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In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 300 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 776 entries, the paper represents a broad snapshot of DFT, anno 2022.

A semiclassical theory of small oscillations is developed for nuclei that are subject to velocity-dependent forces in addition to the usual interatomic forces. When the velocity-dependent forces are due to a strong magnetic field, novel effects arise—for example, the coupling of vibrational, rotational, and translational modes. The theory is first developed using Newtonian mechanics and we provide a simple quantification of the coupling between these types of modes. We also discuss the mathematical structure of the problem, which turns out to be a quadratic eigenvalue problem rather than a standard eigenvalue problem. The theory is then re-derived using the Hamiltonian formalism, which brings additional insight, including a close analogy to the quantum-mechanical treatment of the problem. Finally, we provide numerical examples for the H2, HT, and HCN molecules in a strong magnetic field.

Molecular rotations and vibrations have been extensively studied by chemists for decades, both experimentally using spectroscopic methods and theoretically with the help of quantum chemistry. However, the theoretical investigation of molecular rotations and vibrations in strong magnetic fields requires computationally more demanding tools. As such, proper calculations of rotational and vibrational spectra were not feasible up until very recently. In this work, we present rotational and vibrational spectra for two small linear molecules, H2 and LiH, in strong magnetic fields. By treating the nuclei as classical particles, trajectories for rotations and vibrations are simulated from ab initio molecular dynamics. Born–Oppenheimer potential energy surfaces are calculated at the Hartree–Fock and MP2 levels of theory using London atomic orbitals to ensure gauge origin invariance. For the calculation of nuclear trajectories, a highly efficient Tajima propagator is introduced, incorporating the Berry curvature tensor accounting for the screening of nuclear charges.

The Berry connection and curvature are key components of electronic structure calculations for atoms and molecules in magnetic fields. They ensure the correct translational behavior of the effective nuclear Hamiltonian and the correct center-of-mass motion during molecular dynamics in these environments. In this work, we demonstrate how these properties of the Berry connection and curvature arise from the translational symmetry of the electronic wave function and how they are fully captured by a finite basis set of London orbitals but not by standard Gaussian basis sets. This is illustrated by a series of Hartree–Fock calculations on small molecules in different basis sets. Based on the resulting physical interpretation of the Berry curvature as the shielding of the nuclei by the electrons, we introduce and test a series of approximations using the Mulliken fragmentation scheme of the electron density. These approximations will be particularly useful in ab initio molecular dynamics calculations in a magnetic field since they reduce the computational cost, while recovering the correct physics and up to 95% of the exact Berry curvature.

C–H activation in alkanes poses a major challenge in chemistry due to the inert character of this bond, manifesting the necessity of improved catalysts. Although various metal–oxo complexes are known to facilitate alkane hydroxylation, probing the mechanistic nature of the reaction is difficult due to the extremely fast rebound of the radical intermediate in the postulated oxygen-rebound pathway. Automated reaction mechanism discovery methods, such as the artificial force induced reaction (AFIR) method, enable the efficient exploration of both expected and unexpected reaction pathways, revealing the reaction mechanism. Here, we employed this approach combined with density-functional theory (DFT) to investigate the structure and reactivity of heterometallic cubane complexes similar to the oxygen-evolving complex of photosystem II. For a series of M(O)Co3O4 cubanes, where M(O) is a terminal oxo with M = Cr, Mn, Fe, Mo, Tc, Ru and Rh, we first computed the stability of the possible spin states and the radical (i.e., oxyl) character of the M(O) moiety as a measure of their potential activity in the catalytic hydroxylation of alkanes. DFT calculations on these reactions promoted by Ru(O)Co3O4 and Fe(O)Co3O4 suggest that the latter promotes the hydroxylation of methane with a rate-determining H-abstraction barrier of 24.6 kcal mol-1. The moderate height of this barrier, together with the low cost and low toxicity of iron and cobalt, suggest that the Fe(O)Co3O4 cubane is a promising candidate for the catalytic oxidation of methane to methanol. AFIR calculations showed that the oxygen-rebound pathway yields the lowest-energy profile, thus validating this mechanism for the hydroxylation of alkanes by heterometallic cubanes. Furthermore, unexpected intermediates in which the methyl radical couples with either the metal center or the bridging-oxo ligands were also observed.

A novel implementation for the calculation of molecular gradients under strong magnetic fields is employed at the current-density functional theory level to optimize the geometries of molecular structures, which change significantly under these conditions. An analog of the ab initio random structure search is utilized to determine the ground-state equilibrium geometries for He n and CH n systems at high magnetic field strengths, revealing the most stable structures to be those in high-spin states with a planar geometry aligned perpendicular to the field. The electron and current densities for these systems have also been investigated to develop an explanation of chemical bonding in the strong field regime, providing an insight into the exotic chemistry present in these extreme environments.

The diagonal nonadiabatic term arising from the Born--Oppenheimer wave-function ansatz contains contributions from a vector and scalar potential. The former is provably zero when the wave function can be taken to be real valued, and the latter, known as the diagonal Born--Oppenheimer correction (DBOC), is typically small in magnitude. Therefore, unless high accuracy is sought, the diagonal nonadiabatic term is usually neglected when calculating molecular properties. In the presence of a magnetic field, the wave function is generally complex, and the geometric vector potential gives rise to a screening force that is qualitatively important for molecular dynamics. This screening force is written in terms of the Berry curvature and is added to the bare Lorentz force acting on the nuclei in the presence of the field. In this work, we derive analytic expressions for the Berry curvature and DBOC using both first and second quantization formalisms for the case of generalized and restricted Hartree--Fock theories in a uniform magnetic field. The Berry curvature and DBOC are calculated as a function of the magnetic field strength and the bond distance for the ground-state singlets of H$_2$, LiH, BH, and CH$^+$. We also examine the stability and time-reversal symmetry of the underlying self-consistent field solutions. The character of the DBOC and Berry curvature is found to depend upon the magnetic field and varies between molecules. We also identify instances of broken time-reversal symmetry for the dissociation curves of BH and CH$^+$., 29 Pages, 14 Figures, 34 individual figures (figure panels)

A suite of tools for the analysis of magnetically induced currents is introduced. These are applicable to both the weak-field regime, well described by linear response perturbation theory, and to the strong-field regime, which is inaccessible to such methods. A disc-based quadrature scheme is proposed for the analysis of magnetically induced current susceptibilities, providing quadratures that are consistently defined between different molecular systems and applicable to both planar 2D and general 3D molecular systems in a black-box manner. The applicability of the approach is demonstrated for a range of planar ring systems, the ground and excited states of the benzene molecule, and the ring, bowl, and cage isomers of the C20 molecule in the presence of a weak magnetic field. In the presence of a strong magnetic field, the para- to diamagnetic transition of the BH molecule is studied, demonstrating that magnetically induced currents present a visual interpretation of this phenomenon, providing insight beyond that accessible using linear response methods.

We investigate the helium dimer in strong magnetic fields, focusing on the spectrum of low-lying electronic states and their dissociation curves, at the full configuration-interaction level of theory. To address the loss of cylindrical symmetry and angular momentum as a good quantum number for nontrivial angles between the bond axis and magnetic field, we introduce the almost quantized angular momentum (AQAM) and show that it provides useful information about states in arbitrary orientations. In general, strong magnetic fields dramatically rearrange the spectrum, with the orbital Zeeman effect bringing down states of higher angular momentum below the states with pure $\sigma$ character as the field strength increases. In addition, the spin Zeeman effect pushes triplet states below the lowest singlet; in particular, a field of one atomic unit is strong enough to push a quintet state below the triplets. In general, the angle between the bond axis and the magnetic field also continuously modulates the degree of $\sigma$, $\pi$, and $\delta$ character of bonds and the previously identified perpendicular paramagnetic bonding mechanism is found to be common among excited states. Electronic states with preferred skew field orientations are identified and rationalized in terms of permanent and induced electronic currents.

C–H activation in alkanes poses a major challenge in chemistry due to the inert character of this bond, manifesting the necessity of improved catalysts. Although various metal–oxo complexes are known to facilitate alkane hydroxylation, probing the mechanistic nature of the reaction is difficult due to the extremely fast rebound of the radical intermediate in the postulated oxygen-rebound pathway. Automated reaction mechanism discovery methods, such as the artificial force induced reaction (AFIR) method, enable the efficient exploration of both expected and unexpected reaction pathways, revealing the reaction mechanism. Here, we employed this approach combined with density-functional theory (DFT) to investigate the structure and reactivity of heterometallic cubane complexes similar to the oxygen-evolving complex of photosystem II. For a series of M(O)Co3O4 cubanes, where M(O) is a terminal oxo with M = Cr, Mn, Fe, Mo, Tc, Ru, and Rh, we computed the stability of the possible spin states and the radical (i.e., oxyl) character of the M(O) moiety as a measure of their potential activity in the catalytic hydroxylation of alkanes. DFT calculations on these reactions promoted by Ru(O)Co3O4 and Fe(O)Co3O4 suggest that the latter promotes the hydroxylation of methane with a rate-determining H-abstraction barrier of 24.6 kcal/mol. The moderate height of this barrier, together with the low cost and low toxicity of iron and cobalt, suggests that the Fe(O)Co3O4 cubane is a promising candidate for the catalytic oxidation of methane to methanol. AFIR calculations showed that the oxygen-rebound pathway yields the lowest-energy profile, thus validating this mechanism for the hydroxylation of alkanes by heterometallic cubanes. Furthermore, unexpected intermediates in which the methyl radical couples with either the metal center or the bridging oxo ligands were also observed.

The Berry curvature is essential in Born$-$Oppenheimer molecular dynamics, describing the screening of the nuclei by the electrons in a magnetic field. Parts of the Berry curvature can be understood as the external magnetic field multiplied by an effective charge so that the resulting Berry force behaves like a Lorentz force during the simulations. Here we investigate whether these effective charges can provide insight into the electronic structure of a given molecule or, in other words, whether we can perform a population analysis based on the Berry curvature. To develop our approach, we first rewrite the Berry curvature in terms of charges that partially capture the effective charges and their dependence on the nuclear velocities. With these Berry charges and charge fluctuations, we then construct our population analysis yielding atomic charges and overlap populations. Calculations at the Hartree$-$Fock level reveal that the atomic charges are similar to those obtained from atomic polar tensors. However, since we additionally obtain an estimate for the fluctuations of the charges and a partitioning of the atomic charges into contributions from all atoms, we conclude that the Berry population analysis is a useful alternative tool to analyze the electronic structure of molecules.

In an ultrastrong magnetic field, with field strength B ≈ B0 = 2.35 × 105 T, molecular structure and dynamics differ strongly from that observed on the Earth. Within the Born–Oppenheimer (BO) approximation, for example, frequent (near) crossings of electronic energy surfaces are induced by the field, suggesting that nonadiabatic phenomena and processes may play a more important role in this mixed-field regime than in the weak-field regime on Earth. To understand the chemistry in the mixed regime, it therefore becomes important to explore non-BO methods. In this work, the nuclear-electronic orbital (NEO) method is employed to study protonic vibrational excitation energies in the presence of a strong magnetic field. The NEO generalized Hartree–Fock theory and time-dependent Hartree–Fock (TDHF) theory are derived and implemented, accounting for all terms that result as a consequence of the nonperturbative treatment of molecular systems in a magnetic field. The NEO results for HCN and FHF− with clamped heavy nuclei are compared against the quadratic eigenvalue problem. Each molecule has three semi-classical modes owing to the hydrogen—two precession modes that are degenerate in the absence of a field and one stretching mode. The NEO-TDHF model is found to perform well; in particular, it automatically captures the screening effects of the electrons on the nuclei, which are quantified through the difference in energy of the precession modes.

A cornerstone of current–density functional theory (CDFT) in its paramagnetic formulation is proven. After a brief outline of the mathematical structure of CDFT, the lower semicontinuity and expectation-valuedness of the CDFT constrained-search functional is proven, meaning that there is always a minimizing density matrix in the CDFT constrained-search universal density functional. These results place the mathematical framework of CDFT on the same footing as that of standard DFT.

The dynamics of a molecule in a magnetic field is significantly different form its zero-field counterpart. One important difference in the presence of a field is the Lorentz force acting on the nuclei, which can be decomposed as the sum of the bare nuclear Lorentz force and a screening force due to the electrons. This screening force is calculated from the Berry curvature and can change the dynamics qualitatively. It is therefore important to include the contributions from the Berry curvature in molecular dynamics simulations in a magnetic field. In this work, we present a scheme for calculating the Berry curvature numerically, by a finite-difference technique, addressing challenges related to the arbitrary global phase of the wave function. The Berry curvature is calculated as a function of bond distance for H$_2$ at the restricted and unrestricted Hartree--Fock levels of theory and for CH$^{+}$ as a function of the magnetic field strength at the restricted Hartree--Fock level of theory. The calculations are carried out using basis sets of contracted Gaussian functions equipped with London phase factors (London orbitals) to ensure gauge-origin invariance. In the paper, we also interpret the Berry curvature in terms of atomic charges and discuss its convergence in basis sets with and without London phase factors. Calculation of the Berry curvature allows for its inclusion in \textit{ab initio} molecular dynamics simulations in a magnetic field.

1H NMR spectroscopy has become an important technique for the characterization of transition-metal hydride complexes, whose metal-bound hydrides are often difficult to locate by X-ray diffraction. In this regard, the accurate prediction of 1H NMR chemical shifts provides a useful, but challenging, strategy to help in the interpretation of the experimental spectra. In this work, we establish a density-functional-theory protocol that includes relativistic, solvent, and dynamic effects at a high level of theory, allowing us to report an accurate and reliable interpretation of 1H NMR hydride chemical shifts of iridium polyhydride complexes. In particular, we have studied in detail the hydride chemical shifts of the [Ir6(IMe)8(CO)2H14]2+ complex in order to validate previous assignments. The computed 1H NMR chemical shifts are strongly dependent on the relativistic treatment, the choice of the DFT exchange–correlation functional, and the conformational dynamics. By combining a fully relativistic four-component electronic-structure treatment with ab initio molecular dynamics, we were able to reliably model both the terminal and bridging hydride chemical shifts and to show that two NMR hydride signals were inversely assigned in the experiment., A new strategy by computational 1H NMR spectroscopy was used to predict and support the characterization of complex metal polyhydrides. A density-functional-theory protocol including relativistic, solvent, and dynamic effects at a high level of theory was established for the [Ir6(IMe)8(CO)2H14]2+ complex. The combination of a relativistic four-component electronic-structure treatment with ab initio molecular dynamics provided a means to accurately model both terminal and bridging hydride shifts, showing that two signals were inversely assigned in the NMR experiment.

International audience; We present a detailed non-relativistic study of the atoms H, He, C and K and the molecule CH4 in the center of a spherical soft confinement potential of the form VN (r) = (r/r0) N with stiffness parameter N and confinement radius r0. The soft confinement potential approaches the hard-wall limit as N → ∞, giving a more detailed picture of spherical confinement. The confined hydrogen atom is considered as a base model: it is treated numerically to obtain ground-and excited-state energies and nodal positions of the eigenstates to study the convergence towards the hard-wall limit. We also derive some important analytical relations. The use of Gaussian basis sets is analyzed. We find that, for increasing stiffness parameter N , the convergence towards the basis-set limit becomes problematic. As an application, we report dipole polarizabilities for different values of N and r0 of hydrogen. For helium, we determine electron correlation effects with varying N and r0, and discuss the virial theorem for both soft and hard confinements in the limit r0 → 0. For carbon, a change in the orbital population from 2s 2 2p 2 to 2s 0 2p 4 is observed with decreasing r0, while, for potassium, we observe a change from the 2 S to 2 D ground state at small r0 values. For CH4, we show that the one-particle density becomes more spherical with increasing confinement. A possible application of soft confinement to atoms and molecules under high pressure is discussed. Dedicated to Prof. Jürgen Gauss on the occasion of his 60th birthday

The Dalton Project provides a uniform platform access to the underlying full-fledged quantum chemistry codes Dalton and LSDalton as well as the PyFraME package for automatized fragmentation and parameterization of complex molecular environments. The platform is written in Python and defines a means for library communication and interaction. Intermediate data such as integrals are exposed to the platform and made accessible to the user in the form of NumPy arrays, and the resulting data are extracted, analyzed, and visualized. Complex computational protocols that may, for instance, arise due to a need for environment fragmentation and configuration-space sampling of biochemical systems are readily assisted by the platform. The platform is designed to host additional software libraries and will serve as a hub for future modular software development efforts in the distributed Dalton community.

Strong magnetic fields have a large impact on the dynamics of molecules. In addition to the changes of the electronic structure, the nuclei are exposed to the Lorentz force with the magnetic field being screened by the electrons. In this work, we explore these effects using ab-initio molecular dynamics simulations based on an effective Hamiltonian calculated at the Hartree-Fock level of theory. To correctly include these non-conservative forces in the dynamics, we have designed a series of novel propagators that show both good efficiency and stability in test cases. As a first application, we analyze simulations of He and H$_2$ at two field strengths characteristic of magnetic white dwarfs (0.1 $B_0 = 2.35 \times 10^4$ T and $B_0 = 2.35 \times 10^5$ T). While the He simulations clearly demonstrate the importance of electron screening of the Lorentz force in the dynamics, the extracted rovibrational spectra of H$_2$ reveal a number of fascinating features not observed in the field-free case: couplings of rotations/vibrations with the cyclotron rotation, overtones with unusual selection rules, and hindered rotations that transmute into librations with increasing field strength. We conclude that our presented framework is a powerful tool to investigate molecules in these extreme environments.

Explicitly correlated all-particle Gaussian functions with shifted centers (ECGs) are implemented within the earlier proposed effective variational non-Born-Oppenheimer method for calculating bound states of molecular systems in magnetic field (Adamowicz et al., 2015). The Hamiltonian used in the calculations is obtained by subtracting the operator representing the kinetic energy of the center-of-mass motion from the total laboratory-frame Hamiltonian. Test ECG calculations are performed for the HD molecule.

We report a combined experimental-theoretical study on the 31P NMR chemical shift for a number of trans-platinum(ii) complexes. Validity and reliability of the 31P NMR chemical shift calculations are examined by comparing with the experimental data. A successful computational protocol for the accurate prediction of the 31P NMR chemical shifts was established for trans-[PtCl2(dma)PPh3] (dma = dimethylamine) complexes. The reliability of the computed values is shown to be critically dependent on the level of relativistic effects (two-component vs. four component), choice of density functionals, dynamical averaging, and solvation effects. Snapshots obtained from ab initio molecular dynamics simulations were used to identify those solvent molecules which show the largest interactions with the platinum complex, through inspection by using the non-covalent interaction program. We observe satisfactory accuracy from the full four-component matrix Dirac-Kohn-Sham method (mDKS) based on the Dirac-Coulomb Hamiltonian, in conjunction with the KT2 density functional, and dynamical averaging with explicit solvent molecules.

Quasiparticle energies of the atoms H–Ne have been computed in the GW approximation in the presence of strong magnetic fields with field strengths varying from 0 to 0.25 atomic units (0.25 B 0 =0.25 ℏe −1 a −2 0 ≈58 763 0.25 B0=0.25 ℏe−1a0−2≈58 763 T). The GW quasiparticle energies are compared with equation-of-motion ionization-potential (EOM-IP) coupled-cluster singles-and-doubles (CCSD) calculations of the first ionization energies. The best results are obtained with the evGW@PBE0 method, which agrees with the EOM-IP-CCSD model to within about 0.20 eV. Ionization potentials have been calculated for all atoms in the series, representing the first systematic study of ionization potentials for the first-row atoms at field strengths characteristic of magnetic white dwarf stars. Under these conditions, the ionization potentials increase in a near-linear fashion with the field strength, reflecting the linear field dependence of the Landau energy of the ionized electron. The calculated ionization potentials agree well with the best available literature data for He, Li, and Be.

We report a combined experimental-theoretical study on the 31P NMR chemical shift for a number of trans-platinum(ii) complexes. Validity and reliability of the 31P NMR chemical shift calculations are examined by comparing with the experimental data. A successful computational protocol for the accurate prediction of the 31P NMR chemical shifts was established for trans-[PtCl2(dma)PPh3] (dma = dimethylamine) complexes. The reliability of the computed values is shown to be critically dependent on the level of relativistic effects (two-component vs. four component), choice of density functionals, dynamical averaging, and solvation effects. Snapshots obtained from ab initio molecular dynamics simulations were used to identify those solvent molecules which show the largest interactions with the platinum complex, through inspection by using the non-covalent interaction program. We observe satisfactory accuracy from the full four-component matrix Dirac-Kohn-Sham method (mDKS) based on the Dirac-Coulomb Hamiltonian, in conjunction with the KT2 density functional, and dynamical averaging with explicit solvent molecules.

Interactions of a stationary external magnetic field with the spin and orbital magnetic momenta of a molecule are included in the quantum mechanical model where the Born–Oppenheimer approximation is not assumed. The model is used to calculate some of the lowest-lying internal bound states of the molecule for various strengths of the magnetic field. All-particle explicitly correlated Gaussian functions are used in the calculations.

We compare the performance of three approximate methods for speeding up evaluation of the exchange contribution in Hartree-Fock and hybrid Kohn-Sham calculations: the chain-of-spheres algorithm (COSX; Neese , F. Chem. Phys. 2008 , 356 , 98 - 109 ), the pair-atomic resolution-of-identity method (PARI-K; Merlot , P. J. Comput. Chem. 2013 , 34 , 1486 - 1496 ), and the auxiliary density matrix method (ADMM; Guidon , M. J. Chem. Theory Comput. 2010 , 6 , 2348 - 2364 ). Both the efficiency relative to that of a conventional linear-scaling algorithm and the accuracy of total, atomization, and orbital energies are compared for a subset containing 25 of the 200 molecules in the Rx200 set using double-, triple-, and quadruple-ζ basis sets. The accuracy of relative energies is further compared for small alkane conformers (ACONF test set) and Diels-Alder reactions (DARC test set). Overall, we find that the COSX method provides good accuracy for orbital energies as well as total and relative energies, and the method delivers a satisfactory speedup. The PARI-K and in particular ADMM algorithms require further development and optimization to fully exploit their indisputable potential.

We present a generalisation of the electron localisation function (ELF) to current-density-functional theory as a descriptor for the properties of molecules in the presence of magnetic fields. The resulting current ELF (cELF) is examined for a range of small molecular systems in field strengths up to B0 = 235 kT (one atomic unit). The cELF clearly depicts the compression of the molecular electronic structure in the directions perpendicular to the applied field and exhibits a structure similar to that of the physical current densities. A topological analysis is performed to examine the changes in chemical bonding upon application of a magnetic field.

As guest editors, we are excited to present the Molecular Physics Festschrift in honour of Jurgen Gauss, professor of theoretical chemistry at the Johannes Gutenberg-Universitat Mainz, Germany, on ...

A variety of approaches are presented for the computation of atomic and molecular correlation energies based on the Bethe–Salpeter equation in the framework of the adiabatic-connection fluctuation–dissipation theorem. The performance of the approaches is assessed by computing the total energies of the atoms H—Ne and the atomization energies of the high-accuracy extrapolated ab initio thermochemistry set of small molecules as well as by determining the bond lengths and harmonic vibrational frequencies of the metal monoxides MO with M=Ca—Zn.A variety of approaches are presented for the computation of atomic and molecular correlation energies based on the Bethe–Salpeter equation in the framework of the adiabatic-connection fluctuation–dissipation theorem. The performance of the approaches is assessed by computing the total energies of the atoms H—Ne and the atomization energies of the high-accuracy extrapolated ab initio thermochemistry set of small molecules as well as by determining the bond lengths and harmonic vibrational frequencies of the metal monoxides MO with M=Ca—Zn.

A detailed account of the Kohn–Sham (KS) algorithm from quantum chemistry, formulated rigorously in the very general setting of convex analysis on Banach spaces, is given here. Starting from a Levy–Lieb-type functional, its convex and lower semi-continuous extension is regularized to obtain differentiability. This extra layer allows us to rigorously introduce, in contrast to the common unregularized approach, a well-defined KS iteration scheme. Convergence in a weak sense is then proven. This generalized formulation is applicable to a wide range of different density-functional theories and possibly even to models outside of quantum mechanics.

International audience; A Görling-Levy (GL)-based perturbation theory along the range-separated adiabatic connection is assessed for the calculation of electronic excitation energies. In comparison with the Rayleigh-Schrödinger (RS)-based perturbation theory introduced in a previous work [E. Rebolini, J. Toulouse, A. M. Teale, T. Helgaker, A. Savin, Mol. Phys. 113, 1740 (2015)], this GL-based perturbation theory keeps the ground-state density constant at each order and thus gives the correct ionization energy at each order. Excitation energies up to first order in the perturbation have been calculated numerically for the helium and beryllium atoms and the hydrogen molecule without introducing any density-functional approximations. In comparison with the RS-based perturbation theory, the present GL-based perturbation theory gives much more accurate excitation energies for Rydberg states but similar excitation energies for valence states.

An effective variational non-Born–Oppenheimer method is applied to calculate the ground state of the HD molecule in a strong magnetic field. The Hamiltonian used in the calculations is obtained by subtracting the operator representing the kinetic energy of the center-of-mass motion from the total laboratory-frame Hamiltonian. Orbital basis sets are used for the deuteron, the proton, and the electrons. Based on the calculated expectation values, it is determined that, with increasing field strength, the bond length decreases and the alignment of the molecule with the field increases.

The adiabatic-connection framework has been widely used to explore the properties of the correlation energy in density-functional theory. The integrand in this formula may be expressed in terms of the electron–electron interactions directly, involving intrinsically two-particle expectation values. Alternatively, it may be expressed in terms of the kinetic energy, involving only one-particle quantities. In this work, we explore this alternative representation for the correlation energy and highlight some of its potential for the construction of new density functional approximations. The kinetic-energy based integrand is effective in concentrating static correlation effects to the low interaction strength regime and approaches zero asymptotically, offering interesting new possibilities for modeling the correlation energy in density-functional theory

Abundance mass spectra, obtained upon carefully electrospraying solutions of tert-butanol (TB) in water into a mass spectrometer, display a systematic series of peaks due to mixed H(+)(TB)m(H2O)n clusters. Clusters with m + n = 21 have higher abundance (magic number peaks) than their neighbours when m ≤ 9, while for m9 they have lower abundance. This indicates that the mixed TB-H2O clusters retain a core hydrogen bonded network analogous to that in the famous all-water H(+)(H2O)21 cluster up to the limit m = 9. The limiting value corresponds to the number of dangling O-H groups pointing out from the surface of the degenerated pentagonal dodecahedral, considered to be the lowest energy form of H(+)(H2O)21; the experimental findings therefore support this geometry. The experimental findings are supported by ab initio quantum chemical calculations to provide a consistent framework for the interpretation of these kinds of experiments.

The sources of error in the calculation of nuclear-magnetic-resonance shielding constants determined by density-functional theory are examined. Highly accurate Kohn-Sham wave functions are obtained from coupled-cluster electron density functions and used to define accurate-but current independent-density-functional shielding constants. These new reference values, in tandem with high-accuracy coupled-cluster shielding constants, provide a benchmark for the assessment of errors in common density-functional approximations. In particular the role of errors arising in the diamagnetic and paramagnetic terms is investigated, with particular emphasis on the role of current-dependence in the latter. For carbon and nitrogen the current correction is found to be, in some cases, larger than 10 ppm. This indicates that the absence of this correction in general purpose exchange-correlation functionals is one of the main sources of error in shielding calculations using density functional theory. It is shown that the current correction improves the shielding performance of many popular approximate DFT functionals.