Self-consistent Field Level Research Articles

Theoretical spin-orbit laser cooling for AlZn molecule.

A spin-orbit coupling electronic structure study of the AlZn molecule is conducted to investigate the molecular properties of the low-lying electronic states and their feasibility toward direct laser cooling. This study uses the complete active-space self-consistent field level of theory, followed by the multireference configuration interaction method with Davidson correction (+Q). The potential energy and dipole moment curves and the spectroscopic constants are computed for the low-lying doublet and quartet electronic states in the 2S+1Λ± and Ω(±) representations. The transition dipole moments, the Franck-Condon factors, the Einstein coefficient, the radiative lifetimes, the vibrational branching ratio, and the slowing distance are determined between the lowest spin-orbit bound electronic states. These results show that the molecule AlZn has a high potential for laser cooling through the X2Π1/2 → (2)2Π1/2 transition by utilizing four lasers at a wavelength in the ultraviolet region, reaching a sub-microkelvin temperature limit.

Fundamental Invariant Neural Network (FI-NN) Potential Energy Surface for the OH + CH3OH Reaction with Analytical Forces.

The hydrogen abstraction reaction of OH + CH3OH plays a great role in combustion and atmospheric and interstellar chemistry and has been extensively studied theoretically and experimentally. Theoretically, the numerical gradients with respect to the Cartesian coordinates of atoms in molecular simulations on our recent potential energy surface (PES) for the title reaction trained using the permutationally invariant polynomial neural network (PIP-NN) approach hinder the extensive calculation because of the unaffordable computation cost. To address this issue, we in this work report a new full-dimensional accurate analytical PES for the title reaction using the fundamental invariant neural network (FI-NN) approach based on 140,192 points of the quality UCCSD(T)-F12a/AVTZ. Besides, the spin-orbit (SO) corrections of OH in the entrance channel were determined at the level of complete active space self-consistent field with the AVTZ basis set. As a compromise between computational cost and efficiency, the Δ-machine learning approach was employed to construct the SO-corrected PES. Based on this new FI-NN PES with analytical forces, thermal rate coefficients and various dynamic properties, including the integral cross sections, the differential cross sections, and the product energy partitioning, were determined by running a total of 5.5 million trajectories. The use of analytical gradients of the FI-NN PES accelerated simulations and about 99% of computation cost was saved, compared to that for the PIP-NN PES with numerical gradients. Such a significant acceleration is achieved mainly by replacing PIPs with FIs.

Calculated Aqueous Reduction Potentials of Neutral and Anionic Halogen Diatomic Molecules.

The free energy of hydration, aqueous, and gas phase electron affinity and aqueous reduction potentials of F2, Cl2, Br2, I2, ClF, BrF, IF, BrCl, ICl, IBr, and their corresponding anions were calculated using an electronic structure approach previously developed for these properties for X• and XO•, where X is a halogen which yielded excellent results. The gas phase electron affinities were calculated at the Feller-Peterson-Dixon level based on complete basis set extrapolation of CCSD(T) results with additional corrections. The agreement with the available experimental data is excellent, and the calculations provide a complete set of reliable electron affinities for these diatomic halogens. The hybrid solvation approach uses single point implicit solvation calculations on gas phase optimized clusters with explicit solvent molecules. The gas phase energy calculations were performed using MP2 and CCSD(T)-F12b for tetramer clusters (four explicit waters) and MP2 for octamer clusters (eight explicit waters). The final redox potentials were obtained at the MP2/aug-cc-pVTZ (aT) with a self-consistent reaction field (SMD) level using the octamer clusters. The aqueous reduction potentials of the neutral diatomic halogens are predicted within 0.06 V of the experiment for diatomic neutrals. The same agreement of 0.06 V is predicted for the redox potential resulting from dissociation electron attachment of the diatomic halogen anions. The current work extends reduction potentials for multiple redox couples for which no experimental data is available, for example, those containing iodine and the interhalogen anions. F2•- is predicted to dissociate for its lowest energy structure in both the tetramer and octamer clusters to form solvated F-, HF, and OH•.

Theoretical Insights into the Vibrational Structure of Carbon Dioxide Rare-Gas Complexes.

Two new flexible-monomer two-body ab initio potential energy surfaces (PESs) for the neon and krypton van der Waals complexes with carbon dioxide were developed, extending our previous work on the Ar-CO2 molecule. The accuracy of the PESs was validated by their agreement with the vibrational spectrum of the rare-gas complexes. The intermolecular and intramolecular vibrational excitation energies were computed at the vibrational self-consistent field and vibrational configuration interaction levels of theory. Overall, the agreement between theory and experiment is excellent throughout the vibrational spectra. The observed slight splitting of the bending modes, resulting from their nondegeneracy in the complexes, is confirmed by our computations, and the results qualitatively agree with the experiment. The splitting increases with increasing polarizability of the rare-gas atom. Additionally, we explain a discrepancy in the mode assignment in the intermolecular region of the neon complex with our VCI character assignment.

Theoretical and computational study of benzenium and toluenium isomers.

Four methods of computational quantum chemistry are used in a study of hyperconjugation in protonated aromatic molecules. Benzene, benzenium, toluene, and four isomeric forms of toluenium are examined using the self-consistent field level of theory followed by configuration interaction and coupled cluster calculations, as well as density functional theory. Results for proton affinities, geometric parameters, atomic populations, dipole moments, and polarizabilities are reported. The calculated results are in good agreement with previous computational studies and with experimental data. The presence of hyperconjugation is evident from the shortened carbon-carbon bond lengths in the aromatic ring and concomitant changes in dipole moments and polarizabilities. The proton affinities of benzene and toluene compare well with experimental values. The examination of all of the toluenium isomers reveals that the position of the methyl group has a minor impact on the strength of hyperconjugation, although the most stable isomer is found to be the para form. Mulliken population analyses indicate that the addition of a proton contributes to aromatic hyperconjugation and increases the strength of π-bonds at the expense of σ-bonds.

Theoretical spectroscopy for unraveling the intensity mechanism of the optical and photoluminescent spectra of chiral Re(I) transition metal complexes.

In this work, we present a computational study that is able to predict the optical absorption and photoluminescent properties of the chiral Re(I) family of complexes [fac-ReX(CO)3L], where X is either Cl or I and L is N-heterocyclic carbene extended with π-conjugated [5]-helicenic unit. The computational strategy is based on carefully calibrated time dependent density functional theory calculations and operates in conjunction with an excited state dynamics approach to treat in addition to absorption (ABS) and photoluminescence (PL), electronic circular dichroism (ECD), and circularly polarized luminescence (CPL) spectroscopies, respectively. The employed computational approach provides, an addition, access to the computation of phosphorescence rates in terms of radiative and non-radiative relaxation processes. The chosen molecules consist of representative examples of non-helicenic (NHC) and helicenic diastereomers. The agreement between theoretical and experimental spectra, including absorption (ABS, ECD) and emission (PL, CPL), is excellent, validating a quantitative interpretation of the spectral features on the basis of natural transition orbitals and TheoDore analyses. It is demonstrated that across the set of studied Re(I) diastereomers, the emission process in the case of NHC diastereomers is metal to ligand charge transfer in nature and is dominated by the easy-axis anisotropy of the emissive excited multiplet. On the contrary, in the cases of the helicenic diastereomers, the emission process is intra ligand charge transfer in nature and is dominated by the respective easy-plane anisotropy of the emissive excited multiplet. This affects remarkably the photoluminescent properties of the molecules in terms of PL and CPL spectral band shapes, spin-vibronic coupling, relaxation times, and the respective quantum yields. Spin-vibronic coupling effects are investigated at the level of the state-average complete active space self-consistent field in conjunction with quasi-degenerate second order perturbation theory. It is in fact demonstrated that a spin-vibronic coupling mechanism controls the observed photophysics of this class of Re(I) complexes.

Ab Initio Molecular Cavity Quantum Electrodynamics Simulations Using Machine Learning Models.

We present a mixed quantum-classical simulation of polariton dynamics for molecule-cavity hybrid systems. In particular, we treat the coupled electronic-photonic degrees of freedom (DOFs) as the quantum subsystem and the nuclear DOFs as the classical subsystem and use the trajectory surface hopping approach to simulate non-adiabatic dynamics among the polariton states due to the coupled motion of nuclei. We use the accurate nuclear gradient expression derived from the Pauli-Fierz quantum electrodynamics Hamiltonian without making further approximations. The energies, gradients, and derivative couplings of the molecular systems are obtained from the on-the-fly simulations at the level of complete active space self-consistent field (CASSCF), which are used to compute the polariton energies and nuclear gradients. The derivatives of dipoles are also necessary ingredients in the polariton nuclear gradient expression but are often not readily available in electronic structure methods. To address this challenge, we use a machine learning model with the Kernel ridge regression method to construct the dipoles and further obtain their derivatives, at the same level as the CASSCF theory. The cavity loss process is modeled with the Lindblad jump superoperator on the reduced density of the electronic-photonic quantum subsystem. We investigate the azomethane molecule and its photoinduced isomerization dynamics inside the cavity. Our results show the accuracy of the machine-learned dipoles and their usage in simulating polariton dynamics. Our polariton dynamics results also demonstrate the isomerization reaction of azomethane can be effectively tuned by coupling to an optical cavity and by changing the light-matter coupling strength and the cavity loss rate.

Excited states of ortho-nitrobenzaldehyde as a challenging case for single- and multi-reference electronic structure theory.

We present a large set of vertical excitation calculations for the ortho-nitrobenzaldehyde (oNBA) molecule, which exhibits a very challenging excited-state electronic structure like other nitroaromatic compounds. The single-reference methods produce mostly consistent results up to about 5.5eV. By contrast, the CAS second-order perturbation theory (CASPT2) results depend sensitively on the employed parameters. At the CAS self-consistent field level, the energies of the bright states are strongly overestimated while doubly excited states appear too low and mix with these states. This mixing hampers the CASPT2 step, leading to inconsistent results. Only by increasing the number of states in the state-averaging step to about 40-to cover all bright states embedded in the double excitations-and employing extended multistate CASPT2 couldCASPT2 results consistent with experimentbeobtained. We assign the four bands in the molecule's spectrum: The weakest band at 3.7eV arises from the states, the second one at 4.4eV from the ( ) state, the shoulder at 5.2eV from the ( ) state, and the maximum at 5.7eV from the ( ) states. We also highlight the importance of modern wave function analysis techniques in elucidating the absorption spectrum of challenging molecules.

Excited state calculations using variational quantum eigensolver with spin-restricted ansätze and automatically-adjusted constraints

The ground and excited state calculations at key geometries, such as the Frank–Condon (FC) and the conical intersection (CI) geometries, are essential for understanding photophysical properties. To compute these geometries on noisy intermediate-scale quantum devices, we proposed a strategy that combined a chemistry-inspired spin-restricted ansatz and a new excited state calculation method called the variational quantum eigensolver under automatically-adjusted constraints (VQE/AC). Unlike the conventional excited state calculation method, called the variational quantum deflation, the VQE/AC does not require the pre-determination of constraint weights and has the potential to describe smooth potential energy surfaces. To validate this strategy, we performed the excited state calculations at the FC and CI geometries of ethylene and phenol blue at the complete active space self-consistent field (CASSCF) level of theory, and found that the energy errors were at most 2 kcal mol−1 even on the ibm_kawasaki device.

On the photorelease of nitric oxide by nitrobenzene derivatives: A CASPT2//CASSCF model.

Nitroaromatic compounds can photorelease nitric oxide after UV absorption. The efficiency of the photoreaction depends on the molecular structure, and two features have been pointed out as particularly important for the yield of the process: the presence of methyl groups at the ortho position with respect to the nitro group and the degree of conjugation of the molecule. In this paper, we provide a theoretical characterization at the CASPT2//CASSCF (complete active space second-order perturbation theory//complete active space self-consistent field) level of theory of the photorelease of NO for four molecules derived from nitrobenzene through the addition of ortho methyl groups and/or the elongation of the conjugation. Our previously described mechanism obtained for the photorelease of NO in nitrobenzene has been adopted as a model for the process. According to this model, the process proceeds through a reactive singlet-triplet crossing (STC) region that the system can reach from the triplet 3(πOπ*) minimum. The energy barrier that must be surmounted in order to populate the reactive STC can be associated with the efficiency of the photoreaction. Here, the obtained results display clear differences in the efficiency of the photoreaction in the studied systems and can be correlated with experimental results. Thus, the model proves its ability to highlight the differences in the photoreaction efficiency for the nitroaromatic compounds studied here.

Tightening the Screws: The Importance of Tight d Functions in Coupled-Cluster Calculations up to the CCSDT(Q) Level

It is well established that the basis set convergence of the correlation consistent (cc-pVnZ) basis sets depends on the presence of high-exponent "tight" d functions in the basis set for second-row atoms. The effect has been linked to low-lying 3d virtual orbitals approaching the valence shell. However, since most of this effect is captured at the self-consistent field level, the effect of tight d functions in high-level coupled-cluster calculations has not been extensively studied. Here, we construct an extensive data set of 45 second-row species to examine the effect of tight d functions in CCSD, CCSD(T), CCSDT, and CCSDT(Q) calculations in conjunction with basis sets of up to sextuple-ζ quality. The selected set of molecules covers the gamut from systems where the tight d functions play a relatively minor role (e.g., SiH, SH, SiF, PF3, HOCl, Cl2, and C2Cl2) to challenging systems containing a central second-row atom bonded to many oxygen or fluorine atoms (e.g., PF5, SF6, SO3, ClO3, and HClO4) and systems containing many second-row atoms (e.g., P4, S4, CCl4, and C2Cl6). In conjunction with the cc-pVDZ basis set, we find chemically significant contributions to the total atomization energies (TAEs) of up to ∼2 kcal/mol at the CCSD level, ∼1 kcal/mol at the (T) level, and contributions of up to ∼0.1 kcal/mol for the post-CCSD(T) components. The effects of the tight d functions are diminished with the size of the basis set; however, they are still chemically significant at the CCSD and (T) levels. For example, with the cc-pVTZ basis set, we obtain contributions to the TAEs of up to ∼1.5 and ∼0.3 kcal/mol at the CCSD and (T) levels, respectively, and with the cc-pVQZ basis set, we obtain contributions of up to ∼1.0 and ∼0.2 kcal/mol at the CCSD and (T) levels, respectively. We also find that a simple natural bond orbital population analysis of the 3d orbitals of the second-row atom provides a useful a priori indicator of the magnitude of the effect of tight d functions on post-CCSD(T) contribution to the TAEs in oxide and fluoride systems. These results are particularly important in the context of high-level composite ab initio methods capable of confident benchmark accuracy in thermochemical predictions.

Spin–Orbit Couplings for Nonadiabatic Molecular Dynamics at the ΔSCF Level

A procedure for the calculation of spin-orbit coupling (SOC) at the delta self-consistent field (ΔSCF) level of theory is presented. Singlet and triplet excited electronic states obtained with the ΔSCF method are expanded into a linear combination of singly excited Slater determinants composed of ground electronic state Kohn-Sham orbitals. This alleviates the nonorthogonality between excited and ground electronic states and introduces a framework, similar to the auxiliary wave function at the time-dependent density functional theory (TD-DFT) level, for the calculation of observables. The ΔSCF observables of the formaldehyde system were compared to reference TD-DFT values. Our procedure gives all components (energies, gradients, nonadiabatic couplings, and SOC terms) at the ΔSCF level of theory for conducting efficient, full-atomistic nonadiabatic molecular dynamics with intersystem crossing, particularly in condensed phase systems.

Odd-Number Cyclo[n]Carbons Sustaining Alternating Aromaticity.

Cyclo[n]carbons (n = 5, 7, 9, ..., 29) composed from an odd number of carbon atoms are studied computationally at density functional theory (DFT) and ab initio complete active space self-consistent field (CASSCF) levels of theory to get insight into their electronic structure and aromaticity. DFT calculations predict a strongly delocalized carbene structure of the cyclo[n]carbons and an aromatic character for all of them. In contrast, calculations at the CASSCF level yield geometrically bent and electronically localized carbene structures leading to an alternating double aromaticity of the odd-number cyclo[n]carbons. CASSCF calculations yield a singlet electronic ground state for the studied cyclo[n]carbons except for C25, whereas at the DFT level the energy difference between the lowest singlet and triplet states depends on the employed functional. The BHandHLYP functional predicts a triplet ground state of the larger odd-number cyclo[n]carbons starting from n = 13. Current-density calculations at the BHandHLYP level using the CASSCF-optimized molecular structures show that there is a through-space delocalization in the cyclo[n]carbons. The current density avoids the carbene carbon atom, leading to an alternating double aromaticity of the odd-number cyclo[n]carbons satisfying the antiaromatic [4k+1] and aromatic [4k+3] rules. C11, C15, and C19 are aromatic and can be prioritized in future synthesis. We predict a bond-shift phenomenon for the triplet state of the cyclo[n]carbons leading to resonance structures that have different reactivity toward dimerization.

Lifetimes and intensities study for the γ and β systems of CN radicals extending to very high vibrational state

The γ (A2Π-X2Σ+) and β (B2Σ+-X2Σ+) systems of cyano (CN) radicals were studied using the highly correlated ab initio approach. The complex behavior of the excited-state wave function calculated at the complete active space self-consistent field (CASSCF) and multireference configuration interaction (MRCI) levels has a great influence on the quality of the transition dipole moment curves (TDMCs). Combining the TDMCs and the Rydberg–Klein–Rees (RKR) potential curves at the MRCI + Q/aV5Z-DK level, the spectroscopic parameters of the higher vibrational bands for the γ (v′ = 0–50 ← v″ = 0–53) and β (v′ = 0–33 ← v″ = 0–53) systems were investigated. The radiation lifetimes of the vibrational levels (v′ = 0–15) were obtained. A list of wavelengths and Einstein A coefficients of the lower vibrational bands (v′ = 0–2 ← v'' = 0–2) is provided and compared with other results. The spectral intensities of the γ system 2–0 band and the β system 0–0 band at different temperatures (300, 5000, and 10,000 K) are discussed. As the temperature increases, the bandwidths become broader, and the intensities decrease. These results are relevant for the applications in astrophysics and chemistry, especially in space vehicles.

Insights on the site-selective fragmentation of CF2Cl2 and CH2Cl2 at the chlorine K-edge from ab initio calculations

A theoretical study of CF 2 Cl 2 and CH 2 Cl 2 photoabsorption spectra and photofragmentation profiles at the chlorine K-edge is presented. We simulated the NEXAFS spectra at the Core-Valence Separated Coupled Cluster Singles and Doubles (CVS-CCSD) level and interpreted the photofragmentation profile in terms of the potential energy surfaces (PES) computed at the complete active space self-consistent field (CASSCF) level along the C–Cl bond cleavage for the 1 s Cl → σ C - Cl ∗ , 1 s Cl → 7 b 2 , and 1 s Cl → ∞ states. The PES of CF 2 Cl 2 shows that the chlorine’s 1 s → σ ∗ transition tends to fragment into the CF 2 Cl ∗ radical and the Cl (1s 1 2s 2 2p 6 3s 2 3p 6 ) excited atom, whereas the 1 s Cl → 7 b 2 and 1 s Cl → ∞ states are less prone to undergo this fragmentation channel. The same tendency was observed for the CH 2 Cl 2 molecule, suggesting that the F atom has little influence on the PES.

Assessing the structural stability and vibration properties in beryllium selenide from the (3D) bulk, the (0D) molecule, the (2D) monolayer to the (1D) single walled nanotubes through ab initio simulations

An extensive computational study of beryllium selenide (BeSe) in different arrangements from molecule, bulk, monolayer (h-BeSe), to the single-walled zigzag (n,0) and armchair (n,n) nanotubes (SWBeSeNTs) has been carried out using a combination of ab initio quantum mechanical methods. For the molecule, the electronic computations have been performed using highly correlated ab initio methods, here at the multiconfiguration self-consistent field and multireference configuration interaction level including the Davidson correction (MRCI+Q) in conjunction with the aug-cc-pV5Z basis set as implemented in the MOLPRO program. Accurate potential energy curves of BeSe were generated for the electronic ground state and excited states. A set of vibrational spectroscopic parameters is derived. For the periodic arrangements, structural parameters, phonon frequencies, IR and Raman intensities, and elastic constants are computed via density functional theory with the B3LYP hybrid functional and a Gaussian basis set as implemented in the periodic ab initio CRYSTAL17 code. All results may help in unraveling the different BeSe arrangements when dimensionality reduction occurs.

Accurate potential energy surfaces for the excited state of CF2 molecule

Multi-configurational self-consistent field and Multireference configuration interaction (MCSCF/MRCI) level have been carried out for the lowest two electronic potential energy surfaces (PESs) for excited state of CF2ã(3B1) in Jacobi coordinate. For getting the accurate global PESs, the authors used B-spline fitted method with 34816 potential energy points for each state. Four kinds of PESs in different angles and the significant avoided crossing point were discussed. We found that there are three important isomers and two transion states in the most possible isomerization process, which started from linear geometry to C2v symmetry structure. The needed additional reaction barrier energy is 0.813 eV for this process. In addition the electronic structures were discussed and the result was good agreement with experiment and former’s theoretical calculation works.

ReSpect: Relativistic spectroscopy DFT program package.

With the increasing interest in compounds containing heavier elements, the experimental and theoretical community requires computationally efficient approaches capable of simultaneous non-perturbative treatment of relativistic, spin-polarization, and electron correlation effects. The ReSpect program has been designed with this goal in mind and developed to perform relativistic density functional theory (DFT) calculations on molecules and solids at the quasirelativistic two-component (X2C Hamiltonian) and fully relativistic four-component (Dirac-Coulomb Hamiltonian) level of theory, including the effects of spin polarization in open-shell systems at the Kramers-unrestricted self-consistent field level. Through efficient algorithms exploiting time-reversal symmetry, biquaternion algebra, and the locality of atom-centered Gaussian-type orbitals, a significant reduction of the methodological complexity and computational cost has been achieved. This article summarizes the essential theoretical and technical advances made in the program, supplemented by example calculations. ReSpect allows molecules with >100 atoms to be efficiently handled at the four-component level of theory on standard central processing unit-based commodity clusters, at computational costs that rarely exceed a factor of 10 when compared to the non-relativistic realm. In addition to the prediction of band structures in solids, ReSpect offers a growing list of molecular spectroscopic parameters that range from electron paramagnetic resonance parameters (g-tensor, A-tensor, and zero-field splitting), via (p)NMR chemical shifts and nuclear spin-spin couplings, to various linear response properties using either conventional or damped-response time-dependent DFT (TDDFT): excitation energies, frequency-dependent polarizabilities, and natural chiroptical properties (electronic circular dichroism and optical rotatory dispersion). In addition, relativistic real-time TDDFT electron dynamics is another unique feature of the program. Documentation, including user manuals and tutorials, is available at the program's website http://www.respectprogram.org.

Stimulated X-ray Resonant Raman Spectroscopy of Conical Intersections in Thiophenol.

The conical intersection dynamics of thiophenol is studied by computing the stimulated X-ray resonant Raman spectroscopy signals. The hybrid probing field is constructed of a hard X-ray narrowband femtosecond pulse combined with an attosecond broadband X-ray pulse to provide optimal spectral and temporal resolutions for electronic coherences in the level crossing region. The signal carries phase information about the valence-core electronic coupling in the vicinity of conical intersections. Two conical intersections occurring during the course of the S-H dissociation dynamics can be distinguished by their valence-core transition frequencies computed at the complete active space self-consistent field level. The X-ray pulse is tuned such that the Raman transition at the first conical intersection between 1πσ* and 11ππ* involves higher core levels, while the Raman transition at the second conical intersection between 1πσ* and S0 involves the lowest core level in the sulfur K-edge.

An accurate potential energy surface and ring polymer molecular dynamics study of the Cl + CH4 → HCl + CH3 reaction.

The reaction Cl + CH4 → HCl + CH3, a prototypical bimolecular reaction, has been established as an important proving ground for studying chemical reaction kinetics and dynamics of polyatomic molecules. In this work, a globally accurate full-dimensional potential energy surface (PES) for this reaction is developed by using the permutationally invariant polynomial neural network (PIP-NN) approach based on 74 000 points calculated at the level of the explicitly correlated unrestricted coupled cluster single, double, and perturbative triple level with the augmented correlation corrected valence triple-zeta basis set (UCCSD(T)-F12a/AVTZ). For points in the entrance channel, spin-orbit corrections stemming from Cl(2P) are determined at the level of complete active space self-consistent field (CASSCF) with the AVTZ basis set. With this PES, thermal rate coefficients and kinetic isotope effects are computed for reactions Cl + CH4 → HCl + CH3 and Cl + CD4 → DCl + CD3 using the ring polymer molecular dynamics (RPMD) method, which can provide reliable estimations for thermal rate coefficients effectively. Generally, the agreement with the scattered experimental results is reasonably satisfactory.