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We demonstrate that, if a truncated expansion of a wave function is Large, then the standard excited states computational method, of optimizing one root of a secular equation, according to the theorem of Hylleraas, Undheim and McDonald…
It is proven that the exact excited-state wave function and energy may be obtained by minimizing the energy expectation value of trial wave functions that are constrained only to have the correct nodes of the state of interest. This…
The computation of small concise and comprehensible excited state wave functions is needed because many electronic processes occur in excited states. But since the excited energies are saddle points in the Hilbert space of wave functions,…
The hyperspherical harmonics (HH) provide a complete basis for the expansion of atomic wave functions, but even for two particles the number of harmonics for a given order is not trivial and, as the number of electrons increases, this…
n a recent paper we proposed the expansion of the space of variations in energy calculations by considering the approximate wave function $\psi$ to be a functional of functions $\chi: \psi = \psi[\chi]$ rather than a function. For the…
Determining quantum excited states is crucial across physics and chemistry but presents significant challenges for variational methods, primarily due to the need to enforce orthogonality to lower-energy states, often requiring…
The calculation of excited state energies of electronic structure Hamiltonians has many important applications, such as the calculation of optical spectra and reaction rates. While low-depth quantum algorithms, such as the variational…
The extension of the Rayleigh-Ritz variational principle to ensemble states $\rho_{\mathbf{w}}\equiv\sum_k w_k |\Psi_k\rangle \langle\Psi_k|$ with fixed weights $w_k$ lies ultimately at the heart of several recent methodological…
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…
We demonstrate that, if a truncated expansion of a wave function is small, then the standard excited states computational method, of optimizing one root of a secular equation, may lead to an incorrect wave function - despite the correct…
We calculated the 4He trimer and tetramer ground and excited states with the LM2M2 potential using our Gaussian expansion method (GEM) for ab initio variational calculations of few-body systems. The method has extensively been used for a…
Early work extending the Kohn-Sham theory to excited states utilized an ensemble average of the Hamiltonian considered as a functional of the corresponding average density. We propose and develop an alternative that utilizes the matrix…
Calculating the energy spectrum of a quantum system is an important task, for example to analyse reaction rates in drug discovery and catalysis. There has been significant progress in developing algorithms to calculate the ground state…
The expectation value of the Hamiltonian using a model wave function is widely used to estimate the eigenvalues of electronic Hamiltonians. We explore here a modified formula for models based on long-range interaction. It scales differently…
We calculate the energies of ground and three low lying excited states of confined helium atom centered in an impenetrable spherical box. We perform the calculation by employing variational method with two-parameter variational forms for…
We explore the possibility of calculating electronic excited states by using perturbation theory along a range-separated adiabatic connection. Starting from the energies of a partially interacting Hamiltonian, a first-order correction is…
We investigate an extension of excited state mean-field theory in which the energy expression is augmented with density functional components in an effort to include the effects of weak electron correlations. The approach remains…
We present a variational function that targets excited states directly based on their position in the energy spectrum, along with a Monte Carlo method for its evaluation and minimization whose cost scales polynomially for a wide class of…
Highly precise variational calculations of non-relativistic energies of the (2p^2)^3P^e state of Helium atom are presented.We get an upper bound energy E=-0.71050015565678 a.u.,the lowest yet obtained.
A more reasonable trial ground state wave function is constructed for the relative motion of an interacting two-fermion system in a 1D harmonic potential. At the boundaries both the wave function and its first derivative are continuous and…