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It is also shown that additional plasmon eigenstates are introduced from hybridization of modes across nanogaps between structural features in close proximity to each other. All of these factors contribute to the broadband response of the wrinkled gold structures.In a recent paper, we proposed the adaptive shift method for correcting undersampling bias of the initiator-full configuration interaction (FCI) quantum Monte Carlo. The method allows faster convergence with the number of walkers to the FCI limit than the normal initiator method, particularly for large systems. However, in its application to some systems, mostly strongly correlated molecules, the method is prone to overshooting the FCI energy at intermediate walker numbers, with convergence to the FCI limit from below. In this paper, we present a solution to the overshooting problem in such systems, as well as further accelerating convergence to the FCI energy. This is achieved by offsetting the reference energy to a value typically below the Hartree-Fock energy but above the exact energy. This offsetting procedure does not change the exactness property of the algorithm, namely, convergence to the exact FCI solution in the large-walker limit, but at its optimal value, it greatly accelerates convergence. There is no overhead cost associated with this offsetting procedure and is therefore a pure and substantial computational gain. We illustrate the behavior of this offset adaptive shift method by applying it to the N2 molecule, the ozone molecule at three different geometries (an equilibrium open minimum, a hypothetical ring minimum, and a transition state) in three basis sets (cc-pVXZ, X = D, T, Q), and the chromium dimer in the cc-pVDZ basis set, correlating 28 electrons in 76 orbitals. We show that in most cases, the offset adaptive shift method converges much faster than both the normal initiator method and the original adaptive shift method.We report a systematic investigation of individual and multisite Hubbard-U corrections for the electronic, structural, and optical properties of the metal titanate oxide d0 photocatalysts SrTiO3 and rutile/anatase TiO2. Accurate bandgaps for these materials can be reproduced with local density approximation and generalized gradient approximation exchange-correlation density functionals via a continuous series of empirically derived Ud and Up combinations, which are relatively insensitive to the choice of functional. [https://www.selleckchem.com/products/Docetaxel(Taxotere).html selleck compound] On the other hand, lattice parameters are much more sensitive to the choice of Ud and Up, but in a systematic way that enables the Ud and Up corrections to be used to qualitatively gauge the extent of self-interaction error in the electron density. Modest Ud corrections (e.g., 4 eV-5 eV) yield the most reliable dielectric response functions for SrTiO3 and are comparable to the range of Ud values derived via linear response approaches. For r-TiO2 and a-TiO2, however, the Ud,p corrections that yield accurate bandgaps fail to accurately describe both the parallel and perpendicular components of the dielectric response function. Analysis of individual Ud and Up corrections on the optical properties of SrTiO3 suggests that the most consequential of the two individual corrections is Ud, as it predominately determines the accuracy of the dominant excitation from O-2p to the Ti-3d t2g/eg orbitals. Up, on the other hand, can be used to shift the entire optical response uniformly to higher frequencies. These results will assist high-throughput and machine learning approaches to screening photoactive materials based on d0 photocatalysts.An efficient computational scheme for the calculation of highly accurate ground-state electronic properties of the helium isoelectronic series, permitting uniform description of its members down to the critical nuclear charge Zc, is described. It is based upon explicitly correlated basis functions derived from the regularized Krylov sequences (which constitute the core of the free iterative CI/free complement method of Nakatsuji) involving a term that introduces split length scales. For the nuclear charge Z approaching Zc, the inclusion of this term greatly reduces the error in the variational estimate for the ground-state energy, restores the correct large-r asymptotics of the one-electron density ρ(Z; r), and dramatically alters the manifold of the pertinent natural amplitudes and natural orbitals. The advantages of this scheme are illustrated with test calculations for Z = 1 and Z = Zc carried out with a moderate-size 12th-generation basis set of 2354 functions. For Z = Zc, the augmentation is found to produce a ca. 5000-fold improvement in the accuracy of the approximate ground-state energy, yielding values of various electronic properties with between seven and eleven significant digits. Some of these values, such as those of the norms of the partial-wave contributions to the wavefunction and the Hill constant, have not been reported in the literature thus far. The same is true for the natural amplitudes at Z = Zc, whereas the published data for those at Z = 1 are revealed by the present calculations to be grossly inaccurate. Approximants that yield correctly normalized ρ(1; r) and ρ(Zc; r) conforming to their asymptotics at both r → 0 and r → ∞ are constructed.It is well known that Brillouin's theorem (BT) holds in the restricted open-shell Hartree-Fock (ROHF) method for three kinds of single excitations, c → o, c → v, and o → v, where c, o, and v are the orbitals of the closed, open, and virtual shells, respectively. For these excitations, the conditions imposed by BT on the orbitals of a system under study are physically equivalent to the conditions imposed by the variational principle, and this provides a fundamental meaning of BT. Together with this, BT is not satisfied for some excitations of the kind o → o, in which both orbitals participating in excitation belong to the open shell. This limitation of BT is known, for example, for the helium atom, where BT is satisfied for excitation from the ground state S01 (1s2) to the state S11 of the configuration 1s12s1 and is not satisfied for excitations S11 → S01 and S11 → S21 (2s2). In this work, we prove that Brillouin's conditions for two latter excitations cannot be related to the fundamental conditions imposed by the variational principle due to specific symmetry restrictions.