-orthogonal localized molecular orbitals (NOLMOs). NOLMO is the most localized representation of electronic degrees of freedom and has been used in ground state calculations. In atomic orbital (AO) representation, the sparsity of NOLMO is transferred to the coefficient matrix of molecular orbitals (MOs). Its novel use in TDDFT here leads to a very simple form of time propagation equations which can be solved with linear-scaling effort. We have tested the method for several long-chain saturated and conjugated molecular systems within the self-consistent charge density-functional tight-binding method (SCC-DFTB) and demonstrated its accuracy. This opens up pathways for TDDFT applications to large bio- and nano-systems.

Ground and Electronic Excited States from Pairing Matrix Fluctuation and Particle-Particle Random Phase Approximation

The accurate description of ground and electronic excited states is an important and challenging topic in quantum chemistry. The pairing matrix fluctuation, as a counterpart of the density fluctuation, is applied to this topic. From the pairing matrix fluctuation, the exact electron correlation energy as well as two electron addition/removal energies can be extracted. Therefore, both ground state and excited states energies can be obtained and they are in principle exact with a complete knowledge of the pairing matrix fluctuation. In practice, considering the exact pairing matrix fluctuation is unknown, we adopt its simple approximation --- the particle-particle random phase approximation (pp-RPA) --- for ground and excited states calculations. The algorithms for accelerating the pp-RPA calculation, including spin separation, spin adaptation, as well as an iterative Davidson method, are developed. For ground states correlation descriptions, the results obtained from pp-RPA are usually comparable to and can be more accurate than those from traditional particle-hole random phase approximation (ph-RPA). For excited states, the pp-RPA is able to describe double, Rydberg, and charge transfer excitations, which are challenging for conventional time-dependent density functional theory (TDDFT). Although the pp-RPA intrinsically cannot describe those excitations excited from the orbitals below the highest occupied molecular orbital (HOMO), its performances on those single excitations that can be captured are comparable to TDDFT. The pp-RPA for excitation calculation is further applied to challenging diradical problems and is used to unveil the nature of the ground and electronic excited states of higher acenes. The pp-RPA and the corresponding Tamm-Dancoff approximation (pp-TDA) are also applied to conical intersections, an important concept in nonadiabatic dynamics. Their good description of the double-cone feature of conical intersections is in sharp contrast to the failure of TDDFT. All in all, the pairing matrix fluctuation opens up new channel of thinking for quantum chemistry, and the pp-RPA is a promising method in describing ground and electronic excited states.