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Recent work on incorporating strong-correlation (sc) corrections into the scLH22t local hybrid functional [A. Wodyński and M. Kaupp, J. Chem. Theory Comput. 18, 6111–6123 (2022)] used a hybrid procedure, applying a strong-correlation factor derived from the reverse Becke–Roussel machinery of the KP16/B13 and B13 functionals to the nonlocal correlation term of a local hybrid functional. Here, we show that adiabatic-connection factors for strong-correlation-corrected local hybrids (scLHs) can be constructed in a simplified way based on a comparison of semi-local and exact exchange-energy densities only, without recourse to exchange-hole normalization. The simplified procedure is based on a comparative analysis of Becke's B05 real-space treatment of nondynamical correlation and that in LHs, and it allows us to use, in principle, any semi-local exchange-energy density in the variable used to construct local adiabatic connections. The derivation of competitive scLHs is demonstrated based on either a modified Becke–Roussel or a simpler Perdew–Burke–Ernzerhof (PBE) energy density, leading to the scLH23t-mBR and scLH23t-tPBE functionals, which both exhibit low fractional spin errors while retaining good performance for weakly correlated situations. We also report preliminary attempts toward more detailed modeling of the local adiabatic connection, allowing a reduction of unphysical local maxima in spin-restricted bond-dissociation energy curves (scLH23t-mBR-P form). The simplified derivations of sc-factors reported here provide a basis for future constructions and straightforward implementation of exchange-correlation functionals that escape the zero-sum game between low self-interaction and static-correlation errors. [ABSTRACT FROM AUTHOR]

It has been known for more than a decade that the gauge variance of the kinetic energy density τ leads to additional terms in the magnetic orbital rotation Hessian used in linear-response time-dependent density functional theory (TDDFT), affecting excitation energies obtained with τ-dependent exchange–correlation functionals. While previous investigations found that a correction scheme based on the paramagnetic current density has a small effect on benchmark results, we report more pronounced effects here, in particular, for the popular M06-2X functional and for some other meta-generalized gradient approximations (mGGAs). In the first part of this communication, this is shown by a reassessment of a set of five Ni(II) complexes for which a previous benchmark study that did not impose gauge invariance has found surprisingly large errors for excitation energies obtained with M06-2X. These errors are more than halved by restoring gauge invariance. The variable importance of imposing gauge invariance for different mGGA-based functionals can be rationalized by the derivative of the mGGA exchange energy integrand with respect to τ. In the second part, a large set of valence excitations in small main-group molecules is analyzed. For M06-2X, several selected n → π* and π → π ⊥ * excitations are heavily gauge-dependent with average changes of −0.17 and −0.28 eV, respectively, while π → π ‖ * excitations are marginally affected (−0.04 eV). Similar patterns, but of the opposite signs, are found for SCAN0. The results suggest that reevaluation of previous gauge variant TDDFT results based on M06-2X and other mGGA functionals is warranted. [ABSTRACT FROM AUTHOR]

The strong-correlation factor of the recent KP16/B13 exchange–correlation functional has been adapted and applied to the framework of local hybrid (LH) functionals. The expression identifiable as nondynamical (NDC) and dynamical (DC) correlations in LHs is modified by inserting a position-dependent KP16/B13-style strong-correlation factor qAC(r) based on a local version of the adiabatic connection. Different ways of deriving this factor are evaluated for a simple one-parameter LH based on the local density approximation. While the direct derivation from the LH NDC term fails due to known deficiencies, hybrid approaches, where the factor is determined from the B13 NDC term as in KP16/B13 itself, provide remarkable improvements. In particular, a modified B13 NDC expression using Patra's exchange-hole curvature showed promising results. When applied to the simple LH as a first attempt, it reduces atomic fractional-spin errors and deficiencies of spin-restricted bond dissociation curves to a similar extent as the KP16/B13 functional itself while maintaining the good accuracy of the underlying LH for atomization energies and reaction barriers in weakly correlated situations. The performance of different NDC expressions in deriving strong-correlation corrections is analyzed, and areas for further improvements of strong-correlation corrected LHs and related approaches are identified. All the approaches evaluated in this work have been implemented self-consistently into a developers' version of the Turbomole program. [ABSTRACT FROM AUTHOR]

The performance of various hybrid density functionals is assessed for 105 singlet and 105 corresponding triplet vertical excitation energies from the QUEST database. The overall lowest mean absolute error is obtained with the local hybrid (LH) functional LH12ct-SsirPW92 with individual errors of 0.11 eV (0.11 eV) for singlet (triplet) n → π* excitations and 0.29 eV (0.17 eV) for π → π* excitations. This is slightly better than with the overall best performing global hybrid M06-2X [n → π*: 0.13 eV (0.17 eV), π → π*: 0.30 eV (0.20 eV)], while most other global and range-separated hybrids and some LHs suffer from the "triplet problem" of time-dependent density functional theory. This is exemplified by correlating the errors for singlet and triplet excitations on a state-by-state basis. The excellent performance of LHs based on a common local mixing function, i.e., an LMF constructed from the spin-summed rather than the spin-resolved semilocal quantities, is systematically investigated by the introduction of a spin-channel interpolation scheme that allows us to continuously modulate the fraction of opposite-spin terms used in the LMF. The correlation of triplet and singlet errors is systematically improved for the n → π* excitations when larger fractions of the opposite-spin-channel are used in the LMF, whereas this effect is limited for the π → π* excitations. This strongly supports a previously made hypothesis that attributes the excellent performance of LHs based on a common LMF to cross-spin-channel nondynamical correlation terms. [ABSTRACT FROM AUTHOR]

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy–cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe–Salpeter methods, second-order Møller–Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE's functionality, including excited-state methods, RPA and Green's function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE's current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE's development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted. [ABSTRACT FROM AUTHOR]

With the increasing interest in compounds containing heavier elements, the experimental and theoretical community requires computationally efficient approaches capable of simultaneous non-perturbative treatment of relativistic, spin-polarization, and electron correlation effects. The ReSpect program has been designed with this goal in mind and developed to perform relativistic density functional theory (DFT) calculations on molecules and solids at the quasirelativistic two-component (X2C Hamiltonian) and fully relativistic four-component (Dirac–Coulomb Hamiltonian) level of theory, including the effects of spin polarization in open-shell systems at the Kramers-unrestricted self-consistent field level. Through efficient algorithms exploiting time-reversal symmetry, biquaternion algebra, and the locality of atom-centered Gaussian-type orbitals, a significant reduction of the methodological complexity and computational cost has been achieved. This article summarizes the essential theoretical and technical advances made in the program, supplemented by example calculations. ReSpect allows molecules with >100 atoms to be efficiently handled at the four-component level of theory on standard central processing unit-based commodity clusters, at computational costs that rarely exceed a factor of 10 when compared to the non-relativistic realm. In addition to the prediction of band structures in solids, ReSpect offers a growing list of molecular spectroscopic parameters that range from electron paramagnetic resonance parameters (g-tensor, A-tensor, and zero-field splitting), via (p)NMR chemical shifts and nuclear spin–spin couplings, to various linear response properties using either conventional or damped-response time-dependent DFT (TDDFT): excitation energies, frequency-dependent polarizabilities, and natural chiroptical properties (electronic circular dichroism and optical rotatory dispersion). In addition, relativistic real-time TDDFT electron dynamics is another unique feature of the program. Documentation, including user manuals and tutorials, is available at the program's website http://www.respectprogram.org. [ABSTRACT FROM AUTHOR]

The first systematic evaluation of local hybrid functionals for the calculation of electronic excitation energies within linear-response time-dependent density functional theory (TDDFT) is reported. Using our recent efficient semi-numerical TDDFT implementation [T. M. Maier et al., J. Chem. Theory Comput. 11, 4226 (2015)], four simple, thermochemically optimized one-parameter local hybrid functionals based on local spin-density exchange are evaluated against a database of singlet and triplet valence excitations of organic molecules, and against a mixed database including also Rydberg, intramolecular charge-transfer (CT) and core excitations. The four local hybrids exhibit comparable performance to standard global or range-separated hybrid functionals for common singlet valence excitations, but several local hybrids outperform all other functionals tested for the triplet excitations of the first test set, as well as for relative energies of excited states. Evaluation for the combined second test set shows that local hybrids can also provide excellent Rydberg and core excitations, in the latter case rivaling specialized functionals optimized specifically for such excitations. This good performance of local hybrids for different excitation types could be traced to relatively large exact-exchange (EXX) admixtures in a spatial region intermediate between valence and asymptotics, as well as close to the nucleus, and lower EXX admixtures in the valence region. In contrast, the tested local hybrids cannot compete with the best range-separated hybrids for intra- and intermolecular CT excitation energies. Possible directions for improvement in the latter category are discussed. As the used efficient TDDFT implementation requires essentially the same computational effort for global and local hybrids, applications of local hybrid functionals to excited-state problems appear promising in a wide range of fields. Influences of current-density dependence of local kinetic-energy dependent local hybrids, differences between spin-resolved and "common" local mixing functions in local hybrids, and the effects of the Tamm-Dancoff approximation on the excitation energies are also discussed. [ABSTRACT FROM AUTHOR]

A new approach for the calibration of (semi-)local and exact exchange-energy densities in the context of local hybrid functionals is reported. The calibration functions are derived from only the electron density and its spatial derivatives, avoiding spatial derivatives of the exact-exchange energy density or other computationally unfavorable contributions. The calibration functions fulfill the seven more important out of nine known exact constraints. It is shown that calibration improves substantially the definition of a non-dynamical correlation energy term for generalized gradient approximation (GGA)-based local hybrids. Moreover, gauge artifacts in the potential-energy curves of noble-gas dimers may be corrected by calibration. The developed calibration functions are then evaluated for a large range of energy-related properties (atomization energies, reaction barriers, ionization potentials, electron affinities, and total atomic energies) of three sets of local hybrids, using a simple one-parameter local-mixing. The functionals are based on (a) local spin-density approximation (LSDA) or (b) Perdew-Burke-Ernzerhof (PBE) exchange and correlation, and on (c) Becke-88 (B88) exchange and Lee-Yang-Parr (LYP) correlation. While the uncalibrated GGA-based functionals usually provide very poor thermochemical data, calibration allows a dramatic improvement, accompanied by only a small deterioration of reaction barriers. In particular, an optimized BLYP-based local-hybrid functional has been found that is a substantial improvement over the underlying global hybrids, as well as over previously reported LSDA-based local hybrids. It is expected that the present calibration approach will pave the way towards new generations of more accurate hyper-GGA functionals based on a local mixing of exchange-energy densities. [ABSTRACT FROM AUTHOR]

A persistent challenge in density functional theory is the construction of a nonempirical correlation functional that is compatible with the exact exchange energy. To solve this problem, we develop a correlation factor approach in which an exchange hole model, yielding the exact exchange energy, is multiplied by a correlation factor that turns the exchange hole into an exchange-correlation hole. This results in an accurate correlation energy functional that is determined solely through physical constraints. Subject to the properties of the employed exchange hole model, the proposed correlation factor model to the exchange-correlation energy becomes exact in the high-density limit. In this limit, the exchange-correlation energy is dominated by exchange. [ABSTRACT FROM AUTHOR]

Local hybrid functionals with their position-dependent exact-exchange admixture are a conceptually simple and promising extension of the concept of a hybrid functional. Local hybrids based on a simple mixing of the local spin density approximation (LSDA) with exact exchange have been shown to be successful for thermochemistry, reaction barriers, and a range of other properties. So far, the combination of this generation of local hybrids with an LSDA correlation functional has been found to give the most favorable results for atomization energies, for a range of local mixing functions (LMFs) governing the exact-exchange admixture. Here, we show that the choice of correlation functional to be used with local hybrid exchange crucially influences the parameterization also of the exchange part as well as the overall performance. A novel ansatz for the correlation part of local hybrids is suggested based on (i) range-separation of LSDA correlation into short-range (SR) and long-range (LR) parts, and (ii) partial or full elimination of the one-electron self-correlation from the SR part. It is shown that such modified correlation functionals allow overall larger exact exchange admixture in thermochemically competitive local hybrids than before. This results in improvements for reaction barriers and for other properties crucially influenced by self-interaction errors, as demonstrated by a number of examples. Based on the range-separation approach, a fresh view on the breakdown of the correlation energy into dynamical and non-dynamical parts is suggested. [ABSTRACT FROM AUTHOR]

The isotropic hyperfine coupling constants of the free N(4S) and P(4S) atoms have been evaluated with high-level post-Hartree–Fock and density-functional methods. The phosphorus hyperfine coupling presents a significant challenge to both types of methods. With large basis sets, MP2 and coupled-cluster singles and doubles calculations give much too small values for the phosphorus atom. Triple excitations are needed in coupled-cluster calculations to achieve reasonable agreement with experiment. None of the standard density functionals reproduce even the correct sign of this hyperfine coupling. Similarly, the computed hyperfine couplings depend crucially on the self-consistent treatment in exact-exchange density-functional theory within the optimized effective potential (OEP) method. Well-balanced auxiliary and orbital basis sets are needed for basis-expansion exact-exchange-only OEP approaches to come close to Hartree–Fock or numerical OEP data. Results from the localized Hartree–Fock and Krieger–Li–Iafrate approximations deviate notably from exact OEP data in spite of very similar total energies. Of the functionals tested, only full exact-exchange methods augmented by a correlation functional gave at least the correct sign of the P(4S) hyperfine coupling but with too low absolute values. The subtle interplay between the spin-polarization contributions of the different core shells has been analyzed, and the influence of even very small changes in the exchange-correlation potential could be identified. [ABSTRACT FROM AUTHOR]

Occupied-orbital dependent (OOD) exchange-correlation functionals hold a particularly prominent place in current developments of density functional theory. Their self-consistent implementation is complicated by the fact that their orbital-dependent parts are not explicit but only implicit functionals of electron density, and the exchange-correlation potential may not be obtained straightforwardly by taking the functional derivative with respect to the density. A two-step procedure is required, in which initially the functional derivatives with respect to the orbitals (FDOs) are obtained, which may then be transformed into local and multiplicative potentials by techniques of the optimized-effective potential. In view of the rather large variety of OOD functionals under current study, we report here general, systematic, and transparent expressions of the FDOs of a generalized OOD functional and additionally a matrix-element version in a basis set of atomic orbitals. Explicit FDOs are for the first time derived and numerically tested for one of the currently most complex examples of an OOD functional, Becke’s real-space model of nondynamical correlation (B05 functional) [J. Chem. Phys. 122, 064101 (2005)]. [ABSTRACT FROM AUTHOR]

Local hybrid functionals with position-dependent exact-exchange admixture are a promising new generation of exchange-correlation functionals for a large variety of applications. So far, the local mixing functions (LMFs) determining the position dependence have been largely constructed in an ad hoc manner, albeit based on physical reasoning. Here the basic formalism of the adiabatic connection is employed to investigate the formal basis of local hybrids and to construct a priori LMFs. Both a local spin density approximation to the LMF (AC-LSDA LMF) and generalized gradient approximation approximations (AC-PW91 LMF and AC-PBE LMF) turn out to provide inferior performance when used in local hybrids to compute atomization energies and reaction barriers compared to previous semiempirical LMFs. This is rationalized by limited flexibility of these first-principles LMFs and some basic limitations of the adiabatic connection formalism in this context. Graphical analyses and formal considerations provide nevertheless important new insight into the physical background of local hybrid functionals. [ABSTRACT FROM AUTHOR]

A new relativistic four-component density functional approach for calculations of NMR shielding tensors has been developed and implemented. It is founded on the matrix formulation of the Dirac–Kohn–Sham (DKS) method. Initially, unperturbed equations are solved with the use of a restricted kinetically balanced basis set for the small component. The second-order coupled perturbed DKS method is then based on the use of restricted magnetically balanced basis sets for the small component. Benchmark relativistic calculations have been carried out for the 1H and heavy-atom nuclear shielding tensors of the HX series (X=F,Cl,Br,I), where spin-orbit effects are known to be very pronounced. The restricted magnetically balanced basis set allows us to avoid additional approximations and/or strong basis set dependence which arises in some related approaches. The method provides an attractive alternative to existing approximate two-component methods with transformed Hamiltonians for relativistic calculations of chemical shifts and spin-spin coupling constants of heavy-atom systems. In particular, no picture-change effects arise in property calculations. [ABSTRACT FROM AUTHOR]

Local hybrid functionals with position-dependent exact-exchange admixture are a new class of exchange-correlation functionals in density functional theory that promise to advance the available accuracy in many areas of application. Local hybrids with different local mixing functions (LMFs) governing the position dependence are validated for the heats of formation of the extended G3/99 set, and for two sets of barriers of hydrogen-transfer and heavy-atom transfer reactions (HTBH38 and NHTBH38 databases). A simple local hybrid Lh-SVWN with only Slater and exact exchange plus local correlation and a one-parameter LMF, g(r)=b(τW(r)/τ(r)), performs best and provides overall mean absolute errors for thermochemistry and kinetics that are a significant improvement over standard state-of-the-art global hybrid functionals. In particular, this local hybrid functional does not suffer from the systematic deterioration that standard functionals exhibit for larger molecules. In contrast, local hybrids based on generalized gradient approximation exchange tend to give rise to nonintuitive LMFs, and no improved functionals have been obtained along this route. The LMF is a real-space function and thus can be analyzed in detail. We use, in particular, graphical analyses to rationalize the performance of different local hybrids for thermochemistry and reaction barriers. [ABSTRACT FROM AUTHOR]

The calculation of nuclear shieldings for paramagnetic molecules has been implemented in the ReSpect program, which allows the use of modern density functional methods with accurate treatments of spin-orbit effects for all relevant terms up to order O(α4) in the fine structure constant. Compared to previous implementations, the methodology has been extended to compounds of arbitrary spin multiplicity. Effects of zero-field splittings in high-spin systems are approximately accounted for. Validation of the new implementation is carried out for the 13C and 1H NMR signal shifts of the 3d metallocenes 4VCp2, 3CrCp2, 2MnCp2, 6MnCp2, 2CoCp2, and 3NiCp2. Zero-field splitting effects on isotropic shifts tend to be small or negligible. Agreement with experimental isotropic shifts is already good with the BP86 gradient-corrected functional and is further improved by admixture of Hartree-Fock exchange in hybrid functionals. Decomposition of the shieldings confirms the dominant importance of the Fermi-contact shifts, but contributions from spin-orbit dependent terms are frequently also non-negligible. Agreement with 13C NMR shift tensors from solid-state experiments is of similar quality as for isotropic shifts. [ABSTRACT FROM AUTHOR]

Following the suggestion of local hybrid functionals with position-dependent exact-exchange admixture [J. Jaramillo, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 1068 (2003)], a functional that mixes only local and exact exchange plus local correlation has been constructed. With a simple local mixing function for the position dependence, this Lh-SVWN functional provides atomization energies for the G2-1 set that are competitive with currently available state-of-the-art functionals like, e.g., B3LYP. This is achieved without generalized gradient approximations for exchange or correlation. [ABSTRACT FROM AUTHOR]

Two different sets of approaches for the density-functional calculation of the spin-orbit contributions to zero-field splitting (ZFS) parameters of high-spin systems have been implemented within the same quantum chemistry code ReSpect and have been validated and compared for a series of model systems. The first approach includes spin-orbit coupling variationally in a two-component calculation, using either an all-electron Douglas-Kroll-Hess ansatz or two-component relativistic pseudopotentials. The ZFS parameters are computed directly from energy differences between different relativistic states. Additionally, an approximate second-order perturbation theory approach has been implemented, based on nonrelativistic or scalar relativistic wave functions. For a series of group 16 triplet diatomics and for the octet GdH3 molecules, two-component density functional calculations underestimate the zero-field splitting D systematically by a factor of 2. This may be rationalized readily by the incomplete description of states with ¦MJ¦3, the results depend furthermore sensitively on exchange-correlation functional. Results of the alternative one-component approach agree strikingly with the two-component data for systems with small spin-orbit effects and start to deviate from them only for heavier systems with large spin-orbit effects. These results have fundamental implications for the achievable accuracy of one-component density-functional approaches used widely to compute ZFS parameters in the field of molecular magnetism. Possible refinements of both one-and two-component approaches are discussed. [ABSTRACT FROM AUTHOR]

Hybrid exchange-correlation functionals with position-dependent exact-exchange admixture (local hybrid functionals) have been implemented self-consistently for the first time. Functional derivatives with respect to the occupied orbitals have been derived and were subsequently transformed into local and multiplicative potentials within the framework of the optimized effective potential. The resulting local and multiplicative Kohn-Sham potentials are termed “localized local hybrid” (LLH) potentials. They have been evaluated in calculations of atomization energies for a series of main-group molecules. It is shown that LLH potentials yield somewhat better thermochemical results than non-self-consistent post-GGA calculations with the same local hybrid energy functionals for orbitals obtained with a different potential. The choice of the “local mixing function” (LMF) is discussed. This is the key quantity for the performance of local hybrid functionals that determines the amount of exact-exchange admixture at a given point in space. Careful analyses of average exact-exchange admixtures and of the spatial variation of two different LMFs for various molecules provide insight into the shortcomings of the currently used local hybrid functionals. Beyond a too large average exact-exchange admixture, both LMFs used appear to provide an unbalanced description of exact-exchange admixture across bonds to hydrogen. LLH potentials open the way for property calculations with local hybrid functionals. [ABSTRACT FROM AUTHOR]

A new relativistic two-component density functional approach, based on the Dirac-Kohn-Sham method and an extensive use of the technique of resolution of identity (RI), has been developed and is termed the DKS2-RI method. It has been applied to relativistic calculations of g and hyperfine tensors of coinage-metal atoms and some mercury complexes. The DKS2-RI method solves the Dirac-Kohn-Sham equations in a two-component framework using explicitly a basis for the large component only, but it retains all contributions coming from the small component. The DKS2-RI results converge to those of the four-component Dirac-Kohn-Sham with an increasing basis set since the error associated with the use of RI will approach zero. The RI approximation provides a basis for a very efficient implementation by avoiding problems associated with complicated integrals otherwise arising from the elimination of the small component. The approach has been implemented in an unrestricted noncollinear two-component density functional framework. DKS2-RI is related to Dyall’s [J. Chem. Phys. 106, 9618 (1997)] unnormalized elimination of the small component method (which was formulated at the Hartree-Fock level and applied to one-electron systems only), but it takes advantage of the local Kohn-Sham exchange-correlation operators (as, e.g., arising from local or gradient-corrected functionals). The DKS2-RI method provides an attractive alternative to existing approximate two-component methods with transformed Hamiltonians (such as Douglas-Kroll-Hess [Ann. Phys. 82, 89 (1974); Phys. Rev. A 33, 3742 (1986)] method, zero-order regular approximation, or related approaches) for relativistic calculations of the structure and properties of heavy-atom systems. In particular, no picture-change effects arise in the property calculations. [ABSTRACT FROM AUTHOR]

The first two-component relativistic density-functional approach for the calculation of electronic g-tensors is reported that includes spin polarization using noncollinear spin-density functionals. The method is based on the relativistic Douglas-Kroll-Hess Hamiltonian and has been implemented into the ReSpect program package. Using three self-consistent-field calculations with orthogonal orientations of total magnetization J, the full g-matrix may be obtained. In contrast to previous spin-restricted two-component treatments, results with the new approach agree excellently with spin-polarized one-component calculations for light-atom radicals. Additionally, unlike one-component approaches, the method also reproduces successfully the negative Δg∥-values of heavy-atom 2Σ radicals and the negative Δg⊥ components in cysteinyl. The new method removes effectively the dilemma existing up to now regarding the simultaneous inclusion of spin polarization and higher-order spin-orbit effects in g-tensor calculations. It is straightforwardly applicable to higher than doublet spin multiplicities and has been implemented with hybrid functionals. [ABSTRACT FROM AUTHOR]

A second-order perturbation theory treatment of spin-orbit corrections to hyperfine coupling tensors has been implemented within a density-functional framework. The method uses the all-electron atomic mean-field approximation and/or spin-orbit pseudopotentials in incorporating one- and two-electron spin-orbit interaction within a first-principles framework. Validation of the approach on a set of main-group radicals and transition metal complexes indicates good agreement between all-electron and pseudopotential results for hyperfine coupling constants of the lighter nuclei in the system, except for cases in which scalar relativistic effects become important. The nonrelativistic Fermi contact part of the isotropic hyperfine coupling constants is not always accurately reproduced by the exchange-correlation functionals employed, particularly for the triplet and π-type doublet radicals in the present work. For this reason, ab initio coupled-cluster singles and doubles with perturbative triples results for the first-order contributions have been combined in the validation calculations with the density-functional results for the second-order spin-orbit contributions. In the cases where spin-orbit corrections are of significant magnitude relative to the nonrelativistic first-order terms, they improve the agreement with experiment. Antisymmetric contributions to the hyperfine tensor arise from the spin-orbit contributions and are discussed for the IO[sub 2] radical, whereas rovibrational effects have been evaluated for RhC, NBr, and NI. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Calculates [sup 31]P nuclear magnetic resonance chemical shifts of tetrahalophosphonium cations by density-functional methods. Agreement between theory and experimental literature data; Negative shifts due to large spin-orbit contributions; Isotropic shift measurements; Deviations from the isolated-cation limit.

Examines the density functional analysis of [sup 13]C and [sup 1]H nuclear magnetic resonance chemical shifts and bonding in mercurymethanes and organomercury hydrides. Impact of scalar relativistic effects on the shift; Factors influencing the spin-orbit contributions; Importance of electron correlations in chemical shifts.

Compares the performance of different density functional theory (DFT) and hybrid-DFT approaches for the calculation of 17O chemical shielding in the series of tetrahedral metal oxo complexes. Basis set effects and the performance of different exchange-correlation functionals; Scalar relativistic effects and origins of periodic trends.

We combine a perturbational calculation, using spin-orbit pseudopotentials, of the spin-orbit effect on nuclear shieldings with scalar relativistic effects taken into account self-consistently using quasirelativistic pseudopotentials. The shieldings are calculated for light nuclei in systems containing heavy atoms, for which matching spin-orbit and quasirelativistic pseudopotentials are used. The second-order spin-orbit contribution arising from the magnetic field dependence of the one-electron spin-orbit Hamiltonian is also included. The method is implemented within the framework of density-functional theory and is capable of treating large molecular systems economically. Calculations are presented for the HX and CH[sub 3]X (X=F, Cl, Br, I) molecules, third-row transition metal carbonyls, and a series of methyl mercury compounds. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The correlation factor model is developed in which the spherically averaged exchange-correlation hole of Kohn-Sham theory is factorized into an exchange hole model and a correlation factor. The exchange hole model reproduces the exact exchange energy per particle. The correlation factor is constructed in such a manner that the exchange-correlation energy correctly reduces to exact exchange in the high density and rapidly varying limits. Four different correlation factor models are presented which satisfy varying sets of physical constraints. Three models are free from empirical adjustments to experimental data, while one correlation factor model draws on one empirical parameter. The correlation factor models are derived in detail and the resulting exchange-correlation holes are analyzed. Furthermore, the exchange-correlation energies obtained from the correlation factor models are employed to calculate total energies, atomization energies, and barrier heights. It is shown that accurate, non-empirical functionals can be constructed building on exact exchange. Avenues for further improvements are outlined as well.