Full configuration interaction calculation of BeH adiabatic states

An all-electron full configuration interaction (FCI) calculation of the adiabatic potential energy curves of some of the lower states of BeH molecule is presented. A moderately large ANO basis set of atomic natural orbitals (ANO) augmented with Rydberg functions has been used in order to describe the valence and Rydberg states and their interactions. The Rydberg set of ANOs has been placed on the Be at all bond distances. So, the basis set can be described as 4s3p2d1f/3s2p1d(Be/H)+4s4p2d(Be). The dipole moments of several states and transition dipole strengths from the ground state are also reported as a function of the RBe–H distance. The position and the number of states involved in several avoided crossings present in this system have been discussed. Spectroscopic parameters have been calculated from a number of the vibrational states that result from the adiabatic curves except for some states in which this would be completely nonsense, as it is the case for the very distorted curves of the 3s and 3p math states or the double-well potential of the 4p math state. The so-called “D complex” at 54 050 cm−1 (185.0 nm) is resolved into the three 3d substates (math,math,math). A diexcited valence state is calculated as the lowest state of math symmetry and its spectroscopic parameters are reported, as well as those of the 2 math (4d) state The adiabatic curve of the 4 math state shows a swallow well at large distances (around 4.1 Å) as a result of an avoided crossing with the 3 math state. The probability that some vibrational levels of this well could be populated is discussed within an approached Landau–Zerner model and is found to be high. No evidence is found of the E(4sσ) math state in the region of the “D complex”. Instead, the spectroscopic properties obtained from the (4sσ) 6 math adiabatic curve of the present work seem to agree with those of the experimental F(4pσ) math state. The FCI calculations provide benchmark results for other correlation models for the open-shell BeH system and evidence both the limitations and capabilities of the basis [email protected] [email protected]

Calculations of polarizabilities and hyperpolarizabilities for the Be+^+ ion

The polarizabilities and hyperpolarizabilities of the Be$^+$ ion in the $2^2S$ state and the $2^2P$ state are determined. Calculations are performed using two independent methods: i) variationally determined wave functions using Hylleraas basis set expansions and ii) single electron calculations utilizing a frozen-core Hamiltonian. The first few parameters in the long-range interaction potential between a Be$^+$ ion and a H, He, or Li atom, and the leading parameters of the effective potential for the high-$L$ Rydberg states of beryllium were also computed. All the values reported are the results of calculations close to convergence. Comparisons are made with published results where available.Comment: 18 pp; added details to Sec. I

A parallel algorithm for Hamiltonian matrix construction in electron-molecule collision calculations: MPI-SCATCI

Construction and diagonalization of the Hamiltonian matrix is the rate-limiting step in most low-energy electron -- molecule collision calculations. Tennyson (J Phys B, 29 (1996) 1817) implemented a novel algorithm for Hamiltonian construction which took advantage of the structure of the wavefunction in such calculations. This algorithm is re-engineered to make use of modern computer architectures and the use of appropriate diagonalizers is considered. Test calculations demonstrate that significant speed-ups can be gained using multiple CPUs. This opens the way to calculations which consider higher collision energies, larger molecules and / or more target states. The methodology, which is implemented as part of the UK molecular R-matrix codes (UKRMol and UKRMol+) can also be used for studies of bound molecular Rydberg states, photoionisation and positron-molecule collisions.Comment: Write up of a computer program MPI-SCATCI Computer Physics Communications, in pres

R-matrix calculations of electron impact electronic excitation of BeH

The R-matrix method is used to perform high-level calculations of electron collisions with beryllium mono-hydride at its equilibrium geometry with a particular emphasis on electron impact electronic excitation. Several target and scattering models are considered. The calculations were performed using (1) the UKRMol suite which relies on the use of Gaussian type orbitals (GTOs) to represent the continuum and (2) using the new UKRMol+ suite which allows the inclusion of B-spline type orbitals in the basis for the continuum. The final close-coupling scattering models used the UKRMol+ code and a frozen core, valence full configuration interaction, method based on a diffuse GTO atomic basis set. The calculated electronic properties of the molecule are in very good agreement with state-of-the-art electronic structure calculations. The use of the UKRMol+ suite proved critical since it allowed the use of a large R-matrix sphere (35 Bohr), necessary to contain the diffuse electronic states of the molecule. The corresponding calculations using UKRMol are not possible due to numerical problems associated with the combination of GTO-only continuum and a large R-matrix sphere. This work provides the first demonstration of the utility and numerical stability of the new UKRMol+ code. The inelastic cross sections obtained here present a significant improvement over the results of earlier studies on BeH

Electronic excited states in deep variational Monte Carlo

Obtaining accurate ground and low-lying excited states of electronic systems is crucial in a multitude of important applications. One ab initio method for solving the Schrödinger equation that scales favorably for large systems is variational quantum Monte Carlo (QMC). The recently introduced deep QMC approach uses ansatzes represented by deep neural networks and generates nearly exact ground-state solutions for molecules containing up to a few dozen electrons, with the potential to scale to much larger systems where other highly accurate methods are not feasible. In this paper, we extend one such ansatz (PauliNet) to compute electronic excited states. We demonstrate our method on various small atoms and molecules and consistently achieve high accuracy for low-lying states. To highlight the method’s potential, we compute the first excited state of the much larger benzene molecule, as well as the conical intersection of ethylene, with PauliNet matching results of more expensive high-level methods

The calculation of electron collisions with atoms and molecules

In this thesis electron collisions are studied under two different scattering energy regimes. Firstly, low energy electron-molecule collisions are considered. These typically occur in interstellar medium, planetary atmospheres or industrial plasmas. Under these conditions the electrons cannot be treated classically and so a quantum mechanical approach is used. Using R-matrix theory two targets are studied: nitric oxide (NO) and molecular hydrogen (H$_2$). Owing to new developments in the UKRMol+ code the boundaries of previous R-matrix calculations are pushed to new limits in order to produce accurate cross-sections for electron-impact electronic excitation of H$_2$. This includes the use of a B-spline continuum basis, a triply-augmented target basis and a box size of 100 $a_0$. NO is used as a prototypical example of an open-shell molecule that exhibits mixed Rydberg-like and Valence states. Systems like this are typically difficult to solve using standard quantum chemistry approaches, and so the R-matrix with pseudo-states method is employed to produce a set of improved potential energy curves, capable of being used in further scattering calculations. In the second regime, high energy electron-atom collisions are investigated. These types of collision take place in strongly-driven systems, e.g., atoms in intense laser fields. In this case, the \emph{scattering} electron is provided by the neutral parent atom as it is ionised by the external field. The specific focus of this work is the phenomena of non-sequential double ionisation. A semiclassical Monte-Carlo method is used based on the three step model, which fully accounts for two active electrons, the Coulomb potential and the magnetic-field. Using this model the role of magnetic-field effects in strong-field physics are investigated

Variational Calculation of Fine and Hyperfine Resolved Rovibronic Spectra of Diatomic Molecules

The thesis presents methods for the variational calculation of fine and hyperfine resolved rovibronic spectra of diatomic molecules, as part of the ExoMol and ExoMolHD projects. The theory of these methods has been fully discussed. The corresponding algorithms have been implemented based on previous works of the ExoMol Group. The line lists of two molecules, NO and VO has been calculated, which validates the proposed methods. Nitric oxide is one of the principal oxides of nitrogen, which plays a significant role the investigations of our atmosphere and astrophysics. Due to its importance, the radical has been investigated in numerous theoretical and experimental works. However, there is no NO ultraviolet line list in well-known databases. A major issue in generating a UV line list for NO results from the difficulty of modelling the valence-Rydberg interaction between its B2Π and C2Π states. To address the problem, a spectroscopic model has been proposed to resolve the energy structures of B2Π and C2Π coupled states. Based on the model, an accurate line list, called XABC, has been computed, which covers the pure rotational, vibrational and rovibronic spectra of 14N16O. Vanadium monoxide is also an open shell diatomic system. Its dominating isotopologue 51V16O has non-zero nuclear spin, I = 7/2. The interaction between the spin of unpaired electrons and the nuclear spin yields a very pronounced hyperfine structure. The widely used effective Hamiltonian method for hyperfine structure is not applicable to give accurate line list of VO, as the interactions between the electronic states of VO reshape its line positions and intensities. This thesis presents a variational algorithm for the calculation of hyperfine structure and spectra of diatomic molecules. The hyperfine-resolved IR spectra of VO has been computed from first principles, considering necessary nuclear hyperfine coupling curves

Development of nonorthogonal wavefunction theories and application to multistate reaction processes.

Many prominent areas of technological development rely on exploiting the photochemical response of molecules. An application of particular interest is the control of molecular switches through a combination of different external stimuli. However, despite significant advances in theoretical approaches and numerous cases of successful application of theory, simulating photochemical reactions remains a computational challenge. Theoretical methods for describing excited states can be broadly divided into single-reference response methods and multireference methods. Single reference methods provide reliable semiquantitative results for single excitations. However, these methods cannot describe double-excited states, systems with strongly correlated ground states, or regions of degeneracy on the potential energy surface. The alternative, multireference methods, can provide more accurate results. However, multireference methods require significant technical and chemical insight and become computationally costly as the system size increases. I will discuss my work applying newly developed and well-known methods for understanding multistate processes. I will highlight the limitations and extent of current methodologies that prevent researchers from studying larger and more complex systems. I will also discuss new methodological developments using spin projection, which seeks to overcome several problems of single reference excited state models. I will illustrate the motivation and its performance compared to more established theories. Despite its success, the new method cannot account for ‘multiple correlation mechanisms’. As a result, I will introduce how multiple correlation mechanisms can be exploited to perform nonorthogonal active space decomposition, along with applications and paths for future improvements