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.

Excitation of highly conjugated (porphinato)palladium(II) and (porphinato)platinum(II) oligomers produces long-lived, triplet states at unit quantum yield that absorb strongly over broad spectral domains of the NIR.

Transient dynamical studies of bis[(5,5'-10,20-bis(2,6-bis(3,3-dimethylbutoxy)phenyl)porphinato)palladium(II)]ethyne (PPd(2)), 5,15-bis{[(5'-10,20-bis(2,6-bis(3,3-dimethylbutoxy)phenyl)porphinato)palladium(II)]ethynyl}(10,20-bis(2,6-bis(3,3-dimethylbutoxy)phenyl)porphinato)palladium(II) (PPd(3)), bis[(5,5'-10,20-bis(2,6-bis(3,3-dimethylbutoxy)phenyl)porphinato)platinum(II)]ethyne (PPt(2)), and 5,15-bis{[(5'-10,20-bis(2,6-bis(3,3-dimethylbutoxy)phenyl)porphinato)platinum(II)]ethynyl}(10,20-bis(2,6-bis(3,3-dimethylbutoxy)phenyl)porphinato)platinum(II) (PPt(3)) show that the electronically excited triplet states of these highly conjugated supermolecular chromophores can be produced at unit quantum yield via fast S(1) → T(1) intersystem crossing dynamics (τ(isc): 5.2-49.4 ps). These species manifest high oscillator strength T(1) → T(n) transitions over broad NIR spectral windows. The facts that (i) the electronically excited triplet lifetimes of these PPd(n) and PPt(n) chromophores are long, ranging from 5 to 50 μs, and (ii) the ground and electronically excited absorptive manifolds of these multipigment ensembles can be extensively modulated over broad spectral domains indicate that these structures define a new precedent for conjugated materials featuring low-lying π-π* electronically excited states for NIR optical limiting and related long-wavelength nonlinear optical (NLO) applications.

Spin-state splittings, highest-occupied-molecular-orbital and lowest-unoccupied-molecular-orbital energies, and chemical hardness.

It is known that the exact density functional must give ground-state energies that are piecewise linear as a function of electron number. In this work we prove that this is also true for the lowest-energy excited states of different spin or spatial symmetry. This has three important consequences for chemical applications: the ground state of a molecule must correspond to the state with the maximum highest-occupied-molecular-orbital energy, minimum lowest-unoccupied-molecular-orbital energy, and maximum chemical hardness. The beryllium, carbon, and vanadium atoms, as well as the CH(2) and C(3)H(3) molecules are considered as illustrative examples. Our result also directly and rigorously connects the ionization potential and electron affinity to the stability of spin states.

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.

Major and minor music compared to excited and subdued speech.

The affective impact of music arises from a variety of factors, including intensity, tempo, rhythm, and tonal relationships. The emotional coloring evoked by intensity, tempo, and rhythm appears to arise from association with the characteristics of human behavior in the corresponding condition; however, how and why particular tonal relationships in music convey distinct emotional effects are not clear. The hypothesis examined here is that major and minor tone collections elicit different affective reactions because their spectra are similar to the spectra of voiced speech uttered in different emotional states. To evaluate this possibility the spectra of the intervals that distinguish major and minor music were compared to the spectra of voiced segments in excited and subdued speech using fundamental frequency and frequency ratios as measures. Consistent with the hypothesis, the spectra of major intervals are more similar to spectra found in excited speech, whereas the spectra of particular minor intervals are more similar to the spectra of subdued speech. These results suggest that the characteristic affective impact of major and minor tone collections arises from associations routinely made between particular musical intervals and voiced speech.