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Register a new userHighly accurate potential energy curves for the hydrogen molecule ion
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Potential energy surfaces of the hydrogen molecular ion H$_2^+$ in the Born-Oppenheimer approximation are computed by means of the Riccati-Pade method (RPM). The convergence properties of the method are analyzed for different states. The equilibrium internuclear distance, as well as the corresponding electronic plus nuclear energy, and the associated separation constants, are computed to 40 digits of accuracy for several bound states. For the ground state the same parameters are computed with more than 100 digits of accuracy. Additional benchmark values of the electronic energy at different internuclear distances are given for several additional states. The software implementation of the RPM is given under a free software license. The results obtained in the present work are the most accurate available so far, and further additional benchmarks are made available through the software provided.
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Path integral Monte Carlo approach is used to study the coupled quantum dynamics of the electron and nuclei in hydrogen molecule ion. The coupling effects are demonstrated by comparing differences in adiabatic Born--Oppenheimer and non-adiabatic simulations, and inspecting projections of the full three-body dynamics onto adiabatic Born--Oppenheimer approximation. Coupling of electron and nuclear quantum dynamics is clearly seen. Nuclear pair correlation function is found to broaden by 0.040 a_0 and average bond length is larger by 0.056 a_0. Also, non-adiabatic correction to the binding energy is found. Electronic distribution is affected less, and therefore, we could say that the adiabatic approximation is better for the electron than for the nuclei.
Using a hydrogen molecule as a test system we demonstrate how to compute the effective potential according to the formalism of the new density functional theory (DFT), in which the basic variable is the set of spherically averaged densities instead of the total density, used in the traditional DFT. The effective potential together the external potential, nuclear Coulomb potential, can be substituted in the Schrodinger like differential equation to obtain the spherically averaged electron density of the system. In the new method instead of one three-dimensional low symmetry equation one has to solve as many spherically symmetric equations as there are atoms in the system.
The concept of machine learning configuration interaction (MLCI) [J. Chem. Theory Comput. 2018, 14, 5739], where an artificial neural network (ANN) learns on the fly to select important configurations, is further developed so that accurate ab initio potential energy curves can be efficiently calculated. This development includes employing the artificial neural network also as a hash function for the efficient deletion of duplicates on the fly so that the singles and doubles space does not need to be stored and this barrier to scalability is removed. In addition configuration state functions are introduced into the approach so that pure spin states are guaranteed, and the transferability of data between geometries is exploited. This improved approach is demonstrated on potential energy curves for the nitrogen molecule, water, and carbon monoxide. The results are compared with full configuration interaction values, when available, and different transfer protocols are investigated. It is shown that, for all of the considered systems, accurate potential energy curves can now be efficiently computed with MLCI. For the potential curves of N$_{2}$ and CO, MLCI can achieve lower errors than stochastically selecting configurations while also using substantially less processor hours.
We describe our efforts of the past few years to create a large set of more than 500 highly-accurate vertical excitation energies of various natures ($pi to pi^*$, $n to pi^*$, double excitation, Rydberg, singlet, doublet, triplet, etc) in small- and medium-sized molecules. These values have been obtained using an incremental strategy which consists in combining high-order coupled cluster and selected configuration interaction calculations using increasingly large diffuse basis sets in order to reach high accuracy. One of the key aspect of the so-called QUEST database of vertical excitations is that it does not rely on any experimental values, avoiding potential biases inherently linked to experiments and facilitating theoretical cross comparisons. Following this composite protocol, we have been able to produce theoretical best estimate (TBEs) with the aug-cc-pVTZ basis set for each of these transitions, as well as basis set corrected TBEs (i.e., near the complete basis set limit) for some of them. The TBEs/aug-cc-pVTZ have been employed to benchmark a large number of (lower-order) wave function methods such as CIS(D), ADC(2), CC2, STEOM-CCSD, CCSD, CCSDR(3), CCSDT-3, ADC(3), CC3, NEVPT2, and others (including spin-scaled variants). In order to gather the huge amount of data produced during the QUEST project, we have created a website [https://lcpq.github.io/QUESTDB_website] where one can easily test and compare the accuracy of a given method with respect to various variables such as the molecule size or its family, the nature of the excited states, the type of basis set, etc. We hope that the present review will provide a useful summary of our effort so far and foster new developments around excited-state methods.
We present benchmark integrated and differential cross-sections for electron collisions with H$_2$ using two different theoretical approaches, namely, the R-matrix and molecular convergent close-coupling (MCCC). This is similar to comparative studies conducted on electron-atom collisions for H, He and Mg. Electron impact excitation to the $b ^3Sigma_u^+$, $a ^3Sigma_g^+$, $B ^1Sigma_u^+$, $c ^3Pi_u$, $EF ^1Sigma_g^+$, $C ^1Pi_u$, $e ^3Sigma_u^+$, $h ^3Sigma_g^+$, $B ^1Sigma_u^+$ and $d ^3Pi_u$ excited electronic states are considered. Calculations are presented in both the fixed nuclei and adiabatic nuclei approximations, where the latter is shown only for the $b ^3Sigma_u^+$ state. Good agreement is found for all transitions presented. Where available, we compare with existing experimental and recommended data.
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