Dynamical Correlation Effects Research Articles

Ab Initio Investigation of the Na3[Ln(ODA)3]·2NaClO4·6H2O (Ln = Ce-Yb; ODA = Oxydiacetate) Series.

In this work, the Na3[Ln(ODA)3]·2NaClO4·6H2O (Ln = Ce-Yb; ODA = oxydiacetate) series was analyzed with the ab initio ligand field theory (AILFT) module of the ORCA computational suite. The results were discussed within the framework of the angular overlap model (AOM) and compared to literature data. We find that the structural changes observed across the series exemplifies the effects of the lanthanide contraction also manifesting in the value of the AOM parameters. It is also shown that the complete active space self-consistent field (CASSCF) methodology is sufficient to describe the ligand field interactions in mononuclear lanthanide complexes, and the effects of dynamic correlation, through n-electron valence state perturbation theory (NEVPT2), are discussed. The calculated ligand field parameters of the present work are compared to the experimentally derived values from the literature.

Dynamic correlation and polaronic effects on the correlational properties of finite-temperature electron quantum wire

We study the role of dynamic correlation and polaronic effects on the correlational properties of a GaAs-based electron quantum wire at finite-temperature T. The dynamics of electron correlations is incorporated through the self-consistent mean-field approximation of Hasegawa and Shimizu (the qSTLS theory) and the polaronic effects via the Fröhlich interactions. Results are presented for the static correlation functions, dynamic structure factor and electron’s contact probability over a wide range of T and electron number density r s . We find that for a fixed wire width b and T, electrons undergo a transition from the quantum liquid to Wigner crystal state due to the dynamics of severely correlated electrons at a critical . The inclusion of polaronic effects along with the conventional electron-electron interactions tends to increase r s c significantly at each T ultimately improving the quantum phase diagram. The electron’s contact probability exhibits a non-monotonic T-dependence which remains positive over a broader range of r s owing to the inclusion of polaronic effects. Besides, we explore the effect of phonon contribution on the plasmon energy of the quantum wire at non-zero T and find that there is splitting in the energy into two branches namely, plasmonlike and phononlike with former having energy lower than the latter. Both of the energy modes show consistent blue shift with rise in T, get damp at a critical wave vector q c , and q c decreases with T. Finally, we calculate the finite-T polaronic contribution to the free energy whose magnitude increases with T as r s → 0 and it becomes almost constant at sufficiently high r s .

Digital finance, environmental regulation and emission reduction in manufacturing industry: New evidence incorporating dynamic spatial-temporal correlation and competition

Applying the Peking University Digital Financial Inclusion Index from 2011 to 2018, we explore the dynamic spatial-temporal correlation effects of digital finance and environmental regulation on manufacturing carbon emissions, emphasizing competition and resolving endogeneity issues. The result reveals that: (1) digital finance reduces local carbon emissions while increasing those of neighbors to a large extent, the overall reduction effect gradually emerges over time; (2) environmental regulation mitigates carbon emissions in both the short and long term with a marginal increasing trend; and (3) financial institution competition promotes these reduction effects. Combining “effective markets” and “responsive governments” yields superior emission reduction.

Quantitative Kinetics of HO2 Reactions with Aldehydes in the Atmosphere: High-Order Dynamic Correlation, Anharmonicity, and Falloff Effects Are All Important.

Kinetics provides the fundamental parameters for elucidating sources and sinks of key atmospheric species and for atmospheric modeling more generally. Obtaining quantitative kinetics in the laboratory for the full range of atmospheric temperatures and pressures is quite difficult. Here, we use computational chemistry to obtain quantitative rate constants for the reactions of HO2 with HCHO, CH3CHO, and CF3CHO. First, we calculate the high-pressure-limit rate constants by using a dual-level strategy that combines conventional transition state theory using a high level of electronic structure wave function theory with canonical variational transition state theory including small-curvature tunneling using density functional theory. The wave-function level is beyond-CCSD(T) for HCHO and CCSD(T)-F12a (Level-A) for XCHO (X = CH3, CF3), and the density functional (Level-B) is specifically validated for these reactions. Then, we calculate the pressure-dependent rate constants by using system-specific quantum RRK theory (SS-QRRK) and also by an energy-grained master equation. The two treatments of the pressure dependence agree well. We find that the Level-A//Level-B method gives good agreement with CCSDTQ(P)/CBS. We also find that anharmonicity is an important factor that increases the rate constants of all three reactions. We find that the HO2 + HCHO reaction has a significant dependence on pressure, but the HO2 + CF3CHO reaction is almost independent of pressure. Our findings show that the HO2 + HCHO reaction makes important contribution to the sink for HCHO, and the HO2 + CF3CHO reaction is the dominant sink for CF3CHO in the atmosphere.

Reduced density matrix functional theory from an ab initio seniority-zero wave function: Exact and approximate formulations along adiabatic connection paths

Currently, there is a growing interest in the development of a new hierarchy of methods based on the concept of seniority, which has been introduced quite recently in quantum chemistry. Despite the enormous potential of these methods, the accurate description of both dynamical and static correlation effects within a single and in-principle-exact approach remains a challenge. In this work, we propose an alternative formulation of reduced density-matrix functional theory (RDMFT) where the (one-electron reduced) density matrix is mapped onto an ab initio seniority-zero wave function. In this theory, the exact natural orbitals and their occupancies are determined self-consistently from an effective seniority-zero calculation. The latter involves a universal higher-seniority density matrix functional for which an adiabatic connection (AC) formula is derived and implemented under specific constraints that are related to the density matrix. The pronounced curvature of the (constrained) AC integrand, which is numerically observed in prototypical hydrogen chains and the Helium dimer, indicates that a description of higher-seniority correlations within second-order perturbation theory is inadequate in this context. Applying multiple linear interpolations along the AC or connecting second-order perturbation theory to a full-seniority treatment via Pad\'{e} approximants are better strategies. Such information is expected to serve as a guide in the future design of higher-seniority density-matrix functional approximations.

Dynamical mean-field theory for spin-dependent electron transport in spin-valve devices

We present a combination of density functional theory and dynamical mean-field theory (DMFT) for computing the electron transmission through two-terminal nanoscale devices. The method is then applied to metallic junctions presenting alternating Cu and Co layers, which exhibit spin-dependent charge transport and the giant magnetoresistance (GMR) effect. The calculations show that the coherent transmission through the $3d$ states is greatly suppressed by electron correlations. This is mainly due to the finite lifetime induced by the electron-electron interaction and is directly related to the imaginary part of the computed many-body DMFT self-energy. At the Fermi energy, where in accordance with the Fermi-liquid behavior the imaginary part of the self-energy vanishes, the suppression of the transmission is entirely due to the shifts of the energy spectrum induced by electron correlations. Based on our results, we finally suggest that the GMR measured in Cu/Co heterostructures for electrons with energies about 1 eV above the Fermi energy is a manifestation of dynamical correlation effects.

Dynamical electron correlation and the chemical bond. II. Recoupled pair bonds in the a4Σ- states of CH and CF.

We extended our studies of the effect of dynamical electron correlation on the covalent bonds in the AH and AF series (A = B-F) to the recoupled pair bonds in the excited a4Σ- states of the CH and CF molecules. Dynamical correlation is energetically less important in the a4Σ- states than in the corresponding X2Π states for both molecules, which is reflected in smaller changes in bond energies (De). Changes in the equilibrium bond distance (Re) and vibrational frequency (ωe), on the other hand, are influenced by the changes in the slope and curvature of the dynamical electron correlation energy as a function of the internuclear distance R, EDEC(R). In the CH(a4Σ-) state, these changes are much smaller than in the CH(X2Π) state, but in the CF(a4Σ-) state, they are larger, reflecting a significant difference in the shapes of EDEC(R) curves. At large R, the shape of EDEC(R) curves for covalent and recoupled pair bonds is similar although different in magnitude. For the CH(a4Σ-) state, EDEC(R) has a minimum at R = Re + 0.72 Å as the orbitals associated with the formation of the recoupled pair bond switch places. EDEC(R) for the CF(a4Σ-) state decreases continuously throughout the bound region of the potential energy curve because the dynamical correlation energy associated with the electrons in the lone pair orbitals is increasing. These results support our earlier conclusion that we still have much to learn about the nature of dynamical electron correlation in molecules.

Perturbative Expansion of Nonorthogonal Product Approach for Charge Transfer States.

Modeling of the excited states of multichromophoric systems is crucial for the understanding of photosynthesis functioning. The excitonic Hamiltonian method is widely used for such calculations. Excited states of the combined system are constructed from the wave functions of individual chromophores while their interactions are described by excitonic couplings. In the current study, we enhance a previously proposed nonorthogonal product approach to incorporate dynamic correlation effects accounted for by the multireference perturbation theory. We discuss the problems of constructing the excitonic Hamiltonian including charge transfer states for the molecular systems where the overlap contribution to the excitonic couplings is non-negligible. The benchmark calculations were performed for a model system. It was shown that the overlap component of the excitonic coupling is of great importance. The enhanced method provides an accurate description of the excited state energies and other properties.

On the three lowest spin states of Na13+: Hybrid Density Functional Theory and benchmark CASSCF(12,12)+CASPT2 studies

AbstractThe three lowest spin states (S = 0,1,2) of 12 representative isomers have been estudied using both, KS‐DFT via three hybrid density functionals, and benchmark multireference CASSCF and CASPT2 methods with a couple of Dunning's correlation consistent basis sets. CASSCF(12,12) geometry optimizations were carried out. Since 12 electrons in 12 active orbitals span the chemically‐significant complete valence space, the results of the present study provide benchmarks for . The CASPT2(12,12)/cc‐pVTZ* lowest energy structures are three nearly degenerate singlets (S = 0): an isomer formed from two pentagonal bipyramids fused together (PBPb), a capped centered‐squared antiprism [CSAP‐(1,3)] and an optimum tetrahedral OPTET(II) structure, the last two lying 0.88 and 1.63 kcal/mol above the first, respectively. The lowest triplet (S = 1) and quintet (S = 2) states lie 4.33 and 3.77 kcal/mol above the singlet global minimum, respectively. The latter is a deformed icosahedron while the former is a CSAP‐(1,3). The flatness of the potential energy surface of this cluster suggests a rather strong dynamical character at finite temperature. Prediction of the lowest energy structures and electronic properties is crucially sensitive both to non‐dynamical and dynamical electron correlation treatment. The CASPT2 vertical ionization energy is 3.66 eV, in excellent agreement with the 3.6 ± 0.1 eV experimental figure. All the isomers are found to have a strong multireference character, thus making KS density functional theory fundamentally inappropriate for these systems. Only large multiconfigurational CASSCF wavefunctions provide a reliable zeroth‐order description; then the dynamic correlation effects must be properly taken into account for a truly accurate account of the structural and energetic features of alkali‐metal clusters.

Optimising Elastic Network Models for Protein Dynamics and Allostery: Spatial and Modal Cut-offs and Backbone Stiffness

The family of coarse-grained models for protein dynamics known as Elastic Network Models (ENMs) require careful choice of parameters to represent well experimental measurements or fully-atomistic simulations. The most basic ENM that represents each protein residue by a node at the position of its C-alpha atom, all connected by springs of equal stiffness, up to a cut-off in distance. Even at this level a choice is required of the optimum cut-off distance and the upper limit of elastic normal modes taken in any sum for physical properties, such as dynamic correlation or allosteric effects on binding. Additionally, backbone-enhanced ENM (BENM) may improve the model by allocating a higher stiffness to springs that connect along the protein backbone. This work reports on the effect of varying these three parameters (distance and mode cutoffs, backbone stiffness) on the dynamical structure of three proteins, Catabolite Activator Protein (CAP), Glutathione S-transferase (GST), and the SARS-CoV-2 Main Protease (M pro ). Our main results are: (1) balancing B-factor and dispersion-relation predictions, a near-universal optimal value of 8.5 Å is advisable for ENMs; (2) inhomogeneity in elasticity brings the first mode containing spatial structure not well-resolved by the ENM typically within the first 20; (3) the BENM only affects modes in the upper third of the distribution, and, additionally to the ENM, is only able to model the dispersion curve better in this vicinity; (4) BENM does not typically affect fluctuation-allostery, which also requires careful treatment of the effector binding to the host protein to capture.

Dynamical electron correlation and the chemical bond. I. Covalent bonds in AH and AF (A = B-F).

Dynamical electron correlation has a major impact on the computed values of molecular properties and the energetics of molecular processes. This study focused on the effect of dynamical electron correlation on the spectroscopic constants (Re, ωe, De), and potential energy curves, ΔE(R), of the covalently bound AH and AF molecules, A = B-F. The changes in the spectroscopic constants (ΔRe, Δωe, ΔDe) caused by dynamical correlation are erratic and, at times, even surprising. These changes can be understood based on the dependence of the dynamical electron correlation energies of the AH and AF molecules as a function of the bond distance, i.e., ΔEDEC(R). At large R, the magnitude of ΔEDEC(R) increases nearly exponentially with decreasing R, but this increase slows as R continues to decrease and, in many cases, even reverses at very short R. The changes in ΔEDEC(R) in the region around Re were as unexpected as they were surprising, e.g., distinct minima and maxima were found in the curves of ΔEDEC(R) for the most polar molecules. The variations in ΔEDEC(R) for R ≲ Re are directly correlated with major changes in the electronic structure of the molecules as revealed by a detailed analysis of the spin-coupled generalized valence bond wave function. The results reported here indicate that we have much to learn about the nature of dynamical electron correlation and its effect on chemical bonds and molecular properties and processes.

Wavefunction-based quantum-chemical ab initio calculations for core electron binding energies of small open shell molecules

Core electron binding energies (CEBEs), i.e. ionization energies of 1s core orbitals, are calculated by means of wavefunction-based quantum-chemical ab initio methods for a series of small open-shell molecules containing first-row atoms. The calculations are performed in three steps: (a) Koopmans’ theorem, where the orbitals of the electronic ground state are used unchanged also for the ions, (b) Hartree–Fock or self consistent field (SCF) approximation in which the orbitals are allowed to relax after 1s ionization (ΔSCF), (c) dynamic correlation effects on top of SCF. For open-shell molecules 1s ionization leads to ions in several spin states, mostly to a pair of a triplet and a singlet state. In several cases one or both of these ionic states are only poorly described by a single-reference SCF wavefunction, therefore a multi-reference complete active space self consistent field (CAS-SCF) wavefunction is used instead. The correlation effects are evaluated by means of our multi-reference coupled electron pair approximation program. The accuracy of the calculated CEBEs is in the order of 0.1–0.4 eV. This is in agreement with experimental results for NO and O2. But there exist only very few gas phase data for CEBEs of open-shell molecules.

A double exponential coupled cluster theory in the fragment molecular orbital framework.

Fragmentation-based methods enable electronic structure calculations for large chemical systems through partitioning them into smaller fragments. Here, we have developed and benchmarked a dual exponential operator-based coupled cluster theory to account for high-rank electronic correlation of large chemical systems within the fragment molecular orbital (FMO) framework. Upon partitioning the molecular system into several fragments, the zeroth order reference determinants for each fragment and fragment pair are constructed in a self-consistent manner with two-body FMO expansion. The dynamical correlation is induced through a dual exponential ansatz with a set of fragment-specific rank-one and rank-two operators that act on the individual reference determinants. While the single and double excitations for each fragment are included through the conventional rank-one and rank-two cluster operators, the triple excitation space is spanned via the contraction between the cluster operators and a set of rank-two scattering operators over a few optimized fragment-specific occupied and virtual orbitals. Thus, the high-rank dynamical correlation effects within the FMO framework are computed with rank-one and rank-two parametrization of the wave operator, leading to significant reduction in the number of variables and associated computational scaling over the conventional methods. Through a series of pilot numerical applications on various covalent and non-covalently bonded systems, we have shown the quantitative accuracy of the proposed methodology compared to canonical, as well as FMO-based coupled-cluster single double triple. The accuracy of the proposed method is shown to be systematically improvable upon increasing the number of contractible occupied and virtual molecular orbitals employed to simulate triple excitations.

237Np Mössbauer Isomer Shifts: A Lesson About the Balance of Static and Dynamic Electron Correlation in Heavy Element Complexes.

A large set of neptunium compounds with different oxidation states (III to VII) was assembled to study the Mössbauer isomer shift by wave function calculations and better understand covalency in f-elements complexes. The contact density approach was used to calculate the isomer shift using complete active space self-consistent field (CASSCF) multiconfiguration wave functions, as well as matrix product states [from Density Matrix Renormalization Group (DMRG) algorithms] for large active spaces. Dynamic correlation effects for the isomer shifts were treated via CASPT2 energy derivatives with respect to the nuclear radius. The CASSCF calculations appear to produce different orbital overlocalization errors for low and high Np oxidation states. For compounds with low Np oxidation numbers, the errors can be attributed to the overlocalization of the 5f orbitals. For the compounds with high Np oxidation numbers, the main errors arise from an overlocalization of ligand orbitals and concomitant to weak donation bonding. Attempts to mitigate the overlocalization errors with large active spaces using DMRG were only partially successful, showing that explicit treatment of dynamic correlation is necessary for accurate predictions of Mössbauer isomer shifts. The CASPT2 calculations perform very satisfactorily. For a subset of Np compounds, both static and dynamic correlation effects were substantial. A rational active space selection based on orbital entanglement diagrams proved beneficial for determining the optimal reference wave function.

Elucidating the molecular orbital dependence of the total electronic energy in multireference problems.

The accurate resolution of the chemical properties of strongly correlated systems, such as biradicals, requires the use of electronic structure theories that account for both multi-reference and dynamic correlation effects. A variety of methods exist that aim to resolve the dynamic correlation in multi-reference problems, commonly relying on an exponentially scaling complete-active-space self-consistent-field (CASSCF) calculation to generate reference molecular orbitals (MOs). However, while CASSCF orbitals provide the optimal solution for a selected set of correlated (active) orbitals, their suitability in the quest for the resolution of the total correlation energy has not been thoroughly investigated. Recent research has shown the ability of Kohn-Shan density functional theory to provide improved orbitals for coupled cluster (CC) and Møller-Plesset perturbation theory (MP) calculations. Here, we extend the search for optimal and more cost effective MOs to post-configuration-interaction [post-(CI)] methods, surveying the ability of the MOs obtained with various density functional theory (DFT) functionals, as well as Hartree-Fock and CC and MP calculations to accurately capture the total electronic correlation energy. Applying the anti-Hermitian contracted Schrödinger equation to the dissociation of N2, the calculation of biradical singlet-triplet gaps, and the transition states of bicylobutane isomerization, we demonstrate that DFT provides a cost-effective alternative to CASSCF in providing reference orbitals for post-CI dynamic correlation calculations.

Importance of dynamical electron correlation in diabatic couplings of electron-exchange processes.

We demonstrate the importance of the dynamical electron correlation effect in diabatic couplings of electron-exchange processes in molecular aggregates. To perform a multireference perturbation theory with large active space of molecular aggregates, an efficient low-rank approximation is applied to the complete active space self-consistent field reference functions. It is known that kinetic rates of electron-exchange processes, such as singlet fission, triplet-triplet annihilation, and triplet exciton transfer, are not sufficiently explained by the direct term of the diabatic couplings but efficiently mediated by the low-lying charge transfer states if the two molecules are in close proximity. It is presented in this paper, however, that regardless of the distance of the molecules, the direct term is considerably underestimated by up to three orders of magnitude without the dynamical electron correlation, i.e., the diabatic states expressed in the active space are not adequate to quantitatively reproduce the electron-exchange processes.

Numerical investigation on wheel-rail impact contact solutions excited by rail spalling failure

Rail spalling is a typical form of wheel-rail rolling contact fatigue (RCF), and is a difficult problem that has always existed in railways. Once the wheel rolls across the spalling failure area, there will be a violent dynamic wheel-rail interaction. This paper presents an explicit high-speed 3D wheel-rail rolling contact transient explicit finite element model that considers local rail spalling failure. The dynamic wheel-rail interaction under the condition of differentspalling lengths and contact stress states, as well as plastic strain of the rail when the wheel rolls across the rail spalling, are calculated using the theory of transient wheel-rail dynamics. In addition, the time–frequency analysis is carried out to obtain the distribution characteristics of dynamic response signals such as axle box acceleration, rail vibration acceleration and dynamic vertical wheel-rail force in time domain and frequency domain.Furthermore, when the vehicle travels at a high speed, the speed and radius of the wheelhave little influence on the dynamic vertical wheel-rail force, or on the wavelet energy peak and frequency. The effect of the mutual dynamic correlation is small. But the dynamic vertical wheel-rail force, along with wavelet energy peak and frequency, increase in an approximately linear fashion with the impact acceleration of wheelset and the length of spalling failure. These results can be used to guide the dynamic detection of local defects on rails.

On the role of dynamic electron correlation in non-orthogonal configuration interaction with fragments.

Two different approaches have been implemented to include the effect of dynamic electron correlation in the Non-Orthogonal Configuration Interaction for Fragments (NOCI-F) method. The first is based on shifting the diagonal matrix elements of the NOCI matrix, while the second incorporates the dynamic correlation explicitly in the fragment wave functions used to construct the many-electron basis functions of the NOCI. The two approaches are illustrated for the calculation of the electronic coupling relevant in singlet fission and the coupling of spin moments in organic radicals. Comparison of the calculated diabatic couplings, the NOCI energies and wave functions shows that dynamic electron correlation is not only efficiently but also effectively incorporated by the shifting approach and can largely affect the coupling between electronic states. Also, it brings the NOCI coupling of the spin moments in close agreement with benchmark calculations.

Assessing the Accuracy of Tailored Coupled Cluster Methods Corrected by Electronic Wave Functions of Polynomial Cost.

Tailored coupled cluster theory represents a computationally inexpensive way to describe static and dynamical electron correlation effects. In this work, we scrutinize the performance of various coupled cluster methods tailored by electronic wave functions of polynomial cost. Specifically, we focus on frozen-pair coupled cluster (fpCC) methods, which are tailored by pair-coupled cluster doubles (pCCD), and coupled cluster theory tailored by matrix product state wave functions optimized by the density matrix renormalization group (DMRG) algorithm. As test system, we selected a set of various small- and medium-sized molecules containing diatomics (N2, F2, C2, CN+, CO, BN, BO+, and Cr2) and molecules (ammonia, ethylene, cyclobutadiene, benzene, hydrogen chains, rings, and cuboids) for which the conventional single-reference coupled cluster singles and doubles (CCSD) method is not able to produce accurate results for spectroscopic constants, potential energy surfaces, and barrier heights. Most importantly, DMRG-tailored and pCCD-tailored approaches yield similar errors in spectroscopic constants and potential energy surfaces compared to accurate theoretical and/or experimental reference data. Although fpCC methods provide a reliable description for the dissociation pathway of molecules featuring single and quadruple bonds, they fail in the description of triple or hextuple bond-breaking processes or avoided crossing regions.

Spin waves in doped graphene: A time-dependent spin density functional approach to collective excitations in paramagnetic two-dimensional Dirac fermion gases

In spin-polarized itinerant electron systems, collective spin-wave modes arise from dynamical exchange and correlation (xc) effects. We consider here spin waves in doped paramagnetic graphene with adjustable Zeeman-type band splitting. The spin waves are described using time-dependent spin density functional response theory, treating dynamical xc effects within the Slater and Singwi-Tosi-Land-Sj\"olander approximations. We obtain spin-wave dispersions and spin stiffnesses as a function of doping and spin polarization, and we discuss the prospects for their experimental observation.