High-level Wave Function Methods Research Articles

The Best Models of Bodipy's Electronic Excited State: Comparing Predictions from Various DFT Functionals with Measurements from Femtosecond Stimulated Raman Spectroscopy.

Density functional theory (DFT) and time-dependent DFT (TD-DFT) are pivotal approaches for modeling electronically excited states of molecules. However, choosing a DFT exchange-correlation functional (XCF) among the myriad of alternatives is an overwhelming task that can affect the interpretation of results and lead to erroneous conclusions. The performance of these XCFs to describe the excited-state properties is often addressed by comparing them with high-level wave function methods or experimentally available vertical excitation energies; however, this is a limited analysis that relies on evaluation of a single point in the excited-state potential energy surface (PES). Different strategies have been proposed but are limited by the difficulty of experimentally accessing the electronic excited-state properties. In this work, we have tested the performance of 12 different XCFs and TD-DFT to describe the excited-state potential energy surface of Bodipy (2,6-diethyl-1,3,5,7-tetramethyl-8-phenyldipyrromethene difluoroborate). We compare those results with resonance Raman spectra collected by using femtosecond stimulated Raman spectroscopy (FSRS). By simultaneously fitting the absorption spectrum, fluorescence spectrum, and all of the resonance Raman excitation profiles within the independent mode displaced harmonic oscillator (IMDHO) formalism, we can describe the PES at the Franck-Condon (FC) region and determine the solvent and intramolecular reorganization energy after relaxation. This allows a direct comparison of the TD-DFT output with experimental observables. Our analysis reveals that using vertical absorption energies might not be a good criterion to determine the best XCF for a given molecular system and that FSRS opens up a new way to benchmark the excited-state performance of XCFs of fluorescent dyes.

Geometries and vibrational frequencies with Kohn-Sham methods using σ-functionals for the correlation energy.

Recently, Kohn-Sham (KS) methods with new correlation functionals, called σ-functionals, have been introduced. Technically, σ-functionals are closely related to the well-known random phase approximation (RPA); formally, σ-functionals are rooted in perturbation theory along the adiabatic connection. If employed in a post-self-consistent field manner in a Gaussian basis set framework, then, σ-functional methods are computationally very efficient. Moreover, for main group chemistry, σ-functionals are highly accurate and can compete with high-level wave-function methods. For reaction and transition state energies, e.g., chemical accuracy of 1 kcal/mol is reached. Here, we show how to calculate first derivatives of the total energy with respect to nuclear coordinates for methods using σ-functionals and then carry out geometry optimizations for test sets of main group molecules, transition metal compounds, and non-covalently bonded systems. For main group molecules, we additionally calculate vibrational frequencies. σ-Functional methods are found to yield very accurate geometries and vibrational frequencies for main group molecules superior not only to those from conventional KS methods but also to those from RPA methods. For geometries of transition metal compounds, not surprisingly, best geometries are found for RPA methods, while σ-functional methods yield somewhat less good results. This is attributed to the fact that in the optimization of σ-functionals, transition metal compounds could not be represented well due to the lack of reliable reference data. For non-covalently bonded systems, σ-functionals yield geometries of the same quality as the RPA or as conventional KS schemes combined with dispersion corrections.

Toward chemical accuracy at low computational cost: Density-functional theory with σ-functionals for the correlation energy.

We introduce new functionals for the Kohn-Sham correlation energy that are based on the adiabatic-connection fluctuation-dissipation (ACFD) theorem and are named σ-functionals. Like in the well-established direct random phase approximation (dRPA), σ-functionals require as input exclusively eigenvalues σ of the frequency-dependent KS response function. In the new functionals, functions of σ replace the σ-dependent dRPA expression in the coupling-constant and frequency integrations contained in the ACFD theorem. We optimize σ-functionals with the help of reference sets for atomization, reaction, transition state, and non-covalent interaction energies. The optimized functionals are to be used in a post-self-consistent way using orbitals and eigenvalues from conventional Kohn-Sham calculations employing the exchange-correlation functional of Perdew, Burke, and Ernzerhof. The accuracy of the presented approach is much higher than that of dRPA methods and is comparable to that of high-level wave function methods. Reaction and transition state energies from σ-functionals exhibit accuracies close to 1 kcal/mol and thus approach chemical accuracy. For the 10 966 reactions of the W4-11RE reference set, the mean absolute deviation is 1.25 kcal/mol compared to 3.21 kcal/mol in the dRPA case. Non-covalent binding energies are accurate to a few tenths of a kcal/mol. The presented approach is highly efficient, and the post-self-consistent calculation of the total energy requires less computational time than a density-functional calculation with a hybrid functional and thus can be easily carried out routinely. σ-Functionals can be implemented in any existing dRPA code with negligible programming effort.

Deriving the vibronic coupling constants of the cyclopentadienyl radical with density functional theory and G0W0.

The vibronic coupling constants of the cyclopentadienyl radical have been calculated with G0W0, HF, and density functional theory (DFT) with various exchange-correlation functionals such as PBE, PBE0, LC-ωPBE, and the non-empirically tuned LC-ωPBE*. The vibronic coupling constants for HF and DFT were derived using the gradients of the eigenvalues of the degenerate HOMOs of the closed-shell cyclopentadienyl anion, while the gradients of the corresponding quasiparticle energy levels were used in the case of G0W0. The differences between the linear vibronic constants obtained using HF and DFT were found to be small and reduced further when the G0W0 correction is applied to HF and DFT. Finally, the linear vibronic coupling constants calculated with G0W0 were found to agree well with the values obtained using high level wave function methods in the literature, which suggests that G0W0 can be a useful tool toward the study of vibronic coupling.

The CUAGAU Set of Coupled-Cluster Reference Data for Small Copper, Silver, and Gold Compounds and Assessment of DFT Methods.

We have obtained benchmark data for a set of small molecular systems of Cu, Ag, and Au using coupled-cluster methods. Using this collection of reference data (that we termed the CUAGAU set) for assessing DFT-type methods, we find the MN15-L nonhybrid DFT to be cost-effective for geometry optimization [mean absolute deviation (MAD) in bond length = 0.20 Å], with an accuracy that is comparable to that for the double-hybrid (DH) DFT method DSD-PBEP86 (MAD = 0.19 Å). For the computation of thermochemical properties, among "conventional" (non-MP2-based) DFT methods, the best performance is found for the global-hybrid meta-GGA functional MN15, with an MAD of 11.4 kJ mol-1. We also find the nonhybrid method B97M-rV to have a reasonable performance (MAD = 14.4 kJ mol-1), and it may serve as a cost-effective means for qualitative study. If we look beyond conventional functionals, we find DSD-PBEP86 (MAD = 7.3 kJ mol-1) to be more accurate than even MN15. Nonetheless, this level of accuracy is still not sufficient for quantitative studies. In this regard, high-level wave function methods such as composite procedures that are based on coupled cluster are still indispensable for obtaining reliable reference data for transition-metal species.

Charge transfer excitation energies from ground state density functional theory calculations.

Calculating charge transfer (CT) excitation energies with high accuracy and low computational cost is a challenging task. Kohn-Sham density functional theory (KS-DFT), due to its efficiency and accuracy, has achieved great success in describing ground state problems. To extend to excited state problems, our group recently demonstrated an approach with good numerical results to calculate low-lying and Rydberg excitation energies of an N-electron system from a ground state KS or generalized KS calculations of an (N - 1)-electron system via its orbital energies. In the present work, we explore further the same methodology to describe CT excitations. Numerical results from this work show that performance of conventional density functional approximations (DFAs) is not as good for CT excitations as for other excitations due to the delocalization error. Applying localized orbital scaling correction (LOSC) to conventional DFAs, a recently developed method in our group to effectively reduce the delocalization error, can improve the results. Overall, the performance of this methodology is better than time dependent DFT (TDDFT) with conventional DFAs. In addition, it shows that results from LOSC-DFAs in this method reach similar accuracy to other methods, such as ΔSCF, G0W0 with Bethe-Salpeter equations, particle-particle random phase approximation, and even high-level wavefunction methods like CC2. Our analysis shows that the correct 1/R trend for CT excitation can be captured from LOSC-DFA calculations, stressing that the application of DFAs with the minimal delocalization error is essential within this methodology. This work provides an efficient way to calculate CT excitation energies from ground state DFT.

The Electronic Structure of [Mn(V)═O]: What is the Connection between Oxyl Radical Character, Physical Oxidation State, and Reactivity?

MnV═O functionalities are important in synthetic and bioinorganic chemistry, being relevant to both C–H activation and the O–O bond formation steps in enzymatic water oxidation, for example. The triplet and quintet spin states are believed to be active in these reactions, but they have only been sparingly characterized experimentally. Density functional theory (DFT) gives varying results, depending on the exchange-correlation functional employed, leading to ambiguity about whether the triplet MnV═O is better represented as MnIV–O•. While recent CASPT2 studies confirmed that the MnIV–O• character is exaggerated by hybrid functionals, questions still remain about the nature of this bonding. Using high-level wave function methods, we investigated the fundamental relationship between the spin polarization, diradical character, and the physical oxidation state assignments. We conclude that, in terms of formal oxidation assignment, these species are best described as being between the MnV═O and MnIV–O• extremes...

Spin-State Energetics of Fe(III) and Ru(III) Aqua Complexes: Accurate ab Initio Calculations and Evidence for Huge Solvation Effects.

Aqua complexes of transition metals are useful models for understanding the electronic structure of metal-oxide species relevant in photocatalytic water splitting. Moreover, spin-forbidden d-d transitions of aqua complexes provide valuable experimental data of spin-state energetics, which can be used for benchmarking of computational methods. Here, low-energy spin states of Fe(III) and Ru(III) aqua complexes are studied with an array of DFT and high-level wave function methods (CASPT2, RASPT2, NEVPT2, CCSD(T)-F12, and other coupled cluster methods up to full CCSDT). The results from single-reference and multireference methods are cross-checked, and the amount of multireference character for both considered spin states of [Fe(H2O)6](3+) is carefully analyzed. In addition to small [M(H2O)6](3+) clusters (M = Fe, Ru), we also employ larger models [M(H2O)6·(H2O)12](3+), with explicit water molecules in the second coordination sphere, to describe the situation in aqueous solution. By comparing the results for both types of models, our calculations evidence large and systematic solvation effects on the spin-state energetics. It is found that, due to the interaction with hydrogen-bonded water molecules in the second coordination sphere, the first coordination sphere undergoes a noticeable contraction and deformation. In consequence, the presence of solvation shell affects the relative energies of spin states by as much as 3-4 × 10(3) cm(-1) (∼10 kcal/mol). Once this solvation effect is accounted for, the spin-state energetics from CCSD(T) and NEVPT2 calculations turn out to be in an excellent agreement with the experimental estimates, which was not the case for isolated [M(H2O)6](3+) species is gas phase. We thus postulate that significant discrepancies between theory and experimental data for [Fe(H2O)6](3+) that were previously reported in the literature may be plausibly resolved and attributed to the neglect of explicit solvation effects and also, to some extent, to incompleteness of the active space and/or basis set used in the previous theoretical studies. The findings of this work contradict an anecdotal conjecture that energies of ligand-field (d-d) transitions are almost unaffected by solvation. On the contrary, it is highlighted that medium effects may contribute very significantly to spin-state energetics of transition metal complexes.

Quantum Chemical Benchmark Study on 46 RNA Backbone Families Using a Dinucleotide Unit

We have created a benchmark set of quantum chemical structure-energy data denoted as UpU46, which consists of 46 uracil dinucleotides (UpU), representing all known 46 RNA backbone conformational families. Penalty-function-based restrained optimizations with COSMO TPSS-D3/def2-TZVP ensure a balance between keeping the target conformation and geometry relaxation. The backbone geometries are close to the clustering-means of their respective RNA bioinformatics family classification. High-level wave function methods (DLPNO-CCSD(T) as reference) and a wide-range of dispersion-corrected or inclusive DFT methods (DFT-D3, VV10, LC-BOP-LRD, M06-2X, M11, and more) are used to evaluate the conformational energies. The results are compared to the Amber RNA bsc0χOL3 force field. Most dispersion-corrected DFT methods surpass the Amber force field significantly in accuracy and yield mean absolute deviations (MADs) for relative conformational energies of ∼0.4-0.6 kcal/mol. Double-hybrid density functionals represent the most accurate class of density functionals. Low-cost quantum chemical methods such as PM6-D3H+, HF-3c, DFTB3-D3, as well as small basis set calculations corrected for basis set superposition errors (BSSEs) by the gCP procedure are also tested. Unfortunately, the presently available low-cost methods are struggling to describe the UpU conformational energies with satisfactory accuracy. The UpU46 benchmark is an ideal test for benchmarking and development of fast methods to describe nucleic acids, including force fields.

The performance of density functional approximations for the structures and relative energies of minimum energy crossing points

The structural parameters and relative energies of the minimum-energy crossing points (MECPs) of eight small molecules are calculated using five different representative density functional theory approximations as well as MP2, MP4, and CCSD(T) as a reference. Compared to high-level wavefunction methods, the main structural features of the MECPs of the systems included in this Letter are reproduced reasonably well by density functional approximations, in agreement with previous works. Our results show that when high-level wavefunction methods are computationally prohibitive, density functional approximations offer a good alternative for locating and characterizing the MECP in spin-forbidden chemical reactions.

The effects of perfluorination on carbohydrate–π interactions: computational studies of the interaction of benzene and hexafluorobenzene with fucose and cyclodextrin

The effect of benzene fluorination on C-H...pi interactions is studied using a number of computational methods applied to a range of intermolecular complexes. High level wavefunction methods (CCSD(T)) predict a slightly greater interaction energy for complexes of benzene with methane or fucose, compared to corresponding complexes involving hexafluorobenzene. A number of more approximate treatments, DFT with the M06-2X functional, PM3-D* and MM methods, give interaction energies within 1 kcal mol(-1) of the high level values, and also correctly predict that the interaction energy is slightly greater for benzene compared to hexafluorobenzene. However, the DFT-D model used here predicts that the interaction energy is slightly greater for hexafluorobenzene. Molecular dynamics simulations, employing the GLYCAM-06 force field, validated here, are used to model the complexes of benzene and hexafluorobenzene with beta-cyclodextrin in aqueous solution. We predict the binding free energies of the complexes to be within 0.5 kcal mol(-1), and suggest that the different chemical shifts of the H5 protons observed in the two complexes arise from their slightly different structures, rather than from different binding energies.

Application of high level wavefunction methods in quantum mechanics/molecular mechanics hybrid schemes

In this Perspective, several developments in the field of quantum mechanics/molecular mechanics (QM/MM) approaches are reviewed. Emphasis is placed on the use of correlated wavefunction theory and new state of the art methods for the treatment of large quantum systems. Until recently, computational chemistry approaches to large/complex chemical problems have seldom been considered as tools for quantitative predictions. However, due to the tremendous development of computational resources and new quantum chemical methods, it is nowadays possible to describe the electronic structure of biomolecules at levels of theory which a decade ago were only possible for system sizes of up to 20 atoms. These advances are here outlined in the context of QM/MM. The article concludes with a short outlook on upcoming developments and possible bottlenecks for future applications.

Revisiting Molecular Dissociation in Density Functional Theory: A Simple Model.

A two-electron one-dimensional model of a heteroatomic molecule composed of two open-shell atoms is considered. Including only two electrons isolates and examines the effect that the highest occupied molecular orbital has on the Kohn-Sham potential as the molecule dissociates. We reproduce the characteristic step and peak that previous high-level wave function methods have shown to exist for real molecules in the low-density internuclear region. The simplicity of our model enables us to investigate in detail their development as a function of bond-length, with little computational effort, and derive properties of their features in the dissociation limit. We show that the onset of the step is coincident with the internuclear separation at which an avoided crossing between the ground-state and lowest charge-transfer excited-state is approached. Although the step and peak features have little effect on the ground-state energetics, we discuss their important consequences for dynamics and response.

Evaluation of exchange‐correlation functionals in comparison to B3LYP for the description of silicon and Cu‐doped silicon clusters

AbstractSeveral developed exchange‐correlation functionals in density functional theory have been systematically applied to describe the geometries and electronic properties of small silicon (Sin+1, n < 5) and doped silicon (CuSin) clusters. The performance of the various approaches is done with their critical comparison with B3LYP and available high level wave function methods. Our calculations indicate that all functional give reasonable results. Further, OLYP/6‐311+G* approach generally agrees with B3LYP results. The good performance of OLYP is of significant interest knowing that the hybrid functionals are computationally more demanding than nonhybrid schemes. So, we recommend OLYP/6‐311+G* approach for studying the doped silicon clusters and understanding the electronic properties of silicon by the presence of doped metal impurities. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

Predicting proton transfer barriers with density functional methods

We study the ability of recently developed exchange-correlation functionals to model proton transfer in the H 5O 2 + model for water and in malonaldehyde. We are particularly interested in assessing the accuracy of the VSXC functional developed in our research group and compare it to other hybrid functionals and high-level wavefunction methods like coupled-cluster theory. We find that VSXC and the hybrid functionals all underestimate proton transfer barriers for H 5O 2 + but still give a good sense of the overall nature of the potential energy surface. In malonaldehyde, only VSXC produces a proton transfer activation barrier similar to those provided by high-level coupled-cluster methods.