Linear Response Method Research Articles

Evaluation of redox potentials of cathode materials of alkali-ion batteries using extended DFT+U+U↑↓ method: The role of interactions between the electrons with opposite spins.

Limitations of the DFT+U approach (e.g., in Dudarev's formulation) applied for accurate evaluation of redox potentials of cathode materials of alkali-ion batteries with U parameters calculated via the linear response (LR) method are discussed. In contrast to our previous studies, where redox potentials of several cathode materials have been calculated in a good agreement with experiment (e.g., NaMnO2, LiFePO4, and LiTiS2), herein, we analyze other cathode materials, such as LiNiO2 and Ni- and V-containing phosphates for which this method provides much underestimated redox voltages. We ascribe this limited predictive power of the DFT+U method, parameterized via LR, to the absence of corrections of Coulomb interactions between the electrons with opposite spins. Using the recently proposed extended DFT+U+U↑↓ functional, which includes the aforementioned corrections, we show how redox potentials of Ni- and V-based compounds could be calculated in a much better agreement with experiment, also proposing a procedure of parameterization of such calculations. Thus, our extended method allows us to calculate redox potentials of several important materials more accurately while retaining good agreement with experiment for structures where the standard DFT+U method also accurately predicts electrochemical properties.

Calculated magnetic exchange interactions in brownmillerite Ca2Fe2O5

Brownmillerite Ca2Fe2O5 has gained great interest due to its novel properties and wide range of applications. Here, we present a systematically study of the electronic and magnetic properties of Ca2Fe2O5 with first-principles calculations. Our calculation results indicate that the valences of both octahedral Fe and tetrahedral Fe are +3. Using the first-principle linear response (FPLR) method, we calculate the magnetic exchange interactions J's. J's are short-range and negligible for the Fe-Fe atomic pair longer than 6 Å. Three relatively large exchange interactions determine that the magnetic ground state is G-type antiferromagnetism, which is consistent with the experimental results. The magnetic transition temperature calculated with our J's is in agreement with the experiment. Based on the obtained magnetic exchange parameters, we calculate the spin-wave dispersion. We also use the FPLR method to calculate the Dzyaloshinskii-Moriya interactions.

PNO++: Perturbed Pair Natural Orbitals for Coupled Cluster Linear Response Theory.

Reduced-scaling methods are needed to make accurate and systematically improvable coupled cluster linear response methods for the calculation of molecular properties tractable for large molecules. In this paper, we examine the perturbed pair natural orbital-based PNO++ approach that creates an orbital space optimized for response properties derived from a lower-cost field-perturbed density matrix. We analyze truncation errors in correlation energies, dynamic polarizabilities, and specific rotations from a coupled cluster singles and doubles (CCSD) reference. We find that incorporating a fixed number of orbitals from the pair natural orbital (PNO) space into the PNO++ method-a new method presented here, the "combined PNO++" approach-recovers accuracy in the CCSD correlation energy while preserving the well-behaved convergence behavior of the PNO++ method for linear response properties.

Simulating X‐ray absorption spectra with complete active space self‐consistent field linear response methods

AbstractIn this work, two approaches for simulating X‐ray absorption (XA) spectra with the complete active space self‐consistent field (CASSCF) linear response (LR) method are introduced. The first approach employs the well‐known core‐valence separation (CVS) approximation, which is predominantly used by many other electronic structure methods for simulating X‐ray spectra. The second ansatz uses the harmonic Davidson algorithm for finding interior eigenvalues that lie close to a target excitation energy shift and virtually solves a shifted‐and‐inverted (S&I) generalized eigenvalue problem. LR‐CASSCF K‐edge transition energies are systematically blueshifted though have consistently smaller errors than those of the CAS or restricted active space (RAS) configuration interaction (CI) methods. For simple molecules at which the core hole can only be created at a single site, the state‐specific RASSCF or n‐electron valence second‐order perturbation theory/RASCI gave more accurate principal K‐edge excitation energies. If the core hole can be created at multiple sites, the LR‐CASSCF approaches perform much better than RASSCF. Moreover, we observed that the LR‐CASSCF variants were the only MR methods discussed here that predicted correctly the order of O K‐edge features in the ozone molecule and the permanganate ion. The peak separation of edge features in ozone was as accurate as with equation‐of‐motion coupled cluster singles and doubles. The error of the CVS approximation turned out to be very system dependent and in some cases amounted up to 1.0 eV for the K‐edge excitation energies. Those CVS errors are still acceptable if one considers the observed deviation from the experimental reference by 5–11 eV. The deviations made in the XAS intensities were even more pronounced. CVS and the full S&I oscillator strengths could differ even by a factor of 2.8. Since the S&I approach is at least as efficient as the LR‐CASSCF method for valence excitations, future endeavors to improve the accuracy by accounting for dynamic correlation could be built on top of the full S&I approach.

Computational study of lattice dynamics and thermodynamic properties of energetic solid cyanuric triazide

The structural, vibrational and thermodynamic properties of the cyanuric triazide crystal is investigated through density functional theory (DFT) simulations within the dispersion corrected generalized gradient approximation (GGA + G06) by considering the norm conserving pseudopotentials. Infrared spectra and Born effective charges are computed through linear response method using the density functional perturbation theory (DFPT). The experimentally observed vibrational modes are well reproduced in our calculations. The high intensity infrared absorption bands in the range of 1200–1500 cm−1 originate from the vibrations of the N3 group. The Born effective charges indicate that the compound to be asymmetric. The calculated phonon dispersion curve clearly show the absence of imaginary frequencies along the high symmetry directions, which confirms the dynamical stability of C3N12, and the interaction between the acoustic and low lying optical modes results in enhanced phonon scattering enabling low thermal conductivity in this compound. The phonon partial density of states reveals that the low-frequency regions (below 500 cm−1) are dominated by N atoms. In addition, the compound shows covalent nature owing to the hybridization between C and N atoms. The phonon spectra and thermodynamic properties of C3N12 were computed for the first time, which still awaits experimental confirmation. The temperature-dependent heat capacity and Debye temperature has been discussed in detail. The heat capacity CV of C3N12 increases with temperature, being 98.13 cal/cell.K for T = 306 K. Finally, the entropy, enthalpy and Helmholtz free energy, are investigated and discussed in the framework of the harmonic approximation. From the above results, it can be inferred that cyanuric triazide is an effective initiating explosive, as it possess low-thermal conductivity.

The Extratropical Linear Step Response to Tropical Precipitation Anomalies and Its Use in Constraining Projected Circulation Changes under Climate Warming

AbstractRossby wave trains triggered by tropical convection strongly affect the atmospheric circulation in the extratropics. Using daily gridded observational and reanalysis data, we demonstrate that a technique based on linear response theory effectively captures the linear response in 250-hPa geopotential height anomalies in the Northern Hemisphere using examples of steplike changes in precipitation over selected tropical areas during boreal winter. Application of this method to six models from phase 5 of the Coupled Model Intercomparison Project (CMIP5), using the same tropical forcing, reveals a large intermodel spread in the linear response associated with intermodel differences in Rossby waveguide structure. The technique is then applied to a projected tropicswide precipitation change in the HadGEM2-ES model during 2025–45 December–February, a period corresponding to a 2°C rise in the mean global temperature under the RCP8.5 scenario. The response is found to depend on whether the mean state underlying the technique is calculated using observations, the present-day simulation, or the future projection; indeed, the bias in extratropical response to tropical precipitation because of errors in the basic state is much larger than the projected change in extratropical circulation itself. We therefore propose the linear step response method as a semiempirical method of making near-term future projections of the extratropical circulation, which should assist in quantifying uncertainty in such projections.

Local Molecular Field Theory for Nonequilibrium Systems.

We provide a framework for extending equilibrium local molecular field (LMF) theory to a statistical ensemble evolving under a time-dependent applied field. In this context, the self-consistency of the original LMF equation is achieved dynamically, which provides an efficient method for computing the equilibrium LMF potential, in addition to providing the nonequilibrium generalization. As a concrete example, we investigate water confined between hydrophobic or charged walls, systems that are very sensitive to the treatment of long-ranged electrostatics. We then analyze confined water in the presence of a time-dependent applied electric field, generated by a sinusoidal or abrupt variation of the magnitudes of uniform charge densities on each wall. Very accurate results are found from the time-dependent LMF formalism even for strong static fields and for time-dependent systems that are driven far from equilibrium where linear response methods fail.

Structural electronic and vibrational properties analysis of Li2CaX (X = Sn, Pb) heusler alloys: a comparative study

This study was focused on structural, electronic and vibrational properties of Li2CaSn and Li2CaPb with density functional theory. All properties of these compounds were computed by implementing General Gradient Approximation and using Quantum Espresso software programme. As a result of the calculations, it was found that the lattice parameter is 6.967 Å and bulk modulus is 33.94 GPa for Li2CaSn. Also, these values are 7.062 Å and 29.574 GPa for Li2CaPb. The calculated lattice parameters are in good agreement with the available experimental data. There is no previous theoretical calculation for Li2CaSn and Li2CaPb compounds. It was calculated that Li2CaSn and Li2CaPb have a semi-metal property. The full phonon dispersion curves of Li2CaSn and Li2CaPb compounds in the Heusler type structure were examined using the linear response method. Under 0 kbar pressure, Li2CaPb was unstable while Li2CaSn was dynamically stable. Calculations showed that when 38.42 kbar pressure is applied to the Li2CaPb compound, the Li2CaPb compound becomes dynamically stable. It is believed that this study will shape future studies.

Donor–Pyrene–Acceptor Distance-Dependent Intramolecular Charge-Transfer Process: A State-Specific Solvation Preferred to the Linear-Response Approach

Photoinduced intramolecular charge-transfer (ICT) molecules are important in various applications such as a probe for single-molecule spectroscopy, cell imaging, laser dyes, biomarkers, solar cells, in photosynthesis, etc. Here, we report a new set of substituted pyrene dye molecules, N,N-dimethylamino nitrilo pyrene and its higher analogues, containing pull–push donor (D)–chromophore (π)–acceptor (A) functional groups with enhanced photophysical characteristics like oscillator strength, light-harvesting, and ICT properties. The excited-state ICT process has been established by quantum chemical calculations using the density functional theory method in vacuo and in solvents of different polarity and hydrogen-bonding ability using linear-response (LR) and state-specific (SS) solvation approaches with gradually increasing the D–A distance. The studied molecules show solvent polarity-dependent larger Stokes’ shifts (3609–9016 cm–1, in acetonitrile), higher excited-state dipole moments (11.7–16.8 Debye, in acetonitrile), higher possibilities of highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) electronic transitions, etc., which support the occurrence of the excited-state ICT process. Here, we demonstrate how to increase the efficiency of the ICT process and also tune the ICT fluorescence maximum. We find that with a variation of the D–A distance, studied molecules show a noticeable effect on the spectroscopic and molecular properties such as the position of absorption and fluorescence band maxima, Stokes’ shift, dipole moment, light-harvesting, and ICT properties. We also show that the SS solvation approach is more supportive than the LR method to the ICT process.

Analyzing Magnetically Induced Currents in Molecular Systems Using Current-Density-Functional Theory

A suite of tools for the analysis of magnetically induced currents is introduced. These are applicable to both the weak-field regime, well described by linear response perturbation theory, and to the high-field regime, which is inaccessible to such methods. A disc-based quadrature scheme is proposed for the analysis of magnetically induced current susceptibilities, providing quadratures that are consistently defined between different molecular systems and applicable to both planar 2D and general 3D molecular systems in a black-box manner. The applicability of the approach is demonstrated for a range of planar ring systems, the ground and excited states of the benzene molecule and the ring, bowl and cage isomers of the C_20 molecule in the presence of a weak magnetic field. In the presence of a strong magnetic field, the para- to dia-magnetic transition of the BH molecule is studied, demonstrating that magnetically induced currents present a visual interpretation of this phenomenon, providing insight beyond that accessible using linear-response methods.

Calculated magnetic exchange interactions in the quantum spin chain materials K2CuSO4Cl2 and K2CuSO4Br2

Using density functional calculations, we present a comprehensive study of the electronic and magnetic properties of the quantum spin chain materials ${\mathrm{K}}_{2}{\mathrm{CuSO}}_{4}{\mathrm{Cl}}_{2}$ and ${\mathrm{K}}_{2}{\mathrm{CuSO}}_{4}{\mathrm{Br}}_{2}$. With the first-principles linear response method, we calculate the magnetic exchange parameters, and the theoretical values are in a quantitatively good agreement with experiments. Depending on the signs and magnitudes of the interchain magnetic exchange interactions, we find that the magnetic order of ${\mathrm{K}}_{2}{\mathrm{CuSO}}_{4}{\mathrm{Br}}_{2}$ along the $b$ axis is antiferromagnetic, while ${\mathrm{K}}_{2}{\mathrm{CuSO}}_{4}{\mathrm{Cl}}_{2}$ has strong frustration along the $b$ axis. Based on the obtained magnetic exchange parameters, we successfully reproduce the experimental spin-wave dispersion. We also calculate Dzyaloshinskii-Moriya interactions, which are found to dominate in these compounds compared to the interchain magnetic exchange interactions. Finally, we obtain the phase diagram for these two materials using Monte Carlo simulations. Our results are consistent with previous experiments, giving a complete explanation of the magnetic structure.

Large-scale excited-state calculation using dynamical polarizability evaluated by divide-and-conquer based coupled cluster linear response method.

This study attempted to propose an efficient scheme at the coupled cluster linear response (CCLR) level to perform large-scale excited-state calculations of not only local excitations but also nonlocal ones such as charge transfers and transitions between delocalized orbitals. Although standard applications of fragmentation techniques to the excited-state calculations brought about the limitations that could only deal with local excitations, this study solved the problem by evaluating the excited states as the poles of dynamical polarizability. Because such an approach previously succeeded at the time-dependent density functional theory level [H. Nakai and T. Yoshikawa, J. Chem. Phys. 146, 124123 (2017)], this study was considered as an extension to the CCLR level. To evaluate the dynamical polarizability at the CCLR level, we revisited three equivalent formulas, namely, coupled-perturbed self-consistent field (CPSCF), random phase approximation (RPA), and Green's function (GF). We further extended these formulas to the linear-scaling methods based on the divide-and-conquer (DC) technique. We implemented the CCLR with singles and doubles (CCSDLR) program for the six schemes, i.e., the standard and DC-type CPSCF, RPA, and GF. Illustrative applications of the present methods demonstrated the accuracy and efficiency. Although the standard three treatments could exactly reproduced the conventional frequency-domain CCSDLR results, their computational costs were commonly higher than that of the conventional ones due to large amount of computations for individual frequencies of the external electric field. The DC-type treatments, which approximately reproduced the conventional results, could achieve quasilinear scaling computational costs. Among them, DC-GF was found to exhibit the best performance.

Structural electronic and dynamic properties of Li3Bi and Li2NaBi

We report a study of structural, electronic and dynamic properties of Li3Bi and Li2NaBi via density functional theory. It is found that Li3Bi and Li2NaBi show semiconducting property with an indirect electronic band gap. The calculated structural and electronic parameters (lattice parameters, bulk modulus, bulk modulus derivation) are in a good agreement with the available experimental data. Full phonon spectra of Li3Bi and Li2NaBi materials in the Rock Salt structure were collected using the linear response method. At 0 GPa pressure, Li3Bi is dynamically stable while Li2NaBi, which can be synthesized from Li3Bi by replacing one Bi atom with the Na atom, is unstable. In this study we searched to find the pressure value that makes Li2NaBi dynamically stable. Calculations showed that the Li2NaBi structure becomes stable when 8.62 GPa pressure is applied to the Li2NaBi structure. This study is thought to give direction to the future studies.

Phonon dispersion in two-dimensional solids from atomic probability distributions.

We propose a harmonic linear response (HLR) method to calculate the phonon dispersion relations of two-dimensional layers from equilibrium simulations at finite temperatures. This HLR approach is based on the linear response of the system, as derived from the analysis of its centroid density in equilibrium path integral simulations. In the classical limit, this approach is closely related to those methods that study vibrational properties by the diagonalization of the covariance matrix of atomic fluctuations. The validity of the method is tested in the calculation of the phonon dispersion relations of a graphene monolayer, a graphene bilayer, and graphane. Anharmonic effects in the phonon dispersion relations of graphene are demonstrated by the calculation of the temperature dependence of the following observables: the kinetic energy of the carbon atoms, the vibrational frequency of the optical E2g mode, and the elastic moduli of the layer.

Prediction of Kapitza resistance at fluid-solid interfaces.

Understanding the interfacial heat transfer and thermal resistance at an interface between two dissimilar materials is of great importance in the development of nanoscale systems. This paper introduces a new and reliable linear response method for calculating the interfacial thermal resistance or Kapitza resistance in fluid-solid interfaces with the use of equilibrium molecular dynamics (EMD) simulations. The theoretical predictions are validated against classical molecular dynamics (MD) simulations. MD simulations are carried out in a Lennard-Jones (L-J) system with fluid confined between two solid slabs. Different types of interfaces are tested by varying the fluid-solid interactions (wetting coefficient) at the interface. It is observed that the Kapitza length decreases monotonically with an increasing wetting coefficient as expected. The theory is further validated by simulating under different conditions such as channel width, density, and temperature. Our method allows us to directly determine the Kapitza length from EMD simulations by considering the temperature fluctuation and heat flux fluctuations at the interface. The predicted Kapitza length shows an excellent agreement with the results obtained from both EMD and non-equilibrium MD simulations.

Spin-wave dispersion of 3d ferromagnets based on quasiparticle self-consistent GW calculations

We calculate transverse spin susceptibility in the linear response method based on the ground states determined in the quasi-particle self-consistent $GW$ (QSGW) method. Then we extract spin wave (SW) dispersions from the susceptibility. We treat bcc Fe, hcp Co, fcc Ni, and B2-type FeCo. Because of the better description of the independent-particle picture in QSGW, calculated spin stiffness constants for Fe, Co, and Ni give much better agreement with experiments in QSGW than that in the local density approximation (LDA), where the stiffness for Ni in LDA is two times bigger than the experiment. For Co, both acoustic and optical branches of SWs agree with the experiment. As for FeCo, we have some discrrepancy between the spin stiffness in QSGW and that in the experiment. We may need further theoretical and experimental investigations on the discrepancy.

A systematic determination of hubbard U using the GBRV ultrasoft pseudopotential set

Density-functional theory (DFT) is an increasingly useful tool in modern materials discovery. Advancements in parallel computing allow for high-throughput studies that predict new examples of functional materials such as photovoltaics, electrocatalysts, and thermoelectrics. An impediment to the widespread adoption of DFT is that the method is known to over-delocalize electron density, specifically in d and f orbitals. Without corrections known as post-DFT methods, the over-delocalization effect manifests as inaccurate electronic structures, which leads to a systematic underestimation of electronic bandgap values, or in many cases predicts insulating materials to have fictitious metallic character. One method to fix this deficiency is to add a corrective potential barrier to delocalization, known as the Hubbard U, to delocalized d and f states of an atom to obtain a more accurate electronic band structure. There are ways to formally derive accurate Hubbard U values, but, in practice, U is often treated as a tunable parameter where U values are chosen to match experimentally determined bandgaps. This is problematic for determining U values of materials that have no measured bandgap or have yet to be synthesized. Here we address these issues by using linear response methods to derive Hubbard U values for 3d, 4d, and 5d transition metals using the GBRV set of ultrasoft pseudopotentials. We calculate U values for three distinct crystal structures of binary metal oxides with different oxidation states; NiO (M+2), corundum (M+3), and rutile (M+4) structure types. We show that U values derived from linear response methods follow periodic trends, and that in some cases the same value of U can be applied to different oxidation states and structure types. We use the trends presented here to elucidate a set of best practices which can be applied to further the emergent field of data-enabled materials discovery.

The system thorium-palladium-boron: A DFT study on the stability and properties of Th2Pd15B5

Phase relations in the Th-Pd-B system were determined via electron microprobe and X-ray powder diffraction analyses of ∼20 ternary alloys. Phase equilibria are dominated by the two high-melting thorium borides ThB4, Th1-yB6 and one ternary compound, namely τ1-Th2Pd14+xB5, with a structure deriving from the Sc4Ni29B10-type. Th1-yB6 is the binary starting point of a continuous solid solution up to ThPd0.53B4.28 closely corresponding to the superconducting phase Th1-yPdxB6-2x (x ≤ 0.65; 0 ≤ y ≤ 0.22 at x = 0; TC = 21 K), which was described by Zandbergen et al. in 1995 for x = 0.65 from high resolution electron microscopy. All thorium-rich palladium compounds from 0 to 75 at.% Pd form stable two-phase equilibria with ThB4 without any significant mutual solid solubilities. The solubility of Th in βB has been determined for the first time from a single crystal X-ray study of ThB99: Th atoms occupy sites A1 (occ. = 13%), D (occ. = 11%), and a rather small amount of 2.9% resides in site 18f (Dd-hole).To shed light on the physical properties of the ternary compound, DFT (density functional theory) calculations were performed for two idealized representatives of the τ1-phase, namely for Th2Pd14B5 and Th2Pd15B4. The calculations cover ionic relaxation, electron density of states, band structure and Fermi surfaces, elastic constants (computed via the linear response method) and the phonon density of states. Furthermore the thermodynamic stability (energy of formation) as well as the phonon contribution of the thermodynamic properties, such as the specific heat have been calculated clearly indicating Th2Pd15B4 as the composition thermodynamically more stable than Th2Pd14B5. At the Fermi energy the Pd-d contribution is dominant for both structures, but the number of states is higher for Th2Pd15B4 with DOS(EF) = 13 states/eV/f.u. than for Th2Pd14B5 with DOS(EF) = 8.5 states/eV/f.u. The corresponding Sommerfeld constants, γe = DOS(EF)kBπ2/3 = 30.55 mJ/molK2 for Th2Pd15B4 and 19.98 mJ/molK2 for Th2Pd14B5, clearly indicate metallic behavior of the τ1-phase. In addition, mechanical properties were measured for Th2Pd15B5 and compared with calculated values and data from the literature. Th2Pd15B5 on account of its high content of Pd is only slightly harder than the rather soft and almost ductile binary Pd-borides.

Reliable thermodynamic estimators for screening caloric materials

Reversible, diffusionless, first-order solid-solid phase transitions accompanied by caloric effects are critical for applications in the solid-state cooling and heat-pumping devices. Accelerated discovery of caloric materials requires reliable but faster estimators for predictions and high-throughput screening of system-specific dominant caloric contributions. We assess reliability of the computational methods that provide thermodynamic properties in relevant solid phases at or near a phase transition. We test the methods using the well-studied B2 FeRh alloy as a “fruit fly” in such a materials genome discovery, as it exhibits a metamagnetic transition which generates multicaloric (magneto-, elasto-, and baro-caloric) responses. For lattice entropy contributions, we find that the commonly-used linear-response and small-displacement phonon methods are invalid near instabilities that arise from the anharmonicity of atomic potentials, and we offer a more reliable and precise method for calculating lattice entropy at a fixed temperature. Then, we apply a set of reliable methods and estimators to the metamagnetic transition in FeRh (predicted 346±12 K, observed 353±1 K) and calculate the associated caloric properties, such as isothermal entropy and isentropic temperature changes.

Benchmarks for Electronically Excited States with CASSCF Methods.

The accuracy of three different complete active space (CAS) self-consistent field (CASSCF) methods is investigated for the electronically excited-state benchmark set of SchreiberM.; et al. J. Chem. Phys.2008, 128, 13411018397056. Comparison of the CASSCF linear response (LR) methods MC-RPA and MC-TDA and the state-averaged (SA) CASSCF method is made for 122 singlet excitation energies and 69 oscillator strengths. Of all CASSCF methods, when considering the complete test set, MC-RPA performs best for both excitation energies and oscillator strengths with a mean absolute error (MAE) of 0.74 eV and 51%, respectively. MC-TDA and SA-CASSCF show a similar accuracy for the excitation energies with a MAE of ∼1 eV with respect to more accurate coupled cluster (CC3) excitation energies. The opposite trend is observed for the subset of n → π* excitation energies for which SA-CASSCF exhibits the least deviations (MAE 0.65 eV). By looking at s-tetrazine in more detail, we conclude that better performance for the n → π* SA-CASSCF excitation energies can be attributed to a fortunate error compensation. For oscillator strengths, SA-CASSCF performs worst for the complete test set (MAE 100%) as well as for the subsets of n → π* (MAE 192%) and π → π* excitations (MAE 84.9%). In general, CASSCF gives the worst performance for excitation energies of all excited-state ab initio methods considered so far due to lacking the major part of dynamic electron correlation, though MC-RPA and TD-DFT (BP86) show similar performance. Among all LR-type methods, LR-CASSCF oscillator strengths are the ones with the least accuracy for the same reason. As state-specific orbital relaxation effects are accounted for in LR-CASSCF, oscillator strengths are significantly more accurate than those of MS-CASPT2. Our findings should encourage further developments of response theory-based multireference methods with higher accuracy and feasibility.