Nondynamical Correlation Research Articles

The density matrix functional approach to electron correlation: dynamic and nondynamic correlation along the full dissociation coordinate.

For chemistry an accurate description of bond weakening and breaking is vital. The great advantage of density matrix functionals, as opposed to density functionals, is their ability to describe such processes since they naturally cover both nondynamical and dynamical correlation. This is obvious in the Löwdin-Shull functional, the exact natural orbital functional for two-electron systems. We present in this paper extensions of this functional for the breaking of a single electron pair bond in N-electron molecules, using LiH, BeH(+), and Li2 molecules as prototypes. Attention is given to the proper formulation of the functional in terms of not just J and K integrals but also the two-electron L integrals (K integrals with a different distribution of the complex conjugation of the orbitals), which is crucial for the calculation of response functions. Accurate energy curves are obtained with extended Löwdin-Shull functionals along the complete dissociation coordinate using full CI calculations as benchmark.

Structure, Stability, and Properties of the Trans Peroxo Nitrate Radical: The Importance of Nondynamic Correlation

We report a comparative single-reference and multireference coupled-cluster investigation on the structure, potential energy surface, and IR spectroscopic properties of the trans peroxo nitrate radical, one of the key intermediates in stratospheric NOX chemistry. The previous single-reference ab initio studies predicted an unbound structure for the trans peroxo nitrate radical. However, our Fock space multireference coupled-cluster calculation confirms a bound structure for the trans peroxo nitrate radical, in accordance with the experimental results reported earlier. Further, the analysis of the potential energy surface in FSMRCC method indicates a well-behaved minima, contrary to the shallow minima predicted by the single-reference coupled-cluster method. The harmonic force field analysis, of various possible isomers of peroxo nitrate also reveals that only the trans structure leads to the experimentally observed IR peak at 1840 cm(-1). The present study highlights the critical importance of nondynamic correlation in predicting the structure and properties of high-energy stratospheric NOx radicals.

Assessment of Quantum Mechanical Methods for Copper and Iron Complexes by Photoelectron Spectroscopy.

Broken-symmetry density functional theory (BS-DFT) calculations are assessed for redox energetics [Cu(SCH3)2]1–/0, [Cu(NCS)2]1–/0, [FeCl4]1–/0, and [Fe(SCH3)4]1–/0 against vertical detachment energies (VDE) from valence photoelectron spectroscopy (PES), as a prelude to studies of metalloprotein analogs. The M06 and B3LYP hybrid functionals give VDE that agree with the PES VDE for the Fe complexes, but both underestimate it by ∼400 meV for the Cu complexes; other hybrid functionals give VDEs that are an increasing function of the amount of Hartree–Fock (HF) exchange and so cannot show good agreement for both Cu and Fe complexes. Range-separated (RS) functionals appear to give a better distribution of HF exchange since the negative HOMO energy is approximately equal to the VDEs but also give VDEs dependent on the amount of HF exchange, sometimes leading to ground states with incorrect electron configurations; the LRC-ωPBEh functional reduced to 10% HF exchange at short-range give somewhat better values for both, although still ∼150 meV too low for the Cu complexes and ∼50 meV too high for the Fe complexes. Overall, the results indicate that while HF exchange compensates for self-interaction error in DFT calculations of both Cu and Fe complexes, too much may lead to more sensitivity to nondynamical correlation in the spin-polarized Fe complexes.

Theoretical Studies of the Mechanism of N-Hydroxylation of Primary Aromatic Amines by Cytochrome P450 1A2: Radicaloid or Anionic?

Primary aromatic and heteroaromatic amines are notoriously known as potential mutagens and carcinogens. The major event of the mechanism of their mutagenicity is N-hydroxylation by P450 enzymes, primarily P450 1A2 (CYP1A2), which leads to the formation of nitrenium ions that covalently modify nucleobases of DNA. Energy profiles of the NH bond activation steps of two possible mechanisms of N-hydroxylation of a number of aromatic amines by CYP1A2, radicaloid and anionic, are studied by dispersion-corrected DFT calculations. The classical radicaloid mechanism is mediated by H-atom transfer to the electrophilic ferryl-oxo intermediate of the P450 catalytic cycle (called Compound I or Cpd I), whereas the alternative anionic mechanism involves proton transfer to the preceding nucleophilic ferrous-peroxo species. The key structural features of the catalytic site of human CYP1A2 revealed by X-ray crystallography are maintained in calculations. The obtained DFT reaction profiles and additional calculations that account for nondynamical electron correlation suggest that Cpd I has higher thermodynamic drive to activate aromatic amines than the ferrous-peroxo species. Nevertheless, the anionic mechanism is demonstrated to be consistent with a variety of experimental observations. Thus, energy of the proton transfer from aromatic amines to the ferrous-peroxo dianion splits aromatic amines into two classes with different mutagenicity mechanisms. Favorable or slightly unfavorable barrier-free proton transfer is inherent in compounds that undergo nitrenium ion mediated mutagenicity. Monocyclic electron-rich aromatic amines that do not follow this mutagenicity mechanism show significantly unfavorable proton transfer. Feasibility of the entire anionic mechanism is demonstrated by favorable Gibbs energy profiles of both chemical steps, NH bond activation, and NO bond formation. Taken together, results suggest that the N-hydroxylation of aromatic amines in CYP1A2 undergoes the anionic mechanism. Possible reasons for the apparent inability of Cpd I to activate aromatic amines in CYP1A2 are discussed.

Potential energy curves for Mo2: multi-component symmetry-projected Hartree–Fock and beyond

The molybdenum dimer is an example of a transition metal system with a formal sextuple bond that constitutes a challenging case for ab initio quantum chemistry methods. In particular, the complex binding pattern in the Mo2 molecule requires a high-quality description of non-dynamic and dynamic electron correlation in order to yield the correct shape of the potential energy curve. The present study examines the performance of a recently implemented multi-component symmetry projected Hartree–Fock (HF) approach. In this work, the spin and spatial symmetries of a trial wavefunction written in terms of non-orthogonal Slater determinants are deliberately broken and then restored in a variation-after-projection framework. The resulting symmetry-projected HF wavefunctions, which possess well-defined quantum numbers, can account for static and some dynamic correlations. A single symmetry-projected configuration in a D∞hS-UHF or a D∞hKS-UHF framework offers a reasonable description of the potential energy curve of Mo2, though the binding energy is too small for the former. Our multi-component strategy offers a way to improve on the single configuration result in a systematic way towards the exact wavefunction: in the def2-TZVP basis set considered in this study, a 7-determinant multi-component D∞hS-UHF approach yields a bond length of 2.01 Å, in good agreement with experimental results, while the predicted binding energy is 39.2 mhartree. The results of this exploratory study suggest that a multi-component symmetry-projected HF stategy is a promising alternative in a high-accuracy description of the electronic structure of challenging systems. We also present and discuss some benchmark calculations based on the CEEIS-FCI (correlation energy extrapolation by intrinsic scaling – full configuration interaction) method for selected geometries.

Multireference electron correlation methods with density matrix renormalisation group reference functions

Recent advances in quantum chemical density matrix renormalisation group (DMRG) theory are presented. The DMRG, originally devised as an alternative to the exact diagonalisation in condensed matter physics, has become a powerful quantum chemical method for molecular systems that exhibit a multireference character, e.g., excited states, π-conjugated systems, transition metal complexes, and in particular for large systems by combining it with conventional multireference electron correlation methods. The capability of the current quantum chemical DMRG is demonstrated for an application involving the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems and thus requires the best electronic structure treatment for non-dynamical and dynamical correlation as well as large basis sets.

Analyzing effects of strong electron correlation within Kohn-Sham density-functional theory

A density-functional-theory method for analyzing effects of strong electron correlation is presented, based on a single Kohn-Sham determinant. It yields the population of effectively unpaired (odd) electrons and depicts the strength of nondynamic correlation, both locally and globally. It provides also a quantitative estimate of localized magnetic moments without invoking symmetry-breaking procedures. Preliminary tests on some exemplary systems of strong correlation such as C${}_{2}$, Cr${}_{2}$, the NO dimer, and dissociating H${}_{2}$ and N${}_{2}$ are discussed in comparison with available post-Hartree-Fock wave-function studies. We show that the bond in C${}_{2}$ is unlikely to have diradical character in its ground state, but may have it in some excited state. The singlet ground state of the NO dimer, however, does have a diradical character of the bonding. Quite interestingly, the bond in Cr${}_{2}$ has a quad-radical nature.

Theoretical Studies on the Photoelectron and Absorption Spectra of MnO4–and TcO4–

The tetraoxo pertechnetate anion (TcO4(-)) is of great interest for nuclear waste management and radiopharmceuticals. To elucidate its electronic structure and to compare with that of its lighter congener MnO4(-), the photoelectron and electronic absorption spectra of MnO4(-) and TcO4(-) are investigated with density functional theory (DFT) and ab initio wave function theory (WFT). The vertical electron detachment energies (VDEs) of MnO4(-) obtained with the CR-EOM-CCSD(T) method are in good agreement with the lowest two experimental VDEs; the differences are less than 0.1 eV, representing a significant improvement over the IP-EOM-CCSD(T) result in the literature. Combining our CCSD(T) and CR-EOM-CCSD(T) results, the first five VDEs of TcO4(-) are estimated between 5 and 10 eV with an estimated accuracy of about ±0.2 eV. The vertical excitation energies are determined by using TD-DFT, CR-EOM-CCSD(T), and RAS-PT2 methods. The excitation energies and the assignments of the spectra are analyzed and partly improved. They are compared with reported SAC-CI results and available experimental data. Both dynamic and nondynamic electron correlations are important in the ground and excited states of MnO4(-) and TcO4(-). Nondynamical correlations are particularly relevant in TcO4(-) for reliable prediction of excitation energies. In TcO4(-) one Rydberg state interlaces but does not mix with the valence excited states, and it disappears in the condensed phase.

Jaguar: A high‐performance quantum chemistry software program with strengths in life and materials sciences

Jaguar is anab initioquantum chemical program that specializes in fast electronic structure predictions for molecular systems of medium and large size. Jaguar focuses on computational methods with reasonable computational scaling with the size of the system, such as density functional theory (DFT) and local second‐order Møller–Plesset perturbation theory. The favorable scaling of the methods and the high efficiency of the program make it possible to conduct routine computations involving several thousand molecular orbitals. This performance is achieved through a utilization of the pseudospectral approximation and several levels of parallelization. The speed advantages are beneficial for applying Jaguar in biomolecular computational modeling. Additionally, owing to its superior wave function guess for transition‐metal‐containing systems, Jaguar finds applications in inorganic and bioinorganic chemistry. The emphasis on larger systems and transition metal elements paves the way toward developing Jaguar for its use in materials science modeling. The article describes the historical and new features of Jaguar, such as improved parallelization of many modules, innovations inab initiopKa prediction, and new semiempirical corrections for nondynamic correlation errors in DFT. Jaguar applications in drug discovery, materials science, force field parameterization, and other areas of computational research are reviewed. Timing benchmarks and other results obtained from the most recent Jaguar code are provided. The article concludes with a discussion of challenges and directions for future development of the program. © 2013 Wiley Periodicals, Inc.

Electronic propensity of Cu(II) versus Cu(I) sites in zeolites to activate NO — Spin- and orbital-resolved Cu–NO electron transfer

Electronic factors responsible for the notable decline of NO activation by Cu(II) with respect to Cu(I) sites in zeolites are investigated within spin-resolved analysis of electron transfer channels between the copper center and the substrate. The results of natural orbitals for chemical valence (NOCV) charge transfer analysis for a minimal model of Cu(II) sites in zeolite ZSM-5 ({T1Cu}+ NO) are compared with those for Cu(I)–NO and referenced to an interaction of NO with bare Cu+ cations. The bonding of NO, which is an open-shell and non-innocent ligand, gives rise to a noticeable nondynamical correlation in the adduct with Cu(II) (reflected in a broken-symmetry solution obtained at the density functional theory (DFT) level). Four distinct components of electron transfer between the copper and NO are identified: (i) donation of an unpaired electron from the NO π∥* antibonding orbital to the Cu species, (ii) backdonation from copper d⊥ to the NO antibonding orbital, (iii) “covalent” donation from NO π∥ and Cu d∥ orbitals to the bonding region, and (iv) donation from the nitrogen lone pair to Cus,d. Large variations in channel identity and significance may be noted among studied systems and between spin manifolds: channel i is effective only in the bonding of NO with either a naked Cu+ cation or Cu(II) site. Channel ii comes into prominence only for the model of the Cu(I) site: it strongly activates the NO bond by populating antibonding π*, which weakens the N–O bond, in contrast to channel i depopulating the antibonding orbital and strengthening the N–O bond. Channels iii and iv, however, may contribute to the strength of the bonding between NO and copper, and are of minor importance for the activation of the NO bond. This picture perfectly matches the IR experiment: interaction with either Cu(II) sites or a naked Cu+ cation imposes a comparable blue-shift of NO stretching frequency, while the frequency becomes strongly red-shifted for a Cu(I) site in ZSM-5 due to enhanced π* backdonation.

The Decomposition Pathways of CH<sub>2</sub>SiCl<sub>3</sub>, CH<sub>3</sub>SiCl<sub>2</sub> and CH<sub>2</sub>SiCl<sub>2</sub> in CVD of SiC from MTS/H<sub>2</sub> System

The decomposition pathways in CVD preparing SiC with CH3SiCl3-H2 precursors was searched theoretically, which involves 54 well-defined transition states. The geometries of the species were optimized by employing the B3PW91/6-311G(d,p) method. The transition states as well as their linked intermediates were confirmed with frequency and the intrinsic reaction coordinates analyses. The energy barriers and the reaction energies were evaluated with the accurate model chemistry method at G3(MP2) level after a non-dynamical electronic correlation detection. The heat capacities and entropies were obtained with statistical thermodynamics. The Gibbs free energies at 298.15 K and 1200 K for all of the reactions were reported. The energies at any temperature could be derived classically by using the analytical heat capacities. All the possible elementary reactions, including both direct decomposition and the radical attacking dissociations for CH2SiCl3, CH3SiCl2 and CH2SiCl2 were examined. A free radical reaction mechanism was proposed.

Multiconfigurational Self-Consistent Field Calculations of the Magnetically Induced Current Density Using Gauge-Including Atomic Orbitals.

Nondynamical electron correlation based on a genuine multiconfigurational theory is of considerable importance for a balanced ab initio calculation of aromatic and antiaromatic molecules either with open-shell character or quasi-degeneracy in the electronic states. Among the various aromaticity indices, the calculation of magnetically induced ring current densities (MICD) has emerged as a strong contender, providing both a qualitative and a quantitative description of the effect. We report here the first implementation of MICD at the multiconfigurational self-consistent field (MCSCF) level of theory together with example calculations. This extension makes the method applicable to systems that cannot be appropriately handled with earlier implementations based on a single-reference starting function. We present the formulation of the MCSCF MICD theory along with applications to a prototypical antiaromatic (cyclobutadiene) and an aromatic (benzyne) system, both systems that require a multiconfigurational description. We compare the MCSCF results to those obtained using Hartree-Fock and Kohn-Sham density functional theory and discuss the effects of static correlation on the aromaticity.

Electronic Structure of One-Electron-Oxidized Form of the Methylcobalamin Cofactor: Spin Density Distribution and Pseudo-Jahn–Teller Effect

The electronic and structural properties of the one-electron-oxidized form of methylcobalamin (MeCbl) cofactor have been investigated using density functional theory (DFT) and CASSCF/MC-XQDPT2 calculations. We applied two types of functionals (hybrid and GGA) which produced quite different results in terms of spin density profiles: the B3LYP description was consistent with Co(III) and the π-cation corrin radical while the BP86 result was more in line with the Co(IV) oxidation state. A closer inspection of both outcomes indicates that the oxidized species have a mixed π-cation corrin radical and Co(III)/Co(IV) character. This mixed character was further supported by high-level ab initio CASSCF/MC-XQDPT2 calculations, which reveal the strong mixing of the electronic states due to nondynamical correlation effects. The near degeneracy, which takes place between the ground and first excited state, was consistent with the presence of a pseudo-Jahn-Teller (pJT) effect in the oxidized form of MeCbl. In addition, the DFT-based investigation of the structurally related porphyrin complexes gives a description consistent with corrin-based analogues and reveals that the corrin species have more Co(IV) character. The most important finding of the present study, regardless of the type of functional used, was the significant lowering of dissociation energy (∼35%), which might be due to the partial depopulation of the Co-C σ orbital upon removal of an electron.

The natural orbital functional theory of the bonding in Cr2, Mo2and W2

In this paper, we present for the first time a description based on the natural orbital functional theory (NOFT) of the group VI dimers, namely, Cr(2), Mo(2) and W(2). The PNOF5, Piris Natural Orbital Functional, has been used throughout this work, and the results are compared to multireferential perturbation theory (CASPT2) results. Both methods have been combined with effective core potentials to take into account the scalar relativistic effects. In addition, for Cr(2), an all-electron TZVP quality basis set has also been used to recover the core-valence dynamical correlation. In all cases, PNOF5 shows better behavior than CASPT2, which needs a larger basis set to recover comparable amounts of dynamical correlation. PNOF5 is able to account for the non-dynamical electron correlation, which is responsible for the multireferential nature of these dimers. However, it does not fully recover the dynamical correlation, which is crucial for the accurate description of these challenging potential energy curves. Consequently, PNOF5 predicts longer equilibrium distances and lower dissociation energies than the experimental values. Unlike CASPT2, the PNOF5 results do not significantly improve by using larger basis sets. These new findings represent a major step in the NOFT development, since PNOF5 is the first functional of the natural orbitals reported to yield a chemically balanced and accurate description of these challenging transition metal dimers.

A simple DFT-based diagnostic for nondynamical correlation

We propose a simple DFT-based diagnostic for nondynamical correlation effects, namely Aλ = (1 - TAE[XλC]/TAE[XC])/λ where TAE stands for the molecular total atomization energy, XC is a pure-DFT exchange-correlation functional, and XλC represents the corresponding hybrid with 100λ % Hartree–Fock-type exchange. The diagnostic is a good predictor for sensitivity of energetics to the level of theory, unlike most wavefunction- based diagnostics. For GGA functionals, Aλ values approaching unity indicate severe nondynamical correlation, while values between 0 and about 0.1 indicate systems where correlation is predominantly dynamical in character (or entirely absent). The diagnostic is only weakly sensitive to the basis set (beyond polarized valence double zeta) and can easily be applied to problems beyond the practical reach of wavefunction ab initio methods required for other diagnostics. We also propose a simple measure for the importance of dynamic correlation..

Generalized antisymmetric ordered products, generalized normal ordered products, ordered and ordinary cumulants and their use in many electron correlation problem

The use of cumulants in the direct determination of the 2-particle reduced density matrix (2-RDM), Γ2, via reconstruction schemes where Γ3 and Γ4 are expressed in terms of Γ2 and cumulants to ‘close’ the hierarchy of density equations of Nakatsuji has been systematically developed for about two decades. A challenging aspect of such developments is the imposition of the N-representability conditions on Γ2, all of which are not known. Some reasonable sufficiency conditions and the use of the so-called ‘weak positivity conditions’ have proved to be fruitful but a lot more remains to be done. There is another parallel development involving cumulants where certain ‘model cumulants’ are extracted from a multi-reference model function Ψ0 and dynamical correlation is introduced via a wave operator Ω, acting on Ψ0. The non-dynamical correlation is reflected in the various model cumulants. Such formulations are accomplished in the most compact manner if one uses the notion of generalized normal ordering (GNO) and generalized Wick’s theorem (GWT) with respect to Ψ0. The product of operators in GNO has vanishing expectation value with respect to Ψ0. The GWT expresses a product of n creation/annihilation operators as a sum of m operators in GNO (m⩽n) with products of various cumulants along with appropriate phases. This approach, unlike the reconstruction schemes, uses the model cumulants as intermediaries only which are N-representable by construction. In this paper we will introduce the notion of generalized antisymmetrized ordered products (GOPs) and show how a generalized normal ordering for a product of arbitrary number of creation and annihilation operators can naturally emerge as the limit of a hierarchy of GOP. We argue in this paper that the use of GOP leads naturally to the generalized Wick’s theorem where the normal ordered products are antisymmetric under permutations and have vanishing expectation values with respect to Ψ0. We will also show that, except the pair cumulants, all the higher body cumulants have the antisymmetric property and they are equivalent to the cumulants introduced by Kubo. Finally we formulate an explicitly connected (size-extensive) Internally Contracted Multi-reference Coupled Cluster (IC-MRCC) theory with the CAS type of reference function Ψ0, using the Ansatz for the wave operator Ω as generalized normal ordered exponential of a cluster operator T. The GNO in Ω is with respect to the function Ψ0. Two different schemes for solving the MRCC equations are proposed. One is a formulation where Ψ0 is kept frozen as a starting function and only the cluster amplitudes, Ts, are computed. The other is a scheme where the coefficients entering Ψ0 are relaxed and the coupling with respect to the cluster operators are also included via the MRCC equations. The formulation of the IC-MRCC theories is predicated by the antisymmetric nature of the GNO, which has been explicitly utilized. This completes our earlier program of developing IC-MRCC, where the GNO was exploited but its antisymmetry was implicitly assumed and not proven.

Conical Intersection and Potential Energy Surface Features of a Model Retinal Chromophore: Comparison of EOM-CC and Multireference Methods.

This work investigates the performance of equation-of-motion coupled-cluster (EOM-CC) methods for describing the changes in the potential energy surfaces of the penta-2,4-dieniminium cation, a reduced model of the retinal chromophore of visual pigments, due to dynamical electron correlation effects. The ground-state wave function of this model includes charge-transfer and diradical configurations whose weights vary along different displacements and are rapidly changing at the conical intersection between the ground and the first excited states, making the shape of the potential energy surface sensitive to a balanced description of nondynamical and dynamical correlation. Recently, variational (MRCISD) and perturbative (MRPT2) approaches for including dynamical correlation in CASSCF-based calculations were tested along three representative ground state paths. Here, we use the same three paths to compare the performance of single-reference EOM-CC methods against MRCISD and MRCISD+Q. We find that the spin-flip variant of EOM-CCSD with perturbative inclusion of triple excitations (dT or fT) produces potential energy profiles of the two lowest electronic states in quantitative agreement with MRCISD+Q (our highest-quality reference method). The nonparallelity errors and differences in vertical energy differences of the two surfaces along these scans are less than 1.4 kcal/mol (EOM-SF-CCSD(dT) versus MRCISD+Q). For comparison, the largest error of MRCISD versus MRCISD+Q is 1.7 kcal/mol. Our results show that the EOM-CC methods provide an alternative to multireference approaches and may be used to study photochemical systems like the one used in this work.

O + C2H4 potential energy surface: lowest-lying singlet at the multireference level

In previous studies (West et al. in J Phys Chem A 113(45):12663, 2009; West et al. in Theor Chem Acc 131:1123, 2012), the lowest-lying O(3P) + C2H4 and singlet PES near the ·CH2CH2O· biradical were extensively explored at several levels of theory. In this work, the lowest-lying O(1D) + C2H4 PES is further examined at the multiconfigurational self-consistent field (MCSCF), MRMP2, CR-CC(2,3), GVB-PP, and MR-AQCC levels. This study aims to provide a detailed comparison of these different levels of theory for this particular system. In particular, many reactions for this system involve multiple bond rearrangements and require various degrees of both non-dynamic and dynamic correlation for reasonable energetics. As a result of this variety, coupled cluster results parallel but do not always match up with multireference results as previously anticipated. In the case of the CH2CHOH → oxirane pathway, MCSCF results show the possibility of a two-step mechanism rather than an elementary step, but the case is very difficult to elucidate. In the case of the CH3C:–OH → H2CCO + H2 pathway, a non-traditional NEB MEP at the GVB-PP level and MR-AQCC stationary point determination illustrate the need for a complex treatment of this surface.

Empirical Correction of Nondynamical Correlation Energy for Density Functionals

To provide an efficient means to address nondynamical correlation, an empirical correction for single and double hybrid density functionals has been formulated. The correction utilizes the highest doubly occupied, lowest unoccupied, and singly occupied generalized Kohn-Sham orbitals and, for potential energy curves, a few additional strongly correlated orbitals. Utilizing proposed nondynamical correlation corrections, hybrid BLYP predicted potential energy curves that fit well to those obtained by ab initio multireference methods for the torsional rotation of ethylene and the automerization of cyclobutadiene. The empirical nondynamical correlation corrections, calculated at the transition structures, also reduce the overall errors of B2K-PLYP for the DBH24 and BH76 barrier height data sets. The proposed empirical correction can efficiently enhance the utility of both single and double hybrid density functionals for chemical situations with moderate to significant nondynamical correlation.

Can ORMAS be used for nonadiabatic coupling calculations? SiCH4 and butadiene contours

When appropriately used, the multiconfigurational self-consistent field (MCSCF) approximation is useful in discerning correct electronic structure results. However, with the increasing size of chemical systems of interest, MCSCF rapidly becomes unfeasible due to the requirement of larger active spaces, which lead to computationally unmanageable numbers of configurations. This situation is especially true for complete active space self-consistent field (CASSCF). In particular, reducing this computational expense by using restricted active spaces in solving for gradients and nonadiabatic couplings (NACs) during dynamics runs would save computer time. However, the validity of such restricted spaces is not well-known even for recovering the majority of the nondynamical correlation and inevitably varies between chemical systems across a range of nuclear geometries. As such, we use the recently implemented coupled perturbed–occupation restricted multiple active space (CP-ORMAS) equations (West et al., unpublished) to verify the accuracy of this approximation for gradients and NACs vectors around two specific conical intersection geometries for the silaethylene and butadiene systems. Overall, no excitations between appropriate subspaces show qualitatively reasonable results while single excitations significantly improve ORMAS results relative to the CASSCF level in these particular systems. However, single excitation schemes do not always lead to the correct orbital subspaces, and as a result, seemingly smooth potential energy surfaces (PES) do not always result in smooth analytical gradients and NACs. In addition, while some of the single excitation ORMAS and CASSCF schemes have improper orbitals rotate into the active space, the schemes without excitations (even with more subspaces) do not exhibit this behavior.