The particle-particle random phase approximation (pp-RPA) has been used to investigate excitation problems in our recent paper [Y. Yang, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 224105 (2013)]. It has been shown to be capable of describing double, Rydberg, and charge transfer excitations, which are challenging for conventional time-dependent density functional theory (TDDFT). However, its performance on larger molecules is unknown as a result of its expensive O(N(6)) scaling. In this article, we derive and implement a Davidson iterative algorithm for the pp-RPA to calculate the lowest few excitations for large systems. The formal scaling is reduced to O(N(4)), which is comparable with the commonly used configuration interaction singles (CIS) and TDDFT methods. With this iterative algorithm, we carried out benchmark tests on molecules that are significantly larger than the molecules in our previous paper with a reasonably large basis set. Despite some self-consistent field convergence problems with ground state calculations of (N - 2)-electron systems, we are able to accurately capture lowest few excitations for systems with converged calculations. Compared to CIS and TDDFT, there is no systematic bias for the pp-RPA with the mean signed error close to zero. The mean absolute error of pp-RPA with B3LYP or PBE references is similar to that of TDDFT, which suggests that the pp-RPA is a comparable method to TDDFT for large molecules. Moreover, excitations with relatively large non-HOMO excitation contributions are also well described in terms of excitation energies, as long as there is also a relatively large HOMO excitation contribution. These findings, in conjunction with the capability of pp-RPA for describing challenging excitations shown earlier, further demonstrate the potential of pp-RPA as a reliable and general method to describe excitations, and to be a good alternative to TDDFT methods.

We present an analytical proof and numerical demonstrations of the equivalence of the correlation energy from particle-particle random phase approximation (pp-RPA) and ladder-couple-cluster-doubles (ladder-CCD). These two theories reduce to the identical algebraic matrix equation and correlation energy expressions, under the assumption that the pp-RPA equation is stable. The numerical examples illustrate that the correlation energy missed by pp-RPA in comparison with couple-cluster single and double is largely canceled out when considering reaction energies. This theoretical connection will be beneficial to future pp-RPA studies based on the well established couple cluster theory.

Recent development in particle-particle random phase approximation (pp-RPA) broadens the perspective on ground state correlation energies (van Aggelen et al. Phys. Rev. A, 88, 030501 (2013)) and N ± 2 excitation energies (Yang, et al. J.Chem. Phys.). So far Hartree-Fock and approximated density-functional orbitals have been utilized to evaluate the pp-RPA equation. In this paper, to further explore the fundamentals and the potential use of pairing matrix dependent functionals, we present the linear-response time-dependent density-functional theory with pairing elds with both adiabatic and frequency-dependent kernels. This theory is related to the density-functional theory and time-dependent density-functional theory for superconductors, but is applied to normal non-superconducting systems for our purpose. Due to the lack of the proof of the one-to-one mapping between the pairing matrix and the pairing eld for time-dependent systems, the linear-response theory is established based on the representability assumption of the pairing matrix. The linear response theory justi es the use of approximated density-functionals in the pp-RPA equation. This work sets the fundamentals for future density-functional development to enhance the description of ground state correlation energies and N ± 2 excitation energies.

The particle-particle random phase approximation (pp-RPA) for calculating excitation energies has been applied to diradical systems. With pp-RPA, the two nonbonding electrons are treated in a subspace configuration interaction fashion while the remaining part is described by density functional theory (DFT). The vertical or adiabatic singlet-triplet energy gaps for a variety of categories of diradicals, including diatomic diradicals, carbene-like diradicals, disjoint diradicals, four-π-electron diradicals, and benzynes are calculated. Except for some excitations in four-π-electron diradicals, where four-electron correlation may play an important role, the singlet-triplet gaps are generally well predicted by pp-RPA. With a relatively low O(r(4)) scaling, the pp-RPA with DFT references outperforms spin-flip configuration interaction singles. It is similar to or better than the (variational) fractional-spin method. For small diradicals such as diatomic and carbene-like ones, the error of pp-RPA is slightly larger than noncollinear spin-flip time-dependent density functional theory (NC-SF-TDDFT) with LDA or PBE functional. However, for disjoint diradicals and benzynes, the pp-RPA performs much better and is comparable to NC-SF-TDDFT with long-range corrected ωPBEh functional and spin-flip configuration interaction singles with perturbative doubles (SF-CIS(D)). In particular, with a correct asymptotic behavior and being almost free from static correlation error, the pp-RPA with DFT references can well describe the challenging ground state and charge transfer excitations of disjoint diradicals in which almost all other DFT-based methods fail. Therefore, the pp-RPA could be a promising theoretical method for general diradical problems.

The particle-particle random phase approximation (pp-RPA) provides an approximation to the correlation energy in DFT via the adiabatic connection (van Aggelen, Yang, and Yang, http://arxiv.org/abs/1306.4957). It has virtually no delocalization error nor static correlation error for single-bond systems. However, with its formal O(N 6 ) scaling, the pp-RPA is computationally expensive. In this paper, we implement a spin-separated and spin-adapted pp-RPA algorithm, which reduces the computational cost by a significant factor. We then perform benchmark tests on the G2/97 enthalpies of formation database, DBH24 reaction barrier database and four test sets for non-bonded interactions (HB6/04, CT7/04, DI6/04 and WI9/04). For the G2/97 database, the pp-RPA gives a significantly smaller mean absolute error (8.3 kcal/mol) than the direct particle-hole RPA (ph-RPA) (22.7 kcal/mol). Furthermore, the error in the pp-RPA is nearly constant with the number of atoms in a molecule, while the error in the ph-RPA keeps increasing.For chemical reactions involving typical organic closed-shell molecules, pp-and ph-RPA both give accurate reaction energies. Similarly, both RPAs perform well for reaction barriers and nonbonded interactions. These results suggest that pp-RPA gives reliable energies in chemical applications.The adiabatic connection formalism based on pairing matrix fluctuation is therefore expected to lead to widely applicable and accurate density functionals.

The energy gradient for electronic excited states is of immense interest not only for spectroscopy but also for the theoretical study of photochemical reactions. We present the analytic excited state energy gradient of the particle-particle random phase approximation (pp-RPA). The analytic gradient formula is developed from an approach similar to that of time-dependent density-functional theory (TDDFT). The formula is verified for both the Hartree-Fock and (Generalized) Kohn-Sham reference states via comparison with finite difference results. The excited state potential energy surfaces and optimized geometries of some small molecules are investigated, yielding results of similar or better quality compared to adiabatic TDDFT. The singlet-to-triplet instability in TDDFT resulting in underestimated energies of the lowest triplet states is eliminated by pp-RPA. Charge transfer excitations and double excitations, which are challenging for most adiabatic TDDFT methods, can be reasonably well captured by pp-RPA. Within this framework, ground state potential energy surfaces of stretched single bonds can also be described well.

Accurate computation of singlet-triplet energy gaps of diradicals remains a challenging problem in density-functional theory (DFT). In this work, we propose a variational extension of our previous work [D. H. Ess, E. R. Johnson, X. Q. Hu, and W. T. Yang, J. Phys. Chem. A 115, 76 (2011)], which applied fractional-spin density-functional theory (FS-DFT) to diradicals. The original FS-DFT approach assumed equal spin-orbital occupancies of 0.5 α-spin and 0.5 β-spin for the two degenerate, or nearly degenerate, frontier orbitals. In contrast, the variational approach (VFS-DFT) optimizes the total energy of a singlet diradical with respect to the frontier-orbital occupation numbers, based on a full configuration-interaction picture. It is found that the optimal occupation numbers are exactly 0.5 α-spin and 0.5 β-spin for diradicals such as O(2), where the frontier orbitals belong to the same multidimensional irreducible representation, and VFS-DFT reduces to FS-DFT for these cases. However, for diradicals where the frontier orbitals do not belong to the same irreducible representation, the optimal occupation numbers can vary between 0 and 1. Furthermore, analysis of CH(2) by VFS-DFT and FS-DFT captures the (1)A(1) and (1)B(1) states, respectively. Finally, because of the static correlation error in commonly used density functional approximations, both VFS-DFT and FS-DFT calculations significantly overestimate the singlet-triplet energy gaps for disjoint diradicals, such as cyclobutadiene, in which the frontier orbitals are confined to separate atomic centers.

Photoswitching molecules are utilized for a variety of applications where the rapid manipulation of the molecules' chemical properties and spatial orientations allows for new spatiotemporal control over molecular-scale interactions and processes. Here, we present a hydrazone-containing transition metal chelator, HAPI ((E)-N'-[1-(2-hydroxyphenyl)ethyliden]isonicotinoylhydrazide), that displays dual-wavelength photoswitching behavior. Several of its metal complexes, however, are inert to photoreaction and thereby add another layer of control over the photoswitch system. The light-induced twist in HAPI structure is accompanied by a dramatic change in electronic properties as well as chelator strength. This work introduces HAPI as the prototype for a class of molecules with properties that may be optimized for a variety of experimental applications that take advantage of phototriggered molecular changes.