Complete Configuration Interaction Research Articles

Active Learning Configuration Interaction for Excited-State Calculations of Polycyclic Aromatic Hydrocarbons.

We present the active learning configuration interaction (ALCI) method for multiconfigurational calculations based on large active spaces. ALCI leverages the use of an active learning procedure to find important electronic configurations among the full configurational space generated within an active space. We tested it for the calculation of singlet–singlet excited states of acenes and pyrene using different machine learning algorithms. The ALCI method yields excitation energies within 0.2–0.3 eV from those obtained by traditional complete active-space configuration interaction (CASCI) calculations (affordable for active spaces up to 16 electrons in 16 orbitals) by including only a small fraction of the CASCI configuration space in the calculations. For larger active spaces (we tested up to 26 electrons in 26 orbitals), not affordable with traditional CI methods, ALCI captures the trends of experimental excitation energies. Overall, ALCI provides satisfactory approximations to large active-space wave functions with up to 10 orders of magnitude fewer determinants for the systems presented here. These ALCI wave functions are promising and affordable starting points for the subsequent second-order perturbation theory or pair-density functional theory calculations.

Development and Application of a Complete Active Space Spin-Orbit Configuration Interaction Program Designed for Single Molecule Magnets.

We present a spin‐orbit configuration interaction program which has been tailored for the description of the magnetic properties of polynuclear metal complexes with partially filled d‐ and f‐shells. The spin‐orbit operators are directly included in the configuration interaction program based on Slater‐determinants. The lowest states are obtained by a Block‐Davidson‐type diagonalisation. The usage of localised active orbitals enables the construction of start vectors from tensor products of single‐center wave functions that already include spin‐orbit interaction. This allows for an analysis of the role and the interplay of the different metal centres. Furthermore, in case of weak coupling of the metal centres these tensor products are already close to the final wave functions ensuring fast convergence. In combination with a two‐layer hybrid parallelisation, this makes the program highly efficient. Based on the spin‐orbit coupled wave functions, magnetic D‐tensors, g‐tensors and temperature‐dependent susceptibilities can be calculated. The applicability and performance of the program is shown exemplarily on a trinuclear transition metal (CoIIVIICoII) complex.

On the Accuracy of Mean-Field Spin-Orbit Operators for 3d Transition-Metal Systems.

We present an extensive study of the performance of mean-field approximations to the spin-orbit operators on realistic molecular systems, as widely used in applications like single-molecule magnets, molecular quantum bits, and molecular spintronic devices. The test systems feature a 3d transition-metal center ion (V, Cr, Mn, Fe, Co, and Ni) in various coordinations and a multitude of energetically close-lying open-shell configurations that can couple via the spin-orbit operator. We performed complete active space spin-orbit configuration interaction calculations and compared the full two-electron Breit-Pauli spin-orbit operator to different approximations: the one-center approximation, the spin-orbit mean-field approach with electron densities from different state-averaging procedures, and the atomic mean-field integral approximation. We show that the mean-field approaches can lead to significant errors in the spin-orbital coupling matrix elements, which becomes particularly visible for the computed zero-field splittings. The one-center approximation, keeping all relevant two-electron terms, seems to be a significantly more accurate choice for the examples from our test set.

Sulfur-Containing Analogues of the Reactive [CuOH]2+ Core.

With the aim of drawing comparisons to the highly reactive complex LCuOH (L = bis(2,6-diisopropylphenylcarboxamido)pyridine), the complexes [Bu4N][LCuSR] (R = H or Ph) were prepared, characterized by spectroscopy and X-ray crystallography, and oxidized at low temperature to generate the species assigned as LCuSR on the basis of spectroscopy and theory. Consistent with the smaller electronegativity of S versus O, redox potentials for the LCuSR-/0 couples were ∼50 mV lower than for LCuOH-/0, and the rates of the proton-coupled electron transfer reactions of LCuSR with anhydrous 1-hydroxy-2,2,6,6-tetramethyl-piperidine at -80 °C were significantly slower (by more than 100 times) than the same reaction of LCuOH. Density functional theory (DFT) and time-dependent DFT calculations on LCuZ (Z = OH, SH, SPh) revealed subtle differences in structural and UV-visible parameters. Further comparison to complexes with Z = F, Cl, and Br using complete active space (CAS) self-consistent field and localized orbital CAS configuration interaction calculations along with a valence-bond-like interpretation of the wave functions showed differences with previously reported results ( J. Am. Chem. Soc. 2020, 142, 8514), and argue for a consistent electronic structure across the entire series of complexes, rather than a change in the nature of the ligand field arrangement for Z = F.

Relativistic four-component potential energy curves for the lowest 23 covalent states of molecular astatine (At2).

The potential energy curves (PECs) of all covalent states of Molecular Astatine (At2) have been investigated in this work within a four-component relativistic framework using the MOLFDIR program package. The ground state was determined using multireference configuration interaction with all single and double excitations including Davidson size-extensivity correction (MRCISD+Q) whereas the 22 excited states were treated by complete open shell configuration interaction (COSCI). Spectroscopic constants (Re,ωe,ωexe,ωeye, De,Be,αe,βe,Te) are presented for all states as well as vertical excitations obtained at COSCI, MRCISD and MRCISD+Q levels. In addition, it is also presented accurate extended Rydberg analytical form for the ground state X: (1)0g+.

Spectroscopic, vibrational and structural properties analysis of CaXen (n = 1–4) clusters

A systematic ab initio calculations based on a complete Configuration Interaction (CI) including the pseudo-potential model where the core valence correlation was presented by the Core Polarization Potential (CPP), were employed to determine the geometric structures of CaXen (n = 1–4) neutral clusters. For the diatomic (CaXe) and tri-atomic (CaXe2) systems, the potential energy curves for the ground and several excited states are determined and the different spectroscopic constants are illustrated. Interested structures were seen in the PECs which their effects in the vibrational levels' spacing and the electric dipole moments variations were shown. The agreement with the experimental and the theoretical constants for n = 1 was excellent. Accordingly, for the higher clusters the predicted geometries should be reliable. The bent geometry of CaXe2 ground state with (C2v) symmetry was performed and hence was concluded to be the most adaptable with a bond angle of 54.84° and bond distance dXe-Xe of 8.08 a0. As well as, the bent isomer for the excited states was also studied to illustrate the most compact geometry for each state. For the ground state of CaXe3, the most stable geometry was trigonal-pyramidal with (C3v) symmetry with dXe-Xe = 8.13 a0. And concerned n = 4, four configurations were treated; the tetrahedral structure, the square pyramid structure, the trigonal bipyramid structure with (C3v) symmetry and the trigonal bipyramid structure with (C2v) symmetry. The comparison between their minimal energies showed that the most compact geometry for CaXe4 is the trigonal bipyramid with (C3v) symmetry with dXe-Xe = 8.17 a0. Consequently, this work illustrates that the mechanism of cluster forming is consistent with the calcium location on the xenon clusters' surface model.

Kinetics of the Strongly Correlated CH3O + O2 Reaction: The Importance of Quadruple Excitations in Atmospheric and Combustion Chemistry.

Kinetics measurements on radical-radical reactions are often unavailable experimentally, and obtaining quantitative rate constants for such reactions by theoretical methods is challenging because the transition states and the reactants are often strongly correlated. Treating strongly correlated systems by coupled cluster theory limited to single, double, and triple connected excitations is often inadequate. We therefore use a new method, called GMM(P), for extrapolation to the complete configuration interaction limit to go beyond triple excitations and in particular to approximate the CCSDTQ(P)/CBS limit. Here, we present this method and use it to investigate the CH3O + O2 reaction. The contribution of connected quadruple excitations to the barrier height energy is found to be -3.13 kcal/mol, and adding a quasiperturbative calculation of the effect of connected pentuple excitations brings the post-connected-triples contributions to -3.44 kcal/mol, which corresponds to Boltzmann factors that increase calculated rate constants by factors of 1.0 × 103, 3.3 × 102, and 18 at 250, 298, and 600 K, respectively. We present rate constants for temperatures from 250 to 2000 K, and we find that the Arrhenius activation energy increases from 0.58 to 9.68 kcal/mol over this range. We also find reasonably good accuracy for the barrier height with the MN15-L exchange-correlation functional, and we calculate rate constants by a combination of GMM(P) and MN15-L electronic structure calculations and conventional and variational transition state theory, in particular canonical variational theory with small-curvature tunneling. The present findings have broad implications for obtaining quantitative rate constants for complex reaction systems in atmospheric and combustion chemistry.

A theoretical study on trivalent europium: from the free ion to the water complex.

The energy levels within the (7)F and (5)D manifolds of trivalent europium were computed for the free ion and in the crystal field of 6-9 water molecules. Fully relativistic Kramers pairs configuration interaction (KRCI) calculations were performed with different correlation spaces for the free ion, and with the complete open-shell configuration interaction (COSCI) method including the 4f electrons in the active space for the water clusters. The best agreement with experimental data was found with the KRCI method or when including the spin-other-orbit effect in the COSCI calculations. For the free ion, the (7)F6 multiplet is found only 162 cm(-1) higher compared to experiment, while the (5)D(0-3) multiplets are approximately 3100 cm(-1) too high. In the crystal field of six water molecules, the multiplets with J > 0 split by 48-123 cm(-1). The energy separation (7)F0-(5)D0 of the unsplit multiplets is computed within 255 cm(-1)/247 cm(-1) compared to the experimental data for the free ion/in water. It has been found that the effect of higher coordination number or lower symmetry is small, increasing the transition energies by only about 40 cm(-1) by lowering the (7)F(J) states by the same amount. The hypersensitive transition (5)D0-(7)F2 is computed at 17079 cm(-1) with the KRCI method as compared to the experimental value of 16267 cm(-1).

Towards the assignment of the REMPI spectrum of Ph2O using CIS and TD-DFT methods

Tentative assignment of the low-lying vibrational features of the first electronic excited singlet-state S1 of diphenyl ether (Ph2O), obtained from resonance-enhanced multiphoton ionisation (REMPI) spectroscopy, is performed using CIS and time-dependent density functional theory (TD-DFT) methods. The potential energy surfaces, regarding the rotation of the phenyl rings relatively to the C–O–C plane, are obtained at the B3LYP/6-31G(d) level of theory, for the ground-state of neutral and cationic Ph2O and for its first excited singlet state. The torsional barriers of the ground state of diphenyl ether were studied by means of quantum-chemical perturbations of increasing accuracy and an extrapolation to the complete basis set limit and full configuration interaction (FCI) was performed through the use of correlation consistent basis sets and the continued fraction method. The first adiabatic ionisation energy (AIE) of the twist conformer is computed at 8.60 eV in the FCI limit, much higher than the experimental results of Terlouw et al. (8.09±0.03 eV) and Paiva et al. (7.8±0.1 eV). The B3LYP result of 7.82 eV is, however, in reasonable agreement with the result of Paiva et al.The first singlet excitation energy for the twist conformation is found to be 5.5 eV at the CIS/6-311++G(d,p) level of theory. Some features of the experimental REMPI spectrum, previously obtained by one of the authors, are explained and a new insight on the ionisation energy of diphenyl ether is presented.

Photoabsorption profile and satellite features of the potassium4s→4ptransition perturbed by ground-state helium atoms

Quantal calculations are performed to determine the absorption profile of the broadened potassium resonance line 4p ← 4s in its far wings provoked by helium perturbers. First, the X 2 � + , A 2 �, and B 2 � + potentials, as well as the transition dipole moments, are carefully computed through ab initio methods, based on stateaveraged complete active space self-consistent field multireference configuration interaction (SA-CASSCFMRCI) calculations involving the Davidson and basis-set superposition error (BSSE) corrections. The data are then used to generate the KHe photoabsorption spectra and to examine their behavior with temperature. The theoretical profile is dominated by the free-free transitions and exhibits, in the vicinity of the wavelength position of 693 nm, a satellite peak in the blue wing attributed to the B ← X transitions. The results are compared with previous theoretical and experimental investigations and, in general, good agreement is found.

Global spectroscopy of the water monomer

Given the large energy required for its electronic excitation, the most important properties of the water molecule are governed by its ground potential energy surface (PES). Novel experiments are now able to probe this surface over a very extended energy range, requiring new theoretical procedures for their interpretation. As part of this study, a new, accurate, global spectroscopic-quality PES and a new, accurate, global dipole moment surface are developed. They are used for the computation of the high-resolution spectrum of water up to the first dissociation limit and beyond as well as for the determination of Stark coefficients for high-lying states. The water PES has been determined by combined ab initio and semi-empirical studies. As a first step, a very accurate, global, ab initio PES was determined using the all-electron, internally contracted multi-reference configuration interaction technique together with a large Gaussian basis set. Scalar relativistic energy corrections are also determined in order to move the energy determinations close to the relativistic complete basis set full configuration interaction limit. The electronic energies were computed for a set of about 2500 geometries, covering carefully selected configurations from equilibrium up to dissociation. Nuclear motion computations using this PES reproduce the observed energy levels up to 39 000 cm(-1) with an accuracy of better than 10 cm(-1). Line positions and widths of resonant states above dissociation show an agreement with experiment of about 50 cm(-1). An improved semi-empirical PES is produced by fitting the ab initio PES to accurate experimental data, resulting in greatly improved accuracy, with a maximum deviation of about 1 cm(-1) for all vibrational band origins. Theoretical results based on this semi-empirical surface are compared with experimental data for energies starting at 27 000 cm(-1), going all the way up to dissociation at about 41 000 cm(-1) and a few hundred wavenumbers beyond it.

Excited Li and Na in Hen: Influence of the dimer potential energy curves

The X(2)Σ ground and the A(2)Π and B(2)Σ first two excited states of Li-He and Na-He are determined using high level complete active space self-consistent field-multireference configuration interaction ab initio method. The obtained potentials differ from the ones proposed by Pascale [Phys. Rev. A 28, 632 (1983)], more strongly for the ground than for the excited states. Quantum diffusion Monte Carlo studies of small Li(∗)He(n) and Na(∗)He(n) with n ≤ 5 are performed using a diatomics-in-molecule approach to model the non-pair additive interaction potential. The sensitivity of our results to the A(2)Π and B(2)Σ potentials used is assessed by an analysis of the structure and of the energetics of the clusters. For these small clusters, the physical conclusions are essentially independent of the diatomic curves employed.

Kinetics of the reaction of the heaviest hydrogen atom with H2, the 4Heμ + H2 → 4HeμH + H reaction: Experiments, accurate quantal calculations, and variational transition state theory, including kinetic isotope effects for a factor of 36.1 in isotopic mass

The neutral muonic helium atom (4)Heμ, in which one of the electrons of He is replaced by a negative muon, may be effectively regarded as the heaviest isotope of the hydrogen atom, with a mass of 4.115 amu. We report details of the first muon spin rotation (μSR) measurements of the chemical reaction rate constant of (4)Heμ with molecular hydrogen, (4)Heμ + H(2) → (4)HeμH + H, at temperatures of 295.5, 405, and 500 K, as well as a μSR measurement of the hyperfine coupling constant of muonic He at high pressures. The experimental rate constants, k(Heμ), are compared with the predictions of accurate quantum mechanical (QM) dynamics calculations carried out on a well converged Born-Huang (BH) potential energy surface, based on complete configuration interaction calculations and including a Born-Oppenheimer diagonal correction. At the two highest measured temperatures the agreement between the quantum theory and experiment is good to excellent, well within experimental uncertainties that include an estimate of possible systematic error, but at 295.5 K the quantum calculations for k(Heμ) are below the experimental value by 2.1 times the experimental uncertainty estimates. Possible reasons for this discrepancy are discussed. Variational transition state theory calculations with multidimensional tunneling have also been carried out for k(Heμ) on the BH surface, and they agree with the accurate QM rate constants to within 30% over a wider temperature range of 200-1000 K. Comparisons between theory and experiment are also presented for the rate constants for both the D + H(2) and Mu + H(2) reactions in a novel study of kinetic isotope effects for the H + H(2) reactions over a factor of 36.1 in isotopic mass of the atomic reactant.

Iterative variational approach to finite many-body systems

A procedure is discussed that searches for the best description of the eigenstates of a Hamiltonian of a finite quantum many-body system in terms of a selected set of physically relevant configurations. The procedure resorts to iterative sequences of diagonalizations in spaces of very reduced size. Each diagonalization provides an energy-based importance measure that governs the selection of the configurations to be included in the states. The procedure is strictly variational and preserves the symmetries of the Hamiltonian throughout the iterative process. We report on some test applications to the Na${}_{8}$ metal cluster. A series of calculations is performed on a Hartree-Fock basis for a number of orbitals ranging from 5 to 20. In the case of 5 (10) orbitals, we compare the low-lying spectra generated with our procedure to complete (truncated) configuration interaction calculations. The procedure accurately reproduces the results in the complete space. In the most complex cases of 15 and 20 orbitals (the latter involving a many-particle space of 10${}^{11}$ states), we construct the ground state and study its structure. The analysis highlights the efficiency of the method in generating the most appropriate model space for the description of individual eigenstates of the Hamiltonian.

Precision calculation of the low-lying excited states of the Rf atom

Precision calculations of the ground and low-lying excited electronic states of the Rf atom (Z = 104) were performed. The relativistic effects were taken into account with the Dirac-Coulomb-Breit Hamiltonian. The finite nucleus size was taken into account in the Fermi model (A = 267). The correlation effects were described by the combined scheme that we suggested previously, which proved to be efficient: The relativistic coupled clusters method with one- and two-particle cluster amplitudes in the Fock space was used for describing the correlations of 44 outer electrons of the Rf atoms in a fairly large atomic basis set, and for the four valence electrons occupying the 7s, 7p, and 6d states, the contributions from three- and four-particle cluster amplitudes were taken into account using the complete configuration interaction method, but in a relatively small basis set. The relativistic configuration and term for the ground state of the Rf atom were refined, and the energies of its excitation to low-lying states were calculated. The accuracy of the calculation by the generalized relativistic effective core potential method was evaluated by comparing the results with those obtained similarly using the Dirac-Coulomb-Breit Hamiltonian.

First-Principle Study of Atomic Hydrogen Interaction with a Fluorinated Corannulene Radical

In this work, we study fluorination effects on atomic hydrogen interactions with the fluorinated corannulene radical (C15H10F5), which was built as a model for a partially fluorinated nanotube (or fullerene). Complete active space self-consistent field and multi-reference configuration interaction methods are employed to calculate the potential energy surfaces for both ground and excited electronic states, and the R-matrix quantum dynamics method is used to investigate the atomic hydrogen transmission and reflection dynamics through the five-membered ring in the fluorinated corannulene radical, which includes resonance effects as well as non-adiabatic transitions between the ground and excited electronic states. We also investigate hydrogen adsorptions at two sites in the middle five-membered ring, namely, on top of a carbon atom and in the middle of a carbon–carbon bond. We found that on carbon-top site, the adsorption is almost barrierless, whereas in the middle bond site, there is a barrier to hydrogen adsorption.

Polarization directions of electronic transitions in large conjugated molecules of low symmetry

Advances in experimental techniques for determination of transition moment directions in large molecules call for evaluation of the reliability of angles calculated using the semiempirical SCF-CI PPP method. Two disturbing features are considered: first, the large difference between oscillator strengths calculated by the dipole length and dipole velocity methods; second, the considerable effect of more highly excited configurations on the calculated transition moments and gradients. The two problems can be handled simultaneously if matrix elements of the linear momentum operator are obtained from the resonance integrals, since then the two operators give identical answers using wave functions derived from complete configuration interaction (CI). Numerical investigation on model systems is made of the extent of CI needed for such convergence. For strong transitions, results for polarization directions already reach their limiting values when very limited CI is performed.

Fully relativistic calculations on the potential energy surfaces of the lowest 23 states of molecular chlorine

The electronic structure and spectroscopic properties (R(e), omega(e), omega(e)x(e), beta(e), and T(e)) of the ground state and the 22 lowest excited states of chlorine molecule were studied within a four-component relativistic framework using the MOLFDIR program package. The potential energy curves of all possible 23 covalent states were calculated using relativistic complete open shell configuration interaction approach. In addition, four component multireference configuration interaction with single and double excitation calculations were performed in order to infer the effects due to dynamical correlation in vertical excitations. The calculated properties are in good agreement with the available experimental data.

Ab initio investigations of the unimolecular decay of CS+2 for internal energies lower than 10 eV

One-dimensional potential energy curves of the lowest doublet and quartet states of CS+2 and their mutual spin–orbit interactions have been calculated using the complete active space self-consistent field and internal contracted multi-reference configuration interaction methods. Between the A2Πu and the C2Σ+g states, four doublet satellite states (two 2Πu, one 2Πg and one 2Φu) in addition to the valence B2Σ+u state are found. The two 2Πu states have been already observed in the photoelectron spectra where they were associated with a long vibronic progression. Several quartet states have been also located in the 3–10 eV internal energy range. The avoided crossing regions and the conical intersections for the doublets and the quartets are located. The predissociation mechanisms of the doublet states of CS+2 leading to the first dissociation limit (S+(4Su) + CS(X1Σ+)) are also discussed. They are found to involve vibronic and/or spin–orbit interactions between the doublet and the quartet states.

Electronic structure and molecular spectroscopic constants of ScN and ScP investigated by several quantum chemistry methods

The electronic structure of the ScN and ScP molecules is a subject of controversy and turns out to be a challenging problem in quantum chemistry. We show that the ground-state electronic structure for both molecules depends critically on the choice of methods used which incorporate different ways of accounting for electron correlation. A parallel ab initio, DFT and TD-DFT study is performed for this purpose and uses sufficiently flexible basis sets able to reproduce accurate electronic structures, as well as correct spectroscopic constants. In the ab initio methodology, results have been obtained with methods such as Hartree-Fock (HF), Møller-Plesset perturbation theory (MPn), direct configuration interaction (CI), quadratic configuration interaction (QC), coupled cluster configuration interaction (CC), complete active space self-consistent field (CASSCF) and multireference configuration interaction (CIPSI) methods. In the DFT methodology, various ‘pure’ and ‘hybrid’ density functionals are used and the corresponding results are compared to sophisticated ab initio methods and to available experimental data. All the methods used show that the ground state of both molecules is 1Σ+, but two electronic structure natures, 1Σ+ open-shell or 1Σ+ closed-shell, are competitive and depend on the method employed. All the ab initio methods based on a single determinant wavefunction suffer seriously in predicting clearly the exact nature of the ground state or its correct structural and spectroscopic parameters. However, the ab initio methods based on a multiconfigurational wavefunction appear to be successful in describing correctly, within one shot, the electronic structure and the molecular spectroscopic constants. The ground state, particularly for the ScN molecule, presents an unusual electronic structure: the presence of degenerate determinants, quasidegeneracy with other states and one avoided crossing in the region around the equilibrium distances. The bonding of the ground state is a two open-shell 1Σ+ state described as a π double bond and a Σ dative bond; the real triple bond 1Σ+ state, i.e. closed-shell state, is found to lie higher in energy. The potential energy curves of the lowlying electronic states, the derived electronic structures and various molecular spectroscopic constants are presented and discussed for each method employed.