Correlated Wave Function Calculations Research Articles

Progress towards understanding ultranonlocality through the wave-vector and frequency dependence of approximate exchange-correlation kernels

In the framework of time-dependent density functional theory (TDDFT), the exact exchange-correlation (xc) kernel $f_{xc}(n,q,\omega)$ determines the ground-state energy, excited-state energies, lifetimes, and the time-dependent linear density response of any many-electron system. The recently developed MCP07 xc kernel $f_{xc}(n,q,\omega)$ of A. Ruzsinszky et al. [Phys. Rev. B 101, 245135 (2020)] yields excellent uniform electron gas (UEG) ground-state energies and plausible plasmon lifetimes. As MCP07 is constructed to describe $f_{xc}$ of the UEG, it cannot capture optical properties of real materials. To verify this claim, we follow Nazarov et al. [Phys. Rev. Lett. 102, 113001 (2009)] to construct the long-range, dynamic xc kernel, $\lim_{q\to 0}f_{xc}(n,q,\omega) = -\alpha(\omega)e^2/q^2$, of a weakly inhomogeneous electron gas, using MCP07 and other common xc kernels. The strong wavevector and frequency dependence of the "ultranonlocality" coefficient $\alpha(\omega)$ is demonstrated for a variety of simple metals and semiconductors. We examine how imposing exact constraints on an approximate kernel shapes $\alpha(\omega)$. Comparisons to kernels derived from correlated-wavefunction calculations are drawn.

5-Methoxyquinoline Photobasicity Is Mediated by Water Oxidation.

A mechanism explaining the photobasicity of 5-methoxyquinoline (5-MeOQ) is proposed on the basis of nonadiabatic molecular dynamics simulations using time-dependent hybrid density functional theory (TDDFT) and fewest switches surface hopping (SH) and analysis of existing ultrafast spectroscopy experiments. According to the TDDFT-SH simulations, the rate-determining step is hole transfer from photoexcited 5-MeOQ to adjacent water molecules within ∼5 ps followed by rapid electron-coupled proton transfer and deactivation to the ground state. This fast redox-catalyzed proton transfer mechanism is consistent with simple thermodynamic arguments, correlated wavefunction calculations, and recent isotope substitution time-resolved fluorescence experiments. Although energetically feasible, direct protonation of 5-MeOQ in the S1 state appears to be too slow to contribute significantly to 5-MeOQ photobasicity in aqueous solution.

Subspace Density Matrix Functional Embedding Theory: Theory, Implementation, and Applications to Molecular Systems.

We introduce the subspace density matrix functional embedding theory (sDMFET), in which optimization of the nonlocal embedding potential and subsequent embedded correlated wave function calculations are carried out within a truncated subspace determined by a Schmidt decomposition. As compared to the original density matrix functional embedding theory [K. Yu and E. A. Carter, Proceedings of the National Academy of Sciences 2017 , 114 , E10861 ], the computational cost of sDMFET is significantly reduced while the accuracy is preserved. We perform test calculations for both covalently and noncovalently bound molecular systems to demonstrate the feasibility of our theory.

A toolchain for the automatic generation of computer codes for correlated wavefunction calculations.

In this work, the automated generator environment for ORCA (ORCA-AGE) is described. It is a powerful toolchain for the automatic implementation of wavefunction-based quantum chemical methods. ORCA-AGE consists of three main modules: (1) generation of "raw" equations from a second quantized Ansatz for the wavefunction, (2) factorization and optimization of equations, and (3) generation of actual computer code. We generate code for the ORCA package, making use of the powerful functionality for wavefunction-based correlation calculations that is already present in the code. The equation generation makes use of the most elementary commutation relations and hence is extremely general. Consequently, code can be generated for single reference as well as multireference approaches and spin-independent as well as spin-dependent operators. The performance of the generated code is demonstrated through comparison with efficient hand-optimized code for some well-understood standard configuration interaction and coupled cluster methods. In general, the speed of the generated code is no more than 30% slower than the hand-optimized code, thus allowing for routine application of canonical ab initio methods to molecules with about 500-1000 basis functions. Using the toolchain, complicated methods, especially those surpassing human ability for handling complexity, can be efficiently and reliably implemented in very short times. This enables the developer to shift the attention from debugging code to the physical content of the chosen wavefunction Ansatz. Automatic code generation also has the desirable property that any improvement in the toolchain immediately applies to all generated code. © 2017 Wiley Periodicals, Inc.

Ammonia-modified Co(II) sites in zeolites: spin and electron density redistribution through the Co(II)-NO bond.

Electronic factors essential for the bonding of a non-innocent NO ligand to ammonia-modified Co(2+) sites in cobalt-exchanged zeolites are examined for small cluster models using DFT and advanced correlated wave function calculations. The analysis of charge transfer processes between the NO ligand and the cobalt center involves two protocols: valence-bond expansion of the multiconfiguration CASSCF wave function (in terms of fragment-localized active orbitals) and spin-resolved natural orbitals for chemical valence (SR-NOCV). Applicability of SR-NOCV analysis to transition metal complexes involving non-innocent fragments is critically assessed and the approach based on the CASSCF wave function turns out to be much more robust and systematic for all studied models. It is shown that the character and direction of electron density redistribution through the Co-N-O bond, quantified by relative share of the Co(II)-NO(0), Co(III)-NO(-), and Co(I)-NO(+) resonance structures in the total wave function, fully rationalize the activation of the N-O bond upon NH3 co-ligation (evidenced by calculated and measured red-shift of the NO stretching frequency and commonly ascribed to enhanced backdonation). The huge red-shift of νN-O is attributed to an effective electron transfer between the ammonia-modified Co(ii) centers and the NO antibonding π*-orbitals (related to the increased share of the Co(III)-NO(-) form). Unexpectedly, the effect is stronger for the singlet complex with three NH3 ligands than for that with five NH3 ligands bound to the cobalt center. Our results also indicate that high-efficiency electron transfers between the Co(ii) center and the NO ligand may be enabled for the selected spin state and disabled for the other spin state of the adduct. This illustrates how the cobalt center may serve to fine-tune the electronic communication between the NO ligand and its binding site.

Biofuel Combustion. Energetics and Kinetics of Hydrogen Abstraction from Carbon-1 inn-Butanol by the Hydroperoxyl Radical Calculated by Coupled Cluster and Density Functional Theories and Multistructural Variational Transition-State Theory with Multidimensional Tunneling

Multistructural canonical variational transition-state theory with small-curvature multidimensional tunneling (MS-CVT/SCT) is employed to calculate thermal rate constants for hydrogen-atom abstraction from carbon-1 of n-butanol by the hydroperoxyl radical over the temperature range 250-2000 K. The M08-SO hybrid meta-GGA density functional was validated against CCSD(T)-F12a explicitly correlated wave function calculations with the jul-cc-pVTZ basis set. It was then used to compute the properties of all stationary points and the energies and Hessians of a few nonstationary points along the reaction path, which were then used to generate a potential energy surface by the multiconfiguration Shepard interpolation (MCSI) method. The internal rotations in the transition state for this reaction (like those in the reactant alcohol) are strongly coupled to each other and generate multiple stable conformations, which make important contributions to the partition functions. It is shown that neglecting to account for the multiple-structure effects and torsional potential anharmonicity effects that arise from the torsional modes would lead to order-of-magnitude errors in the calculated rate constants at temperatures of interest in combustion.

What are the most efficient basis set strategies for correlated wave function calculations of reaction energies and barrier heights?

As electronic structure methods are being used to obtain quantitatively accurate reaction energies and barrier heights for increasingly larger systems, the choice of an efficient basis set is becoming more critical. The optimum strategy for achieving basis set convergence can depend on the way that electron correlation is treated and can take advantage of flexibility in the order in which basis functions are added. Here we study several approaches for estimating accurate reaction energies and barrier heights from post-Hartree-Fock electronic structure calculations. First and second, we evaluate methods of estimating the basis set limit of second order Møller-Plesset perturbation theory and of coupled cluster theory with single and double excitations and a quasiperturbative treatment of connected triple excitations by using explicitly correlated basis functions (in the F12a implementation) along with valence, polarization, and diffuse one-electron basis functions. Third, we test the scheme of adding a higher-order correction to MP2 results (sometimes called MP2∕CBS + ΔCCSD(T)). Finally, we evaluate the basis set requirements of these methods in light of comparisons to Weizmann-3.2, Weizmann-4, and CCSDT(2)(Q)∕CBS+CV+R results.

Auxiliary basis sets for density-fitted correlated wavefunction calculations: weighted core-valence and ECP basis sets for post-d elements

We report optimised auxiliary basis sets for the resolution-of-the-identity (or density-fitting) approximation of two-electron integrals in second-order Møller-Plesset perturbation theory (MP2) and similar electronic structure calculations with correlation-consistent basis sets for the post-d elements Ga-Kr, In-Xe, and Tl-Rn. The auxiliary basis sets are optimised such that the density-fitting error is negligible compared to the one-electron basis set error. To check to which extent this criterion is fulfilled we estimated for a test set of 80 molecules the basis set limit of the correlation energy at the MP2 level and evaluated the remaining density-fitting and the one-electron basis set errors. The resulting auxiliary basis sets are only 2-6 times larger than the corresponding one-electron basis sets and lead in MP2 calculations to speed-ups of the integral evaluation by one to three orders of magnitude. The density-fitting errors in the correlation energy are at least hundred times smaller than the one-electron basis set error, i.e. in the order of only 1-100 μH per atom.

Pople Style Basis Sets for the Calculation of NMR Spin-Spin Coupling Constants: the 6-31G-J and 6-311G-J Basis Sets.

We present a modification of the small and popular Pople basis sets, 6-31G and 6-311G, for density functional theory calculations of Fermi contact dominated NMR indirect nuclear spin-spin coupling constants. These new basis sets, 6-31G-J and 6-311G-J, contain twice the number of contracted s-type functions but the same number of contracted p-type functions as the original Pople basis set. For our test set of 12 one-, two- and three-bond coupling constants, the new basis sets augmented with the standard diffuse and polarization functions, i.e., the 6-31+G*-J and 6-311++G**-J basis sets, lead to a maximum deviation of 5 and 2 Hz, respectively, compared to results obtained with the 6 or more times larger aug-pcJ-4 basis set. In correlated wave function calculations using the second-order polarization propagator approximation, the deviations with respect to the aug-ccJ-pVQZ basis set are 8 and 3 Hz and thus slightly larger.

Local orbitals by minimizing powers of the orbital variance

It is demonstrated that a set of local orthonormal Hartree-Fock (HF) molecular orbitals can be obtained for both the occupied and virtual orbital spaces by minimizing powers of the orbital variance using the trust-region algorithm. For a power exponent equal to one, the Boys localization function is obtained. For increasing power exponents, the penalty for delocalized orbitals is increased and smaller maximum orbital spreads are encountered. Calculations on superbenzene, C(60), and a fragment of the titin protein show that for a power exponent equal to one, delocalized outlier orbitals may be encountered. These disappear when the exponent is larger than one. For a small penalty, the occupied orbitals are more local than the virtual ones. When the penalty is increased, the locality of the occupied and virtual orbitals becomes similar. In fact, when increasing the cardinal number for Dunning's correlation consistent basis sets, it is seen that for larger penalties, the virtual orbitals become more local than the occupied ones. We also show that the local virtual HF orbitals are significantly more local than the redundant projected atomic orbitals, which often have been used to span the virtual orbital space in local correlated wave function calculations. Our local molecular orbitals thus appear to be a good candidate for local correlation methods.

Revisiting the Atomic Natural Orbital Approach for Basis Sets: Robust Systematic Basis Sets for Explicitly Correlated and Conventional Correlated ab initio Methods?

The performance of several families of basis sets for correlated wave function calculations on molecules is studied. The widely used correlation-consistent basis set family cc-pVXZ (n = D, T, Q, 5) is compared to a systematic series of atomic natural orbital basis sets (ano-pVXZ). These basis sets are built from the cc-pV6Z primitives in atomic multireference average coupled pair functional (MR-ACPF) calculations. Segmented basis sets optimized for self-consistent field calculations (def2-SVP, def2-TZVPP, and def2-QZVPP as well as "pc-n", n = 1, 2, 3) were also tested. Reference Hartree-Fock energies are determined with the uncontracted aug-cc-pV6Z basis set for a set of 21 small molecules built from H, B, C, N, O, and F. Reference coupled cluster CCSD(T) correlation energies were determined from extrapolation at the cc-pV5Z/cc-pV6Z level. It is found that the ano-pVXZ basis sets outperform the other basis sets. The error in the SCF energies compared to cc-pVXZ basis sets is reduced by about a factor of 3 at each cardinal number. In addition, the ano-pVXZ consistently recovers more correlation energy than their competitors at each cardinal number. The ability of the four families of basis sets to extrapolate SCF and correlation energies to the basis set limit has been investigated. A conclusion by Truhlar is confirmed that the optimum exponent for correlation energy extrapolations at the DZ/TZ level is ∼2.4. All TZ/QZ basis set pairs lead to an optimum exponent close to the expected value of 3. The SCF energy extrapolation proposed by Petersson and co-workers is found to be effective. At the DZ/TZ level, errors in total energies of less than 2 mEh are found for the test set, while at the TZ/QZ level one obtains the total energies within ∼0.3 mEh of the basis set limit. For extrapolation, the "cc" and "ano" bases are found to be similarly successful. Extrapolation results were compared to explicitly correlated calculations with dedicated basis sets (cc-pVXZ-F12) as well as the ano-pVXZ bases. It is found that the ano-pVXZ+ basis sets perform as well as the cc-pVXZ-F12 family (both are of comparable size); additional improvement should be possible by reoptimizing the ANO basis sets for explicitly correlated calculations. The error of the extrapolated energies is about 2-3 times smaller than what was found in the explicitly correlated calculations. However, the error in the explicitly correlated calculations is more systematic, and hence the same conclusion may not hold for the computation of energy differences.

Efficient Diffuse Basis Sets: cc-pVxZ+ and maug-cc-pVxZ.

We combine the diffuse basis functions from the 6-31+G basis set of Pople and co-workers with the correlation-consistent basis sets of Dunning and co-workers. In both wave function and density functional calculations, the resulting basis sets reduce the basis set superposition error almost as much as the augmented correlation-consistent basis sets, although they are much smaller. In addition, in density functional calculations the new basis sets, called cc-pVxZ+ where x = D, T, Q, ..., or x = D+d, T+d, Q+d, ..., give very similar energetic predictions to the much larger aug-cc-pVxZ basis sets. However, energetics calculated from correlated wave function calculations are more slowly convergent with respect to the addition of diffuse functions. We also examined basis sets with the same number and type of functions as the cc-pVxZ+ sets but using the diffuse exponents of the aug-cc-pVxZ basis sets and found very similar performance to cc-pVxZ+; these basis sets are called minimally augmented cc-pVxZ, which we abbreviate as maug-cc-pVxZ.

Efficient Diffuse Basis Sets: cc-pVxZ+ and maug-cc-pVxZ.

We combine the diffuse basis functions from the 6-31+G basis set of Pople and co-workers with the correlation-consistent basis sets of Dunning and co-workers. In both wave function and density functional calculations, the resulting basis sets reduce the basis set superposition error almost as much as the augmented correlation-consistent basis sets, although they are much smaller. In addition, in density functional calculations the new basis sets, called cc-pVxZ+ where x = D, T, Q, ..., or x = D+d, T+d, Q+d, ..., give very similar energetic predictions to the much larger aug-cc-pVxZ basis sets. However, energetics calculated from correlated wave function calculations are more slowly convergent with respect to the addition of diffuse functions. We also examined basis sets with the same number and type of functions as the cc-pVxZ+ sets but using the diffuse exponents of the aug-cc-pVxZ basis sets and found very similar performance to cc-pVxZ+; these basis sets are called minimally augmented cc-pVxZ, which we abbreviate as maug-cc-pVxZ.

Local Electronic Structure around a Single Kondo Impurity

The local electronic structure due to the adsorption of Co on Cu111 is studied using an embedded cluster model, in which the crystal background is taken into account via an effective density functional theory (DFT)-based potential. This approach goes beyond the usual single-impurity Anderson model, where the ground state consists of a singly occupied impurity whose moment is compensated by the background conduction electrons. Ab initio correlated wave function calculations for the embedded cluster provide an alternative picture for this ground state and indicate that the quenching of the Co magnetic moment is due to the formation of metal-metal bonds with the Cu substrate. Low-lying excitations are also studied within the embedding model, and our results are discussed in the context of scanning tunneling microscopy experiments (Manoharan, H. C.; Lutz, C. P.; Eigler, D. M. Nature 2000, 403, 512), which find a sharp tunneling resonance localized in the vicinity of the Co adatom.

Ab initio determination of the rate coefficient for radiative association of

Abstract The interaction potential and electric dipole moment function of the collisional system He ( 1 S ) + H + are calculated at the configuration interaction level of theory using canonical SCF orbitals as orbital basis and employing large atomic basis sets of different flexibility. All the rotation-vibration bound states and rotationally quasi-bound resonance states as well as the corresponding free-bound dipole transition moments are evaluated and used to determine in a rigorous quantum mechanical treatment the rate coefficient for the radiative association He ( 1 S ) + H + → HeH + + hν and its temperature dependence. The results are compared to those obtained in the same way for a highly accurate potential function which is derived from previous directly correlated wavefunction calculations. It turns out that the rate coefficient at low temperatures contains predominantly contributions from a few low-energy resonances which are very sensitive to the shape of the potential and that reliable results thus require extremely accurate interaction potentials. At higher temperatures contributions from the large number of non-resonant continuum states become increasingly dominant and the results for the total rate coefficient are therefore less affected by small changes in the potential function.

The cyclic ozone isomer

Analysis of basis set effects in large correlated wave function calculations is undertaken in relation to the energy separation of the cyclic (D3h) and open (C2v) forms of ozone. The present calculations attain some 60% of the valence correlation energy of ozone with the largest bases, superseding a number of recent investigations of the D3h−C2v separation. The conclusion is reached that these species are isomers corresponding to different local minima on the ground state surface, below the ozone dissociation limit. The energy separation of these species is narrowed down to 40–88 kJ/mol, with the likeliest value, 50±kJ/mol, emerging from the present calculations (’’doulbe zeta plus polarization’’ is in error ∼25 kJ/mol). The formation and implications of the secondary D3h ozone isomer are briefly discussed.

Molecular correlation integrals. Two center one electron integrals containing a function of interparticle distance in one center expansion approximation

AbstractTwo‐center one‐electron integrals needed in certain molecular correlated wave function calculations, using one‐center expansion approximation, have been studied. The form of the basic correlated function used in this study is The parent integral is expressed in terms of an angular integral, and an auxiliary radial integral depending upon the variables r1, r2, and r12. Several analytical formulas, and a recursive formula are derived for the auxiliary integral, and other related integrals. All these formulas are given in computationally useful forms. Logical flow charts and FORTRAN programs were constructed for computing the basic integrals discussed in the paper. Numerical values of some integrals, thus obtained, are tabulated for comparisons.