A benchmark quantum Monte Carlo study of the ground state chromium dimer

We report calculations of the ground state energy and binding curve of the chromium dimer using the variational and diffusion quantum Monte Carlo (VMC and DMC) methods. We examined various single‐determinant and multideterminant wavefunctions multiplied by a Jastrow factor as a trial/guiding wavefunction for VMC/DMC. The molecular orbitals in the single determinants were calculated using restricted or unrestricted Hartree–Fock or density functional theory (DFT) calculations where five commonly used local (SVWN5), semilocal (PW91 and BLYP), and hybrid (B1LYP and B3LYP) functionals were examined. The multideterminant expansions were obtained from the generalized valence bond and (truncated) unrestricted configuration interaction with single and double excitations (UCISD) methods. We also examined a UCISD wavefunction in which UCISD expansions were added to the UB3LYP single‐determinant reference, and their coefficients were optimized at the VMC level. In addition to the wavefunction dependence, the effects of pseudopotentials and backflow transformation were also investigated. The UB3LYP single‐determinant and multideterminant wavefunctions were found to give the variationally best DMC energies within the framework of single‐determinant and multideterminants, respectively, though both the DMC energies were higher than twice the DMC atomic energy. Some of the VMC binding curves show a flat or quite shallow well bottom, which gets recovered deeper by DMC. All the DMC binding curves have a minimum indicating a bound state, but the unrestricted ones overestimate the equilibrium bond length. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Performance of DFT hybrid functionals in the theoretical treatment of H‐bonds: Analysis term‐by‐term

The performance of DFT to reproduce noncovalent interactions like H‐bonds was assessed. Three DFT hybrid functionals (B3LYP, BHandHLYP from Jaguar5.5, and BHandHLYP from G03) were used to calculate the interaction energies and H‐bond distances of several host–guest complexes theoretically designed. Two reference systems (whose experimental data were available) were also calculated at the same levels of theory. In all the cases B3LYP and BHandHLYP from G03 gave rather the same results of interaction energy and distances, whereas the functional BHandHLYP from Jaguar5.5 overestimated the interaction energies and underestimated the H‐bond distances. Considering the construction of each functional, the terms responsible for such differences are the gradient correction to the exchange functional (Becke88) and the correlation functional (VWN, LYP) and not the Hartree–Fock contribution. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Electronic structures of 3d-metal mononitrides

Bond distances, vibrational frequencies, electron affinities, ionization potentials, and dissociation energies of the title molecules in neutral, positively, and negatively charged ions were studied by use of density functional methods B3LYP, BLYP, BHLYP, BPW91, and B3PW91. The calculated results are compared with experiments and previous theoretical studies. It was found that the calculated properties are highly dependent on the functionals employed, in particular for the dissociation energy and vibrational frequency. For neutral species, pure density functional methods BLYP and BPW91 have relatively good performance in reproducing the experimental bond distance and vibrational frequency. For cations, hybrid exchange functional methods B3LYP and B3PW91 are good in predicting the dissociation energy. For both neutral and charged species, BHLYP tends to give smaller dissociation energy.     

Electronic structures of 4d transition metal monoxides by density functional theory

Bond distances, dissociation energies, ionization potentials and electron affinities of 4d transition metal monoxides from YO to CdO and their positive and negative ions were studied by use of density functional methods B3LYP, BLYP, B3PW91, BPW91, B3P86, BP86, SVWN, MPW1PW91 and PBE1PBE. It was found that calculated properties are highly dependent on the functionals employed, especially for dissociation energy. For most neutral species, pure density functionals BLYP, BPW91 and BP86 have good performance in predicting dissociation energy than hybrid density functionals B3LYP, B3PW91 and B3P86. In addition, BLYP gives the largest bond distance compared with other density functional methods, while SVWN gives shortest bond distance, largest dissociation energy and electron affinity. For the ground state, the spin multiplicity of the charged species can be obtained by ± 1 of their corresponding neutral species.     

Broken symmetry density functional study of a mixed‐valence unsymmetrical dinuclear iron complex

Density functional theory (DFT) calculations with different exchange‐correlation functionals were performed for a mixed valence Fe(II)/Fe(III) binuclear complex with μ‐methoxo and two μ‐carboxylate bridging ligands, (1) with geometry optimizations being performed for all possible spin multiplicities (M_S = 2, 4, 6, 8, and 10). Within the exchange‐correlation functionals studied, only the hybrid GGA functionals B3P and B3LYP and also the pure GGA functional RPBE, predicts the geometry with high spin (S = 9/2) to be more stable than the geometry with low spin state (S = 1/2) by 20 kcal/mol, in agreement with the experimental findings. These functionals also predict the same stability order for the different spin states, being M_S = 10>8>6>2>4. The meta‐GGA functionals TPSS and TPSSh and also the pure GGA functionals BLYP and BP86 predict different stability orders. The computed average EPR g‐tensor, g_av, of 2.03, at the B3LYP level, is in good agreement with the experimental findings. Heisenberg exchange coupling constants, J, were calculated within the broken‐symmetry formalism, at the B3LYP level, showing that the two iron centers are antiferromagnetic coupling, with a very weak coupling constant of about ?7 cm^?1, in good agreement with the experimental value. Additionally, the effect of using different multiplicities of the reference geometries on the computed J value is discussed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Benchmark calculations on the adiabatic ionization potentials of M-NH(3) (M=Na,Al,Ga,In,Cu,Ag)

The ground states of the M-NH(3) (M=Na,Al,Ga,In,Cu,Ag) complexes and their cations have been studied with density functional theory and coupled cluster [CCSD(T)] methods. The adiabatic ionization potentials (AIPs) of these complexes are calculated, and these are compared to results from high-resolution zero-electron kinetic energy photoelectron spectroscopy. By extrapolating the CCSD(T) energies to the complete basis set (CBS) limit and including the core-valence, scalar relativistic, spin-orbit, and zero-point corrections, the CCSD(T) method is shown to be able to predict the AIPs of these complexes to better than 6 meV or 0.15 kcal/mol. 27 exchange-correlation functionals, including one in the local density approximation, 13 in the generalized gradient approximation (GGA), and 13 with hybrid GGAs, were benchmarked in the calculations of the AIPs. The B1B95, mPW1PW91, B98, B97-1, PBE1PBE, O3LYP, TPSSh, and HCTH93 functionals give an average error of 0.1 eV for all the complexes studied, with the B98 functional alone yielding a maximum error of 0.1 eV. In addition, the calculated metal-ammonia harmonic stretching frequencies with the CCSD(T) method are in excellent agreement with their experimental values, whereas the B3LYP method tends to underestimate these stretching frequencies. The metal-ammonia binding energies were also calculated at the CCSD(T)/CBS level, and are in excellent agreement with the available experimental values considering the error limits, except for Ag-NH(3) and Ag(+)-NH(3), where the calculations predict stronger bond energies than measured by about 4 kcal/mol, just outside the experimental error bars of +/-3 kcal/mol.     

Reaction energy benchmarks of hydrocarbon combustion by Gaussian basis and plane wave basis approaches

The reaction energies of 275 elementary reactions from the hydrocarbon combustion model GRI-Mech 3.0 were evaluated by electronic structure calculations using both localized Gaussian basis and plane wave basis sets. In the Gaussian basis calculations, the d-polarization function on C, N, and O elements reduces the mean absolute deviation (MAD) from the experimental value by 53%, a significant improvement in computational accuracy. In the plane wave basis calculation using different exchange-correlation (XC) functionals, the MAD values were 0.316–0.426 eV when non-hybrid type XC functionals such as RPBE, PBE, PW91, revPBE, and PBEsol were used. On the other hand, hybrid functionals like B3LYP and HSE06 reduced the MAD values significantly down to 0.182 and 0.233 eV, respectively. The B3LYP results have 49% less MAD compared to the PBE results. These demonstrated the strong advantage of the hybrid functional for calculating gas-phase reaction energies. The present comprehensive benchmarks will be crucial for future microkinetics as well as machine learning studies on the catalytic reactions. © 2019 Wiley Periodicals, Inc.     

Assessment of density functionals for the high-spin/low-spin energy difference in the low-spin iron(II) tris(2,2'-bipyridine) complex.

In the iron(II) low-spin complex [Fe(bpy)3]2+, the zero-point energy difference between the 5T2g(t4(2g)e2g) high-spin and the 1A(1g)(t(6)2g) low-spin states, Delta(E)0HL, is estimated to lie in the range of 2500-5000 cm(-1). This estimate is based on the low-temperature dynamics of the high-spin-->low-spin relaxation following the light-induced population of the high-spin state and on the assumption that the bond-length difference between the two states Delta(r)HL is equal to the average value of approximately 0.2 A, as found experimentally for the spin-crossover system. Calculations based on density functional theory (DFT) validate the structural assumption insofar as the low-spin-state optimised geometries are found to be in very good agreement with the experimental X-ray structure of the complex and the predicted high-spin geometries are all very close to one another for a whole series of common GGA (PB86, PW91, PBE, RPBE) and hybrid (B3LYP, B3LYP*, PBE1PBE) functionals. This confirmation of the structural assumption underlying the estimation of Delta(E)0HL from experimental relaxation rate constants permits us to use this value to assess the ability of the density functionals for the calculation of the energy difference between the HS and LS states. Since the different functionals give values from -1000 to 12000 cm(-1), the comparison of the calculated values with the experimental estimate thus provides a stringent criterion for the performance of a given functional. Based on this comparison the RPBE and B3LYP* functionals give the best agreement with experiment.     

Assessment of new meta and hybrid meta density functionals for predicting the geometry and binding energy of a challenging system: the dimer of H2S and benzene

Noncovalent interactions of a hydrogen bond donor with an aromatic pi system present a challenge for density functional theory, and most density functionals do not perform well for this kind of interaction. Here we test seven recent density functionals from our research group, along with the popular B3LYP functional, for the dimer of H 2S with benzene. The functionals considered include the four new meta and hybrid meta density functionals of the M06 suite, three slightly older hybrid meta functionals, and the B3LYP hybrid functional, and they were tested for their abilities to predict the dissociation energies of three conformations of the H 2S-benzene dimer and to reproduce the key geometric parameters of the equilibrium conformation of this dimer. All of the functionals tested except B3LYP correctly predict which of the three conformations of the dimer is the most stable. The functionals that are best able to reproduce the geometry of the equilibrium conformation of the dimer with a polarized triple-zeta basis set are M06-L, PWB6K, and MPWB1K, each having a mean unsigned relative error across the two experimentally verifiable geometric parameters of only 8%. The success of M06-L is very encouraging because it is a local functional, which reduces the cost for large simulations. The M05-2X functional yields the most accurate binding energy of a conformation of the dimer for which a binding energy calculated at the CCSD(T) level of theory is available; M05-2X gives a binding energy for the system with a difference of merely 0.02 kcal/mol from that obtained by the CCSD(T) calculation. The M06 functional performs well in both categories by yielding a good representation of the geometry of the equilibrium structure and by giving a binding energy that is only 0.19 kcal/mol different from that calculated by CCSD(T). We conclude that the new generation of density functionals should be useful for a variety of problems in biochemistry and materials where aromatic functional groups can serve as hydrogen bond acceptors.     

Benchmarking approximate density functional theory. I. s/d excitation energies in 3d transition metal cations

The performance of a number of different implementations of density functional theory (DFT) for predicting the s/d interconfigurational energies of the 3d transition metal cations is investigated. Systematic comparisons of computed results with experimental data indicate that gradient corrected correlation functionals, like the LYP GGA, efficiently correct the flaws of the LDA, but reveal shortcomings in the treatment of exchange by currently available GGAs. The admixture of exact exchange in hybrid functionals eventually leads to largely reduced errors. Several basis sets available for the 3d elements are tested in combination with the B3LYP functional. Finally, the influence of variations of the admixture of exact exchange is systematically tested. The results reveal that computed s/d excitation energies obtained for the individual ions depend in markedly different ways on the amount of exact exchange admixture and that there is no single optimal and transferable exchange parameter to create a hybrid functional that yields improved results for all ions alike. Several of the recently devised functionals perform as good as or slightly better than the B3LYP functional in the present study. But given the fact that the B3LYP functional has been identified as the most successful DFT method in an overwhelming number of systematic investigations in very many areas of chemical research, there is no persuasive motivation to recommend its replacement by one of the other functionals, as much less is known about their robustness.     

Performance assessment of density-functional methods for study of charge-transfer complexes

Various density functionals are applied to a number of weakly bound intermolecular pi-pi charge-transfer (CT) complexes. Most functionals, including the recently developed mPWPW91 and mPW1PW91, grossly underestimate experimental excitation energies; good agreement is obtained only with the half-and-half hybrid BH&HLYP functional. PW91PW91 provides the best agreement with intermolecular distances measured in crystal, while the BH&HLYP values are about 0.1 A too long. Various hybrid functionals with nonlocal exchange correction provide binding energies that compare favorably with the experimental heats of formation measured in solution.     

Agreement between experiment and hybrid DFT calculations for O--H bond dissociation enthalpies in manganese complexes

Information on the accuracy of DFT functionals for redox reactions in transition metal systems is rather limited. To analyze the performance of some popular functionals for redox reactions in manganese systems, calculated O--H bond dissociation enthalpies for Mn-ligands in six different complexes are compared to experimental results. In this benchmark, B3LYP performs well with a mean absolute error of 3.0 kcal/mol. B98 gives similar results to B3LYP (error of 3.8 kcal/mol). B3LYP* gives lower O--H bond strengths than B3LYP and has a mean error of 5.0 kcal/mol. Compared to B98 and B3LYP, B3LYP* has an error trend for the manganese ligands that is more similar to the error for a free water molecule. The nonhybrid functional BLYP consistently and significantly underestimates the O--H bond strengths by approximately 20 kcal/mol. HCTH407 has a rather large mean error of 9.4 kcal/mol and shows no consistent trend. The results support the use of hybrid functionals and the present computational method for large model systems containing manganese. An example is the oxygen evolving complex in photosystem II where hybrid functionals predict the appearance of a Mn(IV)-oxyl radical before the O--O bond formation step.     

Ab initio investigation of structure and cohesive energy of crystalline urea

The structure and cohesive energy of crystalline urea have been investigated at the ab initio level of calculation. The performance of different Hamiltonians in dealing with a hydrogen-bonded molecular crystal as crystalline urea is assessed. Detailed calculations carried out by adopting both HF and some of the most popular DFT methods in solid-state chemistry are reported. Local, gradient-corrected, and hybrid functionals have been adopted: SVWN, PW91, PBE, B3LYP, and PBE0. First, a 6-31G(d,p) basis set has been adopted, and then the basis set dependence of computed results has been investigated at the B3LYP level. All calculations were carried out by using a development version of the periodic ab initio code CRYSTAL06, which allows full optimization of lattice parameters and atomic coordinates. With the 6-31G(d,p) basis set, structural features are well reproduced by hybrid methods and GGA. LDA gives lattice parameters and hydrogen-bond distances that are too small relative to experiment, while at the HF level the opposite trend is observed. Results show that hybrid methods are more accurate than HF and both LDA and GGA functionals, with a trend in the computed properties similar to that of hydrogen-bonded molecular complexes. When BSSE and ZPE are taken into account, all methods, except LDA, give computed cohesive energies that are underestimated with respect to the experimental sublimation enthalpy. Dispersion energy, not properly taken into account by DFT methods, plays a crucial role. Such a deficiency also affects dramatically the computed crystalline structure, especially when large basis sets are adopted. We show that this is an artifact due to the BSSE. Indeed, with small basis sets the BSSE gives an extra-binding that compensates for the missing dispersion forces, thus yielding structures in fortuitous agreement with experiment.     

Performance of recently developed kinetic energy density functionals for the calculation of hydrogen binding strengths and hydrogen-bonded structures

 The accuracy of predicted hydrogen binding energies and equilibrium structures for a benchmark set of molecules is compared for some recently developed density functionals, Becke's three parameter hybrid method with the Lee, Yang, and Parr (LYP) correlation functional (B3LYP), Becke's half and half functional combined with the LYP correlation functional (BHLYP), Perdew, Burke and Ernzerhof functional (PBE), Van Voorhis, Scuseria exchange correlation functional (VSXC), the hybrid Perdew, Burke and Ernzerhof functional (PBE1PBE), and meta-generalized gradient approximation (meta-GGA). Overall, the hybrid functionals which contain a portion of Hartree–Fock exchange (B3LYP, BHLYP, and PBE1PBE) yield the most accurate results. The kinetic-energy-density-dependent functionals, VSXC and meta-GGA, are significantly less accurate. Received: 10 December 1999 / Accepted: 5 March 2000 / Published online: 21 June 2000     

Structure and stability of the (001) alpha-quartz surface

The structure and surface energies of the cleaved, reconstructed, and fully hydroxylated (001) alpha-quartz surface of various thicknesses are investigated with periodic density functional theory (DFT). The properties of the cleaved and hydroxylated surface are reproduced with a slab thickness of 18 atomic layers, while a thicker 27-layer slab is necessary for the reconstructed surface. The performance of the hybrid DFT functional B3LYP, using an atomic basis set, is compared with the generalised gradient approximation, PBE, employing plane waves. Both methodologies give similar structures and surface energies for the cleaved and reconstructed surfaces, which validates studying these surfaces with hybrid DFT. However, there is a slight difference between the PBE and B3LYP approach for the geometry of the hydrogen bonded network on the hydroxylated surface. The PBE adsorption energy of CO on a surface silanol site is in good agreement with experimental values, suggesting that this method is more accurate for hydrogen bonded structures than B3LYP. New hybrid functionals, however, yield improved weak interactions. Since these functionals also give superior activation energies, we recommend applying the new functionals to contemporary issues involving the silica surface and adsorbates on this surface.     

Spin-forbidden ligand binding to the ferrous-heme group: ab initio and DFT studies

The potential energy surfaces (PESs) and associated energy barriers that characterize the spin-forbidden recombination reactions of the gas-phase ferrous deoxy-heme group with CO, NO, and H2O ligands have been calculated using density functional theory (DFT). The bond energy for binding of O2 has also been calculated. Extensive large basis set CCSD(T) calculations on two small models of the heme group have been used to calibrate the accuracy of different DFT functionals for treating these systems. Pure functionals are shown to overestimate the stability of the low-spin forms of the deoxy-heme model, and to overestimate the binding energy of H2O and CO, whereas hybrid functionals such as B3PW91 and B3LYP yield accurate results. Accordingly, the latter functionals have been used to explore the PESs for binding. CO binding is found to involve a significant barrier of ca. 3 kcal mol-1 due to the need to change from the deoxy-heme quintet ground state to the bound singlet state. Binding of water does not involve a barrier, but the resulting bond is weak and may be further weakened in the protein environment, which should explain why water binding is not usually observed in heme proteins such as myoglobin. NO binding involves a low barrier, which is consistent with observed rapid geminate recombination. The calculated bond energies are in good agreement with previous reported values and in fair agreement with experiment for CO and O2. The value for NO is significantly lower than the experimentally derived bond energy, suggesting that B3LYP is less accurate in this case.     

Structural and electronic properties of polyacetylene and polyyne from hybrid and Coulomb-attenuated density functionals

The bond length alternation (BLA), the highest-occupied-lowest-unoccupied (HO-LU) orbital energy gap, and the corresponding excitation energy are determined for trans-polyacetylene (PA) and polyyne (PY) using density functional theory. Results from the Coulomb-attenuated CAM-B3LYP functional are compared with those from the conventional BHHLYP and B3LYP hybrid functionals. BLA values and HO-LU gaps are determined using both finite oligomer and infinite chain calculations, subject to periodic boundary conditions. TDDFT excitation energies are determined for the oligomers. The oligomer excitation energies and HO-LU gaps are then used, in conjunction with the infinite chain HO-LU gap, to estimate the infinite chain excitation energy. Overall, BHHLYP and CAM-B3LYP give BLA values and excitation energies that are larger and more accurate than those obtained using B3LYP. The results highlight the degree to which excitation energies can be approximated using the HO-LU gaps-at the infinite limit, this approximation works well for B3LYP, but not for the other functionals, where the HO-LU gap is significantly larger. The study provides further evidence for the high-quality theoretical predictions that can be obtained from the CAM-B3LYP functional.     

Theoretical binding affinities and spectra of complexes formed by a cyclic β-peptoid with amino acids

Binding affinities of a cyclic β-peptoid to amino acids were studied using the density functional theory (DFT) at the B3LYP/6-311G(d,p) level after the basis set superior error (BSSE). The host molecule possesses binding ability to amino acids since the binding energies of the complexes formed are negative. The complexes were stabilized via hydrogen bonds between the host and the guest molecules. Based on the B3LYP/6-31G(d) optimized geometries, electronic spectra of the complexes were calculated using the INDO/CIS method. ¹³C NMR spectra and nucleus-independent chemical shift (NICS) values of the complexes were computed at the B3LYP/6-31G(d) level. Carbon atoms in the carboxyl groups of the complexes are shifted downfield relative to those of the host. Some complexes exhibit aromaticity although the host shows anti-aromaticity. Formation of hydrogen bonds leads to cyclic current formation in these complexes.