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Register a new user$sigma$-SCF: A Direct Energy-targeting Method To Mean-field Excited States
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The mean-field solutions of electronic excited states are much less accessible than ground state (e.g. Hartree-Fock) solutions. Energy-based optimization methods for excited states, like $Delta$-scf, tend to fall into the lowest solution consistent with a given symmetry -- a problem known as variational collapse. In this work, we combine the ideas of direct energy-targeting and variance-based optimization in order to describe excited states at the mean-field level. The resulting method, $sigma$-scf, has several advantages. First, it allows one to target any desired excited state by specifying a single parameter: a guess of the energy of that state. It can therefore, in principle, find emph{all} excited states. Second, it avoids variational collapse by using a variance-based, unconstrained local minimization. As a consequence, all states -- ground or excited -- are treated on an equal footing. Third, it provides an alternate approach to locate $Delta$-scf solutions that are otherwise inaccessible by the usual non-aufbau configuration initial guess. We present results for this new method for small atoms (He, Be) and molecules (H2, HF).
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We present a generalization of the variational principle that is compatible with any Hamiltonian eigenstate that can be specified uniquely by a list of properties. This variational principle appears to be compatible with a wide range of electronic structure methods, including mean-field theory, density functional theory, multi-reference theory, and quantum Monte Carlo. Like the standard variational principle, this generalized variational principle amounts to the optimization of a nonlinear function that, in the limit of an arbitrarily flexible wave function, has the desired Hamiltonian eigenstate as its global minimum. Unlike the standard variational principle, it can target excited states and select individual states in cases of degeneracy or near-degeneracy. As an initial demonstration of how this approach can be useful in practice, we employ it to improve the optimization efficiency of excited state mean field theory by an order of magnitude. With this improved optimization, we are able to demonstrate that the accuracy of the corresponding second-order perturbation theory rivals that of singles-and-doubles equation-of-motion coupled cluster in a substantially broader set of molecules than could be explored by our previous optimization methodology.
The authors present a technique using variational Monte Carlo to solve for excited states of electronic systems. The technique is based on enforcing orthogonality to lower energy states, which results in a simple variational principle for the excited states. Energy optimization is then used to solve for the excited states. An application to the well-characterized benzene molecule, in which ~10,000 parameters are optimized for the first 12 excited states.Agreement within approximately 0.15 eV is obtained with higher scaling coupled cluster methods; small disagreements with experiment are likely due to vibrational effects.
This paper reports an implementation of Hartree-Fock linear response with complex orbitals for computing electronic spectra of molecules in a strong external magnetic fields. The implementation is completely general, allowing for spin-restricted, spin-unrestricted, and general two-component reference states. The method is applied to small molecules placed in strong uniform and non-uniform magnetic fields of astrochemical importance at the Random Phase Approximation level of theory. For uniform fields, where comparison is possible, the spectra are found to be qualitatively similar to those recently obtained with equation of motion coupled cluster theory. We also study the behaviour of spin-forbidden excitations with progressive loss of spin symmetry induced by non-uniform magnetic fields. Finally, the equivalence of length and velocity gauges for oscillator strengths when using complex orbitals is investigated and found to hold numerically.
The electronically excited states of methylene (CH$_2$), ethylene (C$_2$H$_4$), butadiene (C$_4$H$_6$), hexatriene (C$_6$H$_8$), and ozone (O$_3$) have long proven challenging due to their complex mixtures of static and dynamic correlations. Semistochastic heat-bath configuration interaction (SHCI), which efficiently and systematically approaches the full configuration interaction (FCI) limit, is used to provide close approximations to the FCI energies in these systems. This article presents the largest FCI-level calculation to date -- on hexatriene using a polarized double-zeta basis (ANO-L-pVDZ), which gives rise to a Hilbert space containing more than $10^{38}$ determinants. These calculations give vertical excitation energies of 5.58 and 5.59 eV respectively for the $2^1{rm A}_{rm g}$ and $1^1{rm B}_{rm u}$ states, showing that they are nearly degenerate. The same excitation energies in butadiene/ANO-L-pVDZ were found to be 6.58 and 6.45 eV. In addition to these benchmarks, our calculations strongly support the presence of a previously hypothesized ring-minimum species of ozone that lies 1.3 eV higher than the open-ring minimum energy structure and is separated from it by a barrier of 1.11 eV.
We introduce natural transition geminals as a means to qualitatively understand a transition where double excitations are important. The first two $A_{1}$ singlet states of the CH cation are used as an initial example. We calculate these states with configuration interaction singles (CIS) and state-averaged Monte Carlo configuration interaction (SA-MCCI). For each method we compare the important natural transition geminals with the dominant natural transition orbitals. We then compare SA-MCCI and full configuration interaction (FCI) with regards to the natural transition geminals using the beryllium atom. We compare using the natural transition geminals with analyzing the important configurations in the CI expansion to give the dominant transition for the beryllium atom and the carbon dimer. Finally we calculate the natural transition geminals for two electronic excitations of formamide.
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