Multireference Configuration Interaction Wave Functions Research Articles

Toward a Unified Analytical Description of Internal Conversion and Intersystem Crossing in the Photodissociation of Thioformaldehyde. I. Diabatic Singlet States.

The photodissociation of thioformaldehyde is an archetypal system for the study of competition between internal conversion and intersystem crossing, which involves its two singlet states (S0 and S1) and two triplet states (T1 and T2). In order to perform accurate dynamic simulations, either quantum or quasi-classical, it is essential to construct an analytical representation for all necessary electronic structure data. In this work, a diabatic potential energy matrix (DPEM), Hd, for the two singlet states (S0 and S1) is reported. The analytical form of DPEM is symmetrized and constructed to reproduce adiabatic energies, energy gradients, and derivative couplings obtained from high-level multireference configuration interaction wave functions. The Hd is fully saturated in the molecular configuration space with a trajectory-guided point sampling approach. This Hd can provide the accurate description of the photodissociation of thioformaldehyde on its singlet states and is also a necessary part for incorporating the spin-orbit couplings into a unified diabatic framework. Preliminary quasi-classical trajectory simulations show that a roaming mechanism also exists in the molecular dissociation channel of thioformaldehyde.

New analysis of the [formula omitted]C[formula omitted]O[formula omitted] (B[formula omitted] - X[formula omitted]) system: Spin-orbit and spin-rotation coupling of the X[formula omitted] state

In the present work a new experimental and theoretical analysis of the B2Σ+→ X2Σ+ system of the molecular ion 12C16O+ is performed. New transitions regarding the vibrational levels v′=4 of the B2Σ+ electronic state and the vibrational level v″=7 of the electronic state X2Σ+ have been recorded. For rationalising the experimental observations, molecular structure calculations were carried out and, from them, a detailed investigation about the fine structure of rotational levels of the X2Σ+ could be performed. For such, the spin-rotational constant, γ, is characterised through the Δg⊥ calculation, the perpendicular component of the electronic g-tensor, in combination with Curl’s relation. At equilibrium geometry, the present Δg⊥ is computed using the multireference configuration interaction wavefunction to be −2430 ppm in agreement with the experimental one [−2344 ppm]. The R-dependence of the g-tensor has been explored in order to estimate the theoretical γv (v=0–7). In addition, the importance of the lowest Π states in this kind of calculation is widely discussed. A comparison between experiment and theory is presented, validating our findings and the methodology employed in our analysis.

Theoretical study of the spin-orbit coupling in the [formula omitted] state of NO

Theoretical spin–orbit coupling (SOC) constants, Av, have been computed for the sixteen lowest vibrational levels of the X2Π ground state. For such, the SOC matrix elements of the radical NO as a function of internuclear distances are investigated by using the Breit-Pauli operator (H^SO) and internally contracted multireference configuration interaction (icMRCI) wavefunctions. Our theoretical results are in excellent agreement with the recent experimental Av values. This analysis has been extended for the A2Σ+ state to study spin–orbit coupling effects in the γ system besides its corresponding potential energy curve.

Magnetic exchange interactions in monolayer CrI3 from many-body wavefunction calculations

The marked interplay between the crystalline, electronic, and magnetic structure of atomically thin magnets has been regarded as the key feature for designing next-generation magneto-optoelectronic devices. In this respect, a detailed understanding of the microscopic interactions underlying the magnetic response of these crystals is of primary importance. Here, we combine model Hamiltonians with multireference configuration interaction wavefunctions to accurately determine the strength of the spin couplings in the prototypical single-layer magnet CrI3. Our calculations identify the (ferromagnetic) Heisenberg exchange interaction J = −1.44 meV as the dominant term, being the inter-site magnetic anisotropies substantially weaker. We also find that single-layer CrI3 features an out-of-plane easy axis ensuing from a single-ion anisotropy A = −0.10 meV, and predict g-tensor in-plane components and out-of-plane component g zz = 1.92. In addition, we assess the performance of a dozen widely used density functionals against our accurate correlated wavefunctions calculations and available experimental data, thereby establishing reference results for future first-principles investigations. Overall, our findings offer a firm theoretical ground to recent experimental observations.

On the nonadiabatic collisional quenching of OH(A) by H2: a four coupled quasi-diabatic state description.

A four-state diabatic potential energy matrix (DPEM), Hd, for the description of the nonadiabatic quenching of OH(A2Σ+) by collisions with H2 is reported. The DPEM is constructed as a fit to adiabatic energies, energy gradients, and derivative couplings obtained exclusively from multireference configuration interaction wave functions. A four-adiabatic-electronic-state representation is used in order to describe all energetically accessible regions of the nuclear coordinate space. Partial permutation-inversion symmetry is incorporated into the representation. The fit is based on electronic structure data at 42 882 points, described by over 1.6 million least squares equations with a root mean square (mean unsigned) error of 178(83) cm-1. Comparison of ab initio and Hd determined minima, saddle points, and energy minimized points on C2v, Cs, C∞v, and C1 (noncoplanar) portions of two conical intersection seams are used to establish the accuracy of the Hd.

Analytic non-adiabatic derivative coupling terms for spin-orbit MRCI wavefunctions. II. Derivative coupling terms and coupling angle for KHeA2Π1/2⇔KHeB2Σ1/2.

A method for calculating the analytic nonadiabatic derivative coupling terms (DCTs) for spin-orbit multi-reference configuration interaction wavefunctions is reviewed. The results of a sample calculation using a Stuttgart basis for KHe are presented. Additionally, the DCTs are compared with a simple calculation based on the Nikitin's 3 × 3 description of the coupling between the Σ and Π surfaces, as well as a method based on Werner's analysis of configuration interaction coefficients. The nonadiabatic coupling angle calculated by integrating the radial analytic DCTs using these different techniques matches extremely well. The resultant nonadiabatic energy surfaces for KHe are presented.

Potential Energy Curves for Formation of the CH2O2 Criegee Intermediate on the 3CH2 + 3O2 Singlet and Triplet Potential Energy Surfaces.

The potential energy curves (PECs) for the interaction of 3CH2 with 3O2 in singlet and triplet potential energy surfaces (PESs) leading to singlet and triplet Criegee intermediates (CH2OO) are studied using electronic structure calculations. The bonding mechanism is interpreted by analyzing the ground state multireference configuration interaction (MRCI) wave function of the reacting species and at all points along the PES. The interaction of 3CH2 with 3O2 on the singlet surface leads to a flat long-range attractive PEC lacking any maxima or minima along the curve. The triplet surface stems into a maximum along the curve resulting in a transition state with an energy barrier of 5.3 kcal/mol at CASSCF(4,4)/cc-pVTZ level. The resulting 3CH2OO is less stable than the 1CH2OO. In this study, the biradical character (β) is used as a measure to understand the difference in the topology of the singlet and triplet PECs and the relation of the biradical nature of the species with their structures. The 3CH2OO has a larger biradical character than 1CH2OO, and because of the larger bond order of 1CH2OO, the C-O covalent bond becomes harder to break, thereby stabilizing 1CH2OO. Thus, this study provides insights into the shape of the PEC obtained from the reaction between 3CH2 and 3O2 in terms of their bonding nature and from the shape of the curves, the temperature dependence or independence of the rate of the reaction is discussed.

Vibronic and spin-orbit coupling effects in the absorption spectra of pyrazine: A quantum chemical approach

Derivatives of dipole transition moments between spin?orbit coupled (SOC) multireference configuration interaction wave functions have been used in conjunction with vibrational frequencies from density functional theories to compute vibronic S1?S0 (11B3u11Ag ) and T1?S0 (13B3u?11Ag) absorption spectra in Herzberg?Teller approximation. The experimentally known spectra are well reproduced. The calculations reveal unexpectedly small spin?orbit couplings between the 13B3u (3n?*) state and nearby optically bright 1B2u (1??*) states, thus explaining the absence of the 1b1g10 (v10a10 ) fundamental in the vibrational fine-structure of the T1?S0 transition. Adiabatically, two triplet states are found below the S1 state. The out-of-plane distorted T2 minimum results from a pseudo Jahn?Teller interaction between two 3??* states of B1u and B2u symmetry. At the D2h-symmetric S0 and S1 minimum geometries, the latter states are located well above S1. The S1 and T2 potentials intersect at geometries far away from the Franck?Condon region. This explains the apparently contradictory results that the linewidth in the higher energy regime above the T1?S0 origin suddenly broadens while no trace of a second triplet state, located energetically below the S1 origin, could be identified in phosphorescence excitation spectra of the ultracold isolated pyrazine molecule.

Carbon monoxide activation by atomic thorium: ground and excited state reaction pathways.

Multi-reference configuration interaction (MRCI) and single reference coupled cluster calculations are performed for the ThCO and OThC isomers. Scalar and spin-orbit relativistic effects are considered through a relativistic pseudopotential and the coupling of MRCI wavefunctions via the Breit-Pauli spin-orbit Hamiltonian. Optimized geometries, excitation energies, and vibrational frequencies are reported for both isomers. Full potential energy profiles are constructed for the Th+CO reaction and the conversion of the produced ThCO to OThC. Linear ThCO was found to be more stable than the highly ionic bent OThC system by about 4 kcal mol-1. The interconversion barrier is estimated to be around 30 kcal mol-1. Our results are in agreement with earlier experimental data for the two isomers. The lowest lying states of Th do not populate f-orbitals and resemble the electronic structure of Ti. Therefore, the ability of the two atoms to activate the C[triple bond, length as m-dash]O bond is compared. OTiC is found to be about 40 kcal mol-1 less stable than TiCO revealing the efficiency of Th and possibly other f-block elements to activate multiple chemical bonds as opposed to d-block metals.

Theoretical calculations of rotationally inelastic collisions of He with NaK(A (1)Σ(+)): Transfer of population, orientation, and alignment.

We have performed extensive calculations to investigate thermal energy, rotationally inelastic collisions of NaK (A(1)Σ(+)) with He. We determined a potential energy surface using a multi-reference configuration interaction wave function as implemented by the GAMESS electronic structure code, and we have performed coupled channel scattering calculations using the Arthurs and Dalgarno formalism. We also calculate the Grawert coefficients B(λ)(j, j') for each j → j' transition. These coefficients are used to determine the probability that orientation and alignment are preserved in collisions taking place in a cell environment. The calculations include all rotational levels with j or j' between 0 and 50, and total (translational and rotational) energies in the range 0.0002-0.0025 a.u. (∼44-550 cm(-1)). The calculated cross sections for transitions with even values of Δj tend to be larger than those for transitions with odd Δj, in agreement with the recent experiments of Wolfe et al. (J. Chem. Phys. 134, 174301 (2011)). The calculations of the energy dependence of the cross sections and the calculations of the fraction of orientation and alignment preserved in collisions also exhibit distinctly different behaviors for odd and even values of Δj. The calculations also indicate that the average fraction of orientation or alignment preserved in a transition becomes larger as j increases. We interpret this behavior using the semiclassical model of Derouard, which also leads to a simple way of visualizing the distribution of the angles between the initial and final angular momentum vectors j and j'. Finally, we compare the exact quantum results for j → j' transitions with results based on the simpler, energy sudden approximation. That approximation is shown to be quite accurate.

Intersystem-crossing and phosphorescence rates in fac-Ir(III)(ppy)3: a theoretical study involving multi-reference configuration interaction wavefunctions.

We have employed combined density functional theory and multi-reference configuration interaction methods including spin-orbit coupling (SOC) effects to investigate the photophysics of the green phosphorescent emitter fac-tris-(2-phenylpyridine)iridium (fac-Ir(ppy)3). A critical evaluation of our quantum chemical approaches shows that a perturbational treatment of SOC is the method of choice for computing the UV/Vis spectrum of this heavy transition metal complex while multi-reference spin-orbit configuration interaction is preferable for calculating the phosphorescence rates. The particular choice of the spin-orbit interaction operator is found to be of minor importance. Intersystem crossing (ISC) rates have been determined by Fourier transformation of the time correlation function of the transition including Dushinsky rotations. In the electronic ground state, fac-Ir(ppy)3 is C3 symmetric. The calculated UV/Vis spectrum is in excellent agreement with experiment. The effect of SOC is particularly pronounced for the metal-to-ligand charge transfer (MLCT) band in the visible region of the absorption spectrum which does not only extend its spectral onset towards longer wavelengths but also experiences a blue shift of its maximum. Pseudo-Jahn-Teller interaction leads to asymmetric coordinate displacements in the lowest MLCT states. Substantial electronic SOC and a small energy gap make ISC an ultrafast process in fac-Ir(ppy)3. For the S1↝T1 non-radiative transition, we compute a rate constant of kISC = 6.9 × 10(12) s(-1) which exceeds the rate constant of radiative decay to the electronic ground state by more than six orders of magnitude, in agreement with the experimental observation of a subpicosecond ISC process and a triplet quantum yield close to unity. As a consequence of the geometric distortion in the T1 state, the T1 → S0 transition densities are localized on one of the phenylpyridyl moieties. In our best quantum chemical model, we obtain phosphorescence decay times of 264 μs, 13 μs, and 0.9 μs, respectively, for the T1,I, T1,II, and T1,III fine-structure levels in dichloromethane (DCM) solution. In addition to reproducing the correct orders of magnitude for the individual phosphorescence emission probabilities, our theoretical study gives insight into the underlying mechanisms. In terms of intensity borrowing from spin-allowed transitions, the low emission probability of the T1,I substate is caused by the mutual cancellation of contributions from several singlet states to the total transition dipole moment. Their contributions do not cancel but add up in case of the much faster T1,III → S0 emission while the T1,II → S0 emission is dominated by intensity borrowing from a single spin-allowed process, i.e., the S2 → S0 transition.

Ab initio study on the low-lying excited states of gas-phase PH+ cation including spin–orbit coupling

Ab initio calculations have been performed on the low-lying excited and ground states of PH+. The potential energy curves (PECs) of the Λ–S states were calculated with multi-reference configuration interaction (MRCI) method along with the basis sets at 5-ξ level. In order to improve the PECs, the Davidson(+Q) correction and the Scalar relativistic effect are included. The corresponding spectroscopic constants were determined and good agreements with the available measurement were found. The interactions of the A2Δ–4Π and 12Σ+–4Π by the spin–orbit coupling (SOC) effect were well described by the spin–orbit matrix elements. The SOC effect makes the original 8 Λ–S states split into 15Ω states. The Ω=1/2 state generated from the X2Π state is confirmed to the ground Ω state. And the SOC splitting for the X2Π is calculated to be 294cm−1. The SOC effect has large effect on the PECs of the A2Δ and 12Σ+ states, leading to much more shallow potential wells as well as potential barriers. The analysis of the wavefunction for the Ω states shows that the strong spin–orbit interaction exists near the crossing points of the PECs for the Λ–S states. The transition dipole moments (TDMs) of transitions A2Δ–X2Π and 12Σ−–X2Π are evaluated with the MRCI wavefunction. Based on the TDMs along with the calculated Franck–Condon factors, the radiative lifetimes for the selected vibrational levels of A2Δ and 12Σ− states are predicted at the microseconds (μs). Good agreement with the measurement shows that the lowest vibrational level for A2Δ state is almost uninfluenced by the perturbation via the SOC effect.

Ab initio study of the RbSr electronic structure: potential energy curves, transition dipole moments, and permanent electric dipole moments.

Excited states and the ground state of the diatomic molecule RbSr were calculated by post Hartree-Fock molecular orbital theory up to 22000 cm(-1). We applied a multireference configuration interaction calculation based on multiconfigurational self-consistent field wave functions. Both methods made use of effective core potentials and core polarization potentials. Potential energy curves, transition dipole moments, and permanent electric dipole moments were determined for RbSr and could be compared with other recent calculations. We found a good agreement with experimental spectra, which have been obtained recently by helium nanodroplet isolation spectroscopy. For the lowest two asymptotes (Rb (5s (2)S) + Sr (5s4d (3)P°) and Rb (5p (2)P°) + Sr (5s(2) (1)S)), which exhibit a significant spin-orbit coupling, we included relativistic effects by two approaches, one applying the Breit-Pauli Hamiltonian to the multireference configuration interaction wave functions, the other combining a spin-orbit Hamiltonian and multireference configuration interaction potential energy curves. Using the results for the relativistic potential energy curves that correspond to the Rb (5s (2)S) + Sr (5s4d (3)P°) asymptote, we have simulated dispersed fluorescence spectra as they were recently measured in our lab. The comparison with experimental data allows to benchmark both methods and demonstrate that spin-orbit coupling has to be included for the lowest states of RbSr.

Theoretical description of electronically excited vinylidene up to 10 eV: first high level ab initio study of singlet valence and Rydberg states.

The first quantitative description of the Rydberg and valence singlet electronic states of vinylidene lying in the 0-10 eV region is performed by using large scale ab initio calculations. A deep analysis of Rydberg-valence interactions has been achieved thanks to the comprehensive information contained in the accurate Multi-Reference Configuration Interaction wavefunctions and an original population analysis highlighting the respective role played by orbital and state mixing in such interactions. The present theoretical approach is thus adequate for dealing with larger than diatomic Rydberg systems. The nine lowest singlet valence states have been optimized. Among them, some are involved in strong Rydberg-valence interactions in the region of the Rydberg state equilibrium geometry. The Rydberg states of vinylidene present a great similarity with the acetylene isomer, concerning their quantum defects and Rydberg molecular orbital character. As in acetylene, strong s-d mixing is revealed in the n = 3 s-d supercomplex. Nevertheless, unlike in acetylene, the close-energy of the two vinylidene ionic cores (2)A1 and (2)B1 results into two overlapped Rydberg series. These Rydberg series exhibit local perturbations when an accidental degeneracy occurs between them and results in avoided crossings. In addition, some Δl = 1 (s-p and p-d) mixings arise for some Rydberg states and are rationalized in term of electrostatic interaction from the electric dipole moment of the ionic core. The strongest dipole moment of the (2)B1 cationic state also stabilizes the lowest members of the n = 3 Rydberg series converging to this excited state, as compared to the adjacent series converging toward the (2)A1 ionic ground state. The overall energies of vinylidene Rydberg states lie above their acetylene counterpart. Finally, predictions for optical transitions in singlet vinylidene are suggested for further experimental spectroscopic characterization of vinylidene.

Potential energy curves for the ground and low-lying excited states of CuAg.

The ground and low-lying excited states of heteronuclear diatomic CuAg are examined by multi-reference configuration interaction (MRCI) method. Relativistic effects were treated and probed in two steps. Scalar terms were considered using the spin-free DKH Hamiltonian as a priori and spin-orbit coupling was calculated perturbatively via the spin-orbit terms of the Breit-Pauli Hamiltonian based on MRCI wavefunctions. Potential energy curves of the spin-free states and their corresponding Ω components correlating with the separated atom limits (2)S(Cu) + (2)S(Ag) and (2)D(Cu) + (2)S(Ag) are obtained. The results are in fine agreement with the experimental measurements and tentative conclusions for the ion-pair B0(+) state are confirmed by our theoretical calculations. Illustrative results are presented to reveal the relative importance and magnitude of the scalar and spin-orbit effects on the spectroscopic properties of this molecule. Time dependent density functional theory calculations, using the LDA, BLYP, B3LYP, and SAOP functionals have been carried out for CuAg and the accuracy of TD-DFT has been compared with ab initio results.

Potential energy surfaces for the C2[formula omitted]+H[formula omitted] system. Application: Rotational dynamics of C2[formula omitted] on the ground adiabatic and diabatic [formula omitted] surfaces

Adiabatic and diabatic potential energy surfaces (PESs) of the ground and the first excited electronic states for the interaction of C2(X1Σg+,a3Πu)+H(2S) system have been computed from the ab initio multi-reference configuration interaction wave functions including Davidson correction (MRCI+Q), using the augmented correlation-consistent valence quadruple-zeta (aug-cc-pVQZ) basis set of Dunning. Mixing angle and coupling potential have been calculated for all selected ab initio geometries. The C2 bond length was fixed at the experimental equilibrium distance re=2.348bohr of C2(X1Σg+) state. Quantum mechanical coupled states rotational dynamics application has been done on the ground adiabatic and diabatic PESs.

Study of electron capture and ionization in proton collisions with N2 using ab initio methods

Electron capture cross sections in collisions of protons with the nitrogen molecule are obtained with two semiclassical ab initio methods: one uses multireference configuration interaction wavefunctions while the other is based on monoelectronic wavefunctions and the independent particle approximation. The accuracy and usefulness of this last, simplified, approach is discussed in view of its applicability to study larger systems.

On the Bonding Nature of Ozone (O3) and Its Sulfur-Substituted Analogues SO2, OS2, and S3: Correlation between Their Biradical Character and Molecular Properties

We investigate the bonding mechanism in ozone (O3) and its sulfur-substituted analogues, SO2, OS2, and S3. By analyzing their ground-state multireference configuration interaction wave functions, we demonstrate that the bonding in these systems can be represented as a mixture of a closed-shell structure with one and a half bonds between the central and terminal atoms and an open-shell structure with a single bond and two lone electrons on each terminal atom (biradical). The biradical character (β) further emerges as a simple measure of the relative contribution of those two classical Lewis structures emanating from the interpretation of the respective wave functions. Our analysis yields a biradical character of 3.5% for OSO, 4.4% for SSO, 11% for S3, 18% for O3, 26% for SOO, and 35% for SOS. The size/electronegativity of the end atoms relative to the central one is the prevalent factor for determining the magnitude of β: smaller and more electronegative central atoms better accommodate a pair of electrons facilitating the localization of the remaining two lone π-electrons on each of the end atoms, therefore increasing the weight of the second picture in the mixed bonding scenario (larger β). The proposed mixture of these two bonding scenarios allows for the definition of the bond order of the covalent bonds being (3-β)/2, and this accounts for the different O-O, S-S, or S-O bond lengths in the triatomic series. The biradical character was furthermore found to be a useful concept for explaining several structural and energetic trends in the series: larger values of β mark a smaller singlet-triplet splitting, closer bond lengths in the ground (1)A' and the first excited (3)A' states, and larger bond dissociation and atomization energies in the ground state. The latter explains the relative energy difference between the OSS/SOS and OOS/OSO isomers due to their different β values.

Fitting coupled potential energy surfaces for large systems: Method and construction of a 3-state representation for phenol photodissociation in the full 33 internal degrees of freedom using multireference configuration interaction determined data

A recently reported algorithm for representing adiabatic states coupled by conical intersections using a quasi-diabatic state Hamiltonian in four and five atom systems is extended to treat nonadiabatic processes in considerably larger molecules. The method treats all internal degrees of freedom and uses electronic structure data from ab initio multireference configuration interaction wave functions with nuclear configuration selection based on quasi-classical surface hopping trajectories. The method is shown here to be able to treat ∼30 internal degrees of freedom including dissociative and large amplitude internal motion. Two procedures are introduced which are essential to the algorithm, a null space projector which removes basis functions from the fitting process until they are needed and a partial diagonalization technique which allows for automated, but accurate, treatment of the vicinity of extended seams of conical intersections of two or more states. These procedures are described in detail. The method is illustrated using the photodissociaton of phenol, C6H5OH(X̃(1)A(')) + hv → C6H5OH(Ã(1)A('), B̃(1)A('')) → C6H5O(X̃(2)B1, Ã(2)B2) + H as a test case. Ab initio electronic structure data for the 1,2,3(1)A states of phenol, which are coupled by conical intersections, are obtained from multireference first order configuration interaction wave functions. The design of bases to simultaneously treat large amplitude motion and dissociation is described, as is the ability of the fitting procedure to smooth the irregularities in the electronic energies attributable to the orbital changes that are inherent to nonadiabatic processes.

Analysis of and remedies for unphysical ground states of the multireference averaged coupled-pair functional

A Multireference Configuration Interaction (MRCI) wavefunction includes both static and dynamic electron correlation. MRCI's well-known flaw, a lack of size extensivity, can be ameliorated with the Multireference Averaged Coupled-Pair Functional (MRACPF). However, the original MRACPF is frequently unstable, sometimes producing unphysical results. The more Multireference Averaged Quadratic Coupled-Cluster and MRACPF2 functionals also occasionally exhibit unphysical behavior. We find that these instabilities are avoided crossings with unphysical solutions to the MRACPF equations. We present two approaches to avoid the undesirable unphysical solutions.