Accurate assignments of the unoccupied molecular orbitals involved in electronic excitations are crucial to the interpretation of experimental spectra. Here we present an automated approach to the orbital assignment of excited states by introducing a unique orbital basis known as localized intrinsic valence virtual orbitals (LIVVOs), which are a special case of the previously reported valence virtual orbitals. The LIVVOs are used to quantify the local contributions to particle orbitals from orthogonality-constrained density functional theory, providing an assignment with atomic-level/angular momentum shell specificity. This localized set also allows us to define the total valence character of an excited state. We highlight the utility of our approach by studying the local orbital changes in core-excited states at the sulfur K-edge of ethanethiol and benzenethiol as well as the oxygen K-edge spectrum of the water monomer and dimer.

In this work we propose a novel approach to solve the Schrödinger equation which combines projection onto the ground state with a path-filtering truncation scheme. The resulting projector configuration interaction (PCI) approach realizes a deterministic version of the full configuration interaction quantum Monte Carlo (FCIQMC) method [Booth, G. H.; Thom, A. J. W.; Alavi, A. J. Chem. Phys. 2009, 131, 054106]. To improve upon the linearized imaginary-time propagator, we develop an optimal projector scheme based on an exponential Chebyshev expansion in the limit of an infinite imaginary time step. After writing the exact projector as a path integral in determinant space, we introduce a path filtering procedure that truncates the size of the determinantal basis and approximates the Hamiltonian. The path filtering procedure is controlled by one real threshold that determines the accuracy of the PCI energy and is not biased toward any determinant. Therefore, the PCI approach can equally well describe static and dynamic electron correlation effects. This point is illustrated in benchmark computations on N2 at both equilibrium and stretched geometries. In both cases, the PCI achieves chemical accuracy with wave functions that contain less than 0.5% determinants of full CI space. We also report computations on the ground state of C2 with up to quaduple-ζ basis sets and wave functions as large as 200 million determinants, which allow a direct comparison of the PCI, FCIQMC, and density matrix renormalization group (DMRG) methods. The size of the PCI wave function grows modestly with the number of unoccupied orbitals, and its accuracy may be tuned to match that of FCIQMC and DMRG.

Orthogonality constrained density functional theory (OCDFT) provides near-edge X-ray absorption (NEXAS) spectra of first-row elements within one electronvolt from experimental values. However, with increasing atomic number, scalar relativistic effects become the dominant source of error in a nonrelativistic OCDFT treatment of core–valence excitations. In this work we report a novel implementation of the spin-free exact-two-component (X2C) one-electron treatment of scalar relativistic effects and its combination with a recently developed OCDFT approach to compute a manifold of core–valence excited states. The inclusion of scalar relativistic effects in OCDFT reduces the mean absolute error of second-row elements core–valence excitations from 10.3 to 2.3 eV. For all the excitations considered, the results from X2C calculations are also found to be in excellent agreement with those from low-order spin-free Douglas–Kroll–Hess relativistic Hamiltonians. The X2C-OCDFT NEXAS spectra of three organotitanium complexes (TiCl4, TiCpCl3, TiCp2Cl2) are in very good agreement with unshifted experimental results and show a maximum absolute error of 5–6 eV. In addition, a decomposition of the total transition dipole moment into partial atomic contributions is proposed and applied to analyze the nature of the Ti pre-edge transitions in the three organotitanium complexes.

We introduce a multireference version of the driven similarity renormalization group (DSRG) approach [Evangelista, F. A. J. Chem. Phys. 2014, 141, 054109] based on a generalized reference wave function and operator normal ordering [Kutzelnigg, W.; Mukherjee, D. J. Chem. Phys. 1997, 107, 432]. We perform a perturbative analysis of the corresponding equations at second order and derive a novel multireference perturbation theory, termed DSRG-MRPT2. The DSRG-MRPT2 energy equation can be written in a simple and compact form and can be solved via a noniterative procedure that requires at most the three-body density cumulant of the reference. Importantly, even at the perturbation level, the multireference DSRG is free from the intruder-state problem. We propose an optimal range of the DSRG flow parameter that consistently yields reliable potential energy curves with minimal nonparallelism error. We find that the DSRG-MRPT2 can describe the potential energy curves of HF and N2, and the singlet–triplet gap of p-benzyne with an accuracy similar to that of other multireference perturbation theories.

Orthogonality constrained density functional theory (OCDFT) [F. A. Evangelista, P. Shushkov and J. C. Tully, J. Phys. Chem. A, 2013, 117, 7378] is a variational time-independent approach for the computation of electronic excited states. In this work we extend OCDFT to compute core-excited states and generalize the original formalism to determine multiple excited states. Benchmark computations on a set of 13 small molecules and 40 excited states show that unshifted OCDFT/B3LYP excitation energies have a mean absolute error of 1.0 eV. Contrary to time-dependent DFT, OCDFT excitation energies for first- and second-row elements are computed with near-uniform accuracy. OCDFT core excitation energies are insensitive to the choice of the functional and the amount of Hartree–Fock exchange. We show that OCDFT is a powerful tool for the assignment of X-ray absorption spectra of large molecules by simulating the gas-phase near-edge spectrum of adenine and thymine.

Orthogonality constrained density functional theory (OCDFT) [F. A. Evangelista, P. Shushkov and J. C. Tully, J. Phys. Chem. A, 2013, 117, 7378] is a variational time-independent approach for the computation of electronic excited states. In this work we extend OCDFT to compute core-excited states and generalize the original formalism to determine multiple excited states. Benchmark computations on a set of 13 small molecules and 40 excited states show that unshifted OCDFT/B3LYP excitation energies have a mean absolute error of 1.0 eV. Contrary to time-dependent DFT, OCDFT excitation energies for first- and second-row elements are computed with near-uniform accuracy. OCDFT core excitation energies are insensitive to the choice of the functional and the amount of Hartree–Fock exchange. We show that OCDFT is a powerful tool for the assignment of X-ray absorption spectra of large molecules by simulating the gas-phase near-edge spectrum of adenine and thymine.