Modeling temporary anions in density functional theory: calculation of the Fukui function

Two approaches are investigated for modeling electron densities of temporary anions in density functional theory (DFT). Both rely on an artificial binding of the excess electron, in one case by a compact basis set and in the other by a potential wall. The key feature of the calculations is that the degree of binding is controlled in both cases by knowledge of the negative electron affinity of the corresponding neutral, approximated in terms of DFT local functional frontier orbital eigenvalues and vertical ionization potential, A=-(epsilon(LUMO)+epsilon(HOMO))-I. To illustrate the two approaches, Fukui functions for nucleophilic attack are determined in four molecules with increasingly negative electron affinities. They yield very similar results, which are notably different to those determined without artificial electron binding. The use of a potential wall has the attractive feature that large, diffuse basis sets can be used, avoiding the need for a compact basis, tailored to a particular molecule.

On the position of the potential wall in DFT temporary anion calculations

A simple method was recently proposed [D. J. Tozer and F. De Proft, J. Chem. Phys., 2007, 127, 034108] for performing explicit density functional theory (DFT) calculations on temporary anions. The excess electron in the anion is bound by a potential wall, the position of which is determined by a single parameter lambda, chosen to reproduce an approximate, theoretical negative electron affinity in the corresponding neutral. In the present study, the system-dependence of lambda and the sensitivity of the negative affinities to this parameter are investigated for 34 organic molecules. The results demonstrate that the system-dependent lambda values can be replaced by a global, average value, with minimal effect on the affinities. It follows that the orbitals, electron density, and other properties of a temporary anion can be determined from a single DFT calculation on that anion, using a large, diffuse basis set. As an illustration, singly occupied molecular orbitals and spin densities are determined for the anions of guanine and adenine nucleobases. Despite the use of a diffuse basis set, the method yields quantities that are localised in the molecular framework, associated with vertical electron affinities of -1.2 eV and -0.8 eV, respectively.

Modeling the adiabatic connection in H2

Full configuration interaction (FCI) data are used to quantify the accuracy of approximate adiabatic connection (AC) forms in describing the ground state potential energy curve of H2, within spin-restricted density functional theory (DFT). For each internuclear separation R, accurate properties of the AC are determined from large basis set FCI calculations. The parameters in the approximate AC form are then determined so as to reproduce these FCI values exactly, yielding an exchange-correlation energy expressed entirely in terms of FCI-derived quantities. This is combined with other FCI-derived energy components to give the total electronic energy; comparison with the FCI energy quantifies the accuracy of the AC form. Initial calculations focus on a [1/1]-Padé-based form. The potential energy curve determined using the procedure is a notable improvement over those from existing DFT functionals. The accuracy near equilibrium is quantified by calculating the bond length and vibrational wave numbers; errors in the latter are below 0.5%. The molecule dissociates correctly, which can be traced to the use of virtual orbital eigenvalues in the slope in the noninteracting limit, capturing static correlation. At intermediate R, the potential energy curve exhibits an unphysical barrier, similar to that noted previously using the random phase approximation. Alternative forms of the AC are also considered, paying attention to size extensivity and the behavior in the strong-interaction limit; none provide an accurate potential energy curve for all R, although good accuracy can be achieved near equilibrium. The study demonstrates how data from correlated ab initio calculations can provide valuable information about AC forms and highlight areas where further theoretical progress is required.

Evaluation of ⟨Ŝ2⟩ in density functional theory

The evaluation of <S2> in density functional theory (DFT) is considered. Wang et al. [J. Chem. Phys. 102, 3477 (1995)] have derived an approximate, local density expression for <S2> and in the present study their formula is evaluated using densities from unrestricted Hartree-Fock (UHF) and a range of DFT exchange-correlation functionals. The results are compared with those obtained by evaluating the conventional UHF expression using the Kohn-Sham orbitals, which is appropriate for the noninteracting system. A generalized gradient approximation for <S2> is then proposed and investigated.

Magnetization transfer ratio in Alzheimer disease: comparison with volumetric measurements

BACKGROUND AND PURPOSE

Alzheimer disease (AD) is accompanied by macroscopic atrophy on volumetric MR imaging. A few studies have also demonstrated reduction in magnetization transfer ratio (MTR), suggesting microstructural changes in remaining brain tissue. This study assessed the value of measuring MTR in addition to volumetric MR in differentiating patients with AD from control subjects.

MATERIALS AND METHODS

Volumetric T1-weighted images and 3D MTR maps were obtained from 18 patients with AD and 18 age-matched control subjects. Whole-brain (WB) and total hippocampal (Hc) volumes were measured using semiautomated techniques and adjusted for total intracranial volume. Mean MTR was obtained for WB and in the Hc region. Histogram analysis was performed for WB MTR. Among patients, associations between volumetric and MTR parameters and the Mini-Mental State Examination (MMSE) were explored.

RESULTS

Patients with AD had significantly reduced WB volume (P<.0001) and mean WB MTR (P=.002) and Hc volume (P<.0001) and Hc mean MTR (P<.0001) compared with control subjects. Histogram analysis of WB MTR revealed significant reduction in the 25th percentile point in patients with AD (P=.03). Both WB volume and mean MTR were independently associated with case-control status after adjusting for the other using linear regression models. However, measuring Hc mean MTR added no statistically significant discriminatory value over and above Hc volume measurement alone. Of all MR imaging parameters, only WB volume was significantly correlated with MMSE (r=0.47, P=.048).

CONCLUSIONS

This study demonstrates the independent reduction of WB volume and mean MTR in AD. This suggests that the 2 parameters reflect complementary aspects of the AD pathologic lesion at macrostructural and microstructural levels.

Transition metal NMR chemical shifts from optimized effective potentials

Metal shielding constants and chemical shifts are determined for nine transition metal complexes using an uncoupled formalism with orbitals and eigenvalues determined using the Yang-Wu implementation [W. Yang and Q. Wu, Phys. Rev. Lett. 89, 143002 (2002)] of the optimized effective potential approach in density functional theory. Preliminary calculations using generalized gradient approximation functionals quantify the influence of the variables in the optimized effective potential implementation. In particular, a flexible potential expansion is necessary for a precise calculation of these quantities. Hybrid functionals are then considered. Expanding the potential in the primary orbital basis yields chemical shifts that are a notable improvement over conventional hybrid values, and which are a marginal improvement over those obtained using a high-quality generalized gradient approximation. Similar shifts are obtained using a more flexible potential expansion, although care is required to avoid unphysical structure in the exchange-correlation potential.

Combining insights from solid-state NMR and first principles calculation: applications to the 19F NMR of octafluoronaphthalene

Advances in solid-state NMR methodology and computational chemistry are applied to the (19)F NMR of solid octafluoronaphthalene. It is demonstrated experimentally, and confirmed by density functional theory (DFT) calculations, that the spectral resolution in the magic-angle spinning spectrum is limited by the anisotropy of the bulk magnetic susceptibility (ABMS). This leads to the unusual observation that the resolution improves as the sample is diluted. DFT calculations provide assignments of each of the peaks in the (19)F spectrum, but the predictions are close to the limits of accuracy and correlation information from 2-D NMR is invaluable in confirming the assignments. The effects of non-Gaussian lineshapes on the use of 2-D NMR for mapping correlations of spectral frequencies (e.g. due to the ABMS) are also discussed.

Calculation of negative electron affinity and aqueous anion hardness using Kohn–Sham HOMO and LUMO energies

An important chemical property emerging from density-functional theory is the hardness, which can be evaluated as half of the difference between the vertical ionisation energy and electron affinity of the system. For many gas phase molecules, however, the electron affinity is negative and standard ways of evaluating this property are troublesome. In this contribution, we investigate an unconventional approximation for the electron affinity, based on the Kohn-Sham orbital energies of the frontier orbitals and the ionisation potential. It is shown that, for a large series of molecules possessing negative electron affinities, this methodology yields reasonable values for this quantity and that the correlation of the computed values with the experimental affinities from electron transmission spectroscopy is superior to other theoretical approaches. In a second part of this contribution, the hardness of a series of stable negative ions is evaluated in aqueous solution.

A semiempirical generalized gradient approximation exchange-correlation functional

We describe our attempts to improve upon the quality of the KT1 and KT2 generalized gradient approximation (GGA) exchange-correlation functionals [T. W. Keal and D. J. Tozer, J. Chem. Phys. 119, 3015 (2003)], through the introduction of additional gradient-corrected exchange and correlation terms. A GGA functional, denoted KT3, is presented, which maintains the high quality main-group nuclear magnetic resonance shielding constants obtained with KT1 and KT2; results are 2-3 times more accurate than conventional GGA and hybrid functionals. For the extensive range of systems considered in this study, KT3 also provides atomization energies, ionization potentials, electron affinities, proton affinities, bond angles, and electronic polarizabilities that are comparable to, or that surpass, those of the best present-day GGAs. Furthermore, it provides equilibrium molecular bond lengths and diatomic harmonic vibrational wave numbers that are as accurate as those from the best hybrid functionals. Further improvements are required in the description of classical chemical reaction barriers.

Sources of variation in multi-centre brain MTR histogram studies: body-coil transmission eliminates inter-centre differences

OBJECT

1. Identify sources of variation affecting Magnetisation Transfer Ratio (MTR) histogram reproducibility between-centres. 2. Demonstrate complete elimination of inter-centre difference.

MATERIALS AND METHODS

Six principle sources of variation were summarised and analysed. These are: the imager coil used for radiofrequency (RF) transmission, imager stability, the shape and other parameters describing the Magnetisation Transfer (MT) pulse, the MT sequence used (including its parameters), the image segmentation methodology, and the histogram generation technique. Transmit field nonuniformity and B1 errors are often the largest factors. PLUMB (Peak Location Uniformity in MTR histograms of the Brain) plots are a convenient way of visualising differences. Five multi-centres studies were undertaken to investigate and minimise differences.

RESULTS

Transmission using a body coil, with a close-fitting array of surface coils for reception, gave the best uniformity. Differences between two centres, having MR imagers from different manufacturers, were completely eliminated by using body coil excitation, making a small adjustment to the MT pulse flip angle, and carrying out segmentation at a single centre. Histograms and their peak location and height values were indistinguishable.

CONCLUSIONS

Body coil excitation is preferred for multi-centre studies. Analysis (segmentation and histogram generation) should ideally be carried out at a single site.

Neoadjuvant chemotherapy in breast cancer: early response prediction with quantitative MR imaging and spectroscopy

A prospective study was undertaken in women undergoing neoadjuvant chemotherapy for locally advanced breast cancer in order to determine the ability of quantitative magnetic resonance imaging (MRI) and proton spectroscopy (MRS) to predict ultimate tumour response (percentage decrease in volume) or to detect early response. Magnetic resonance imaging and MRS were carried out before treatment and after the second of six treatment cycles. Pharmacokinetic parameters were derived from T₁-weighted dynamic contrast-enhanced MRI, water apparent diffusion coefficient (ADC) was measured, and tissue water : fat peak area ratios and water T₂ were measured using unsuppressed one-dimensional proton spectroscopic imaging (30 and 135 ms echo times). Pharmacokinetic parameters and ADC did not detect early response; however, early changes in water : fat ratios and water T₂ (after cycle two) demonstrated substantial prognostic efficacy. Larger decreases in water T₂ accurately predicted final volume response in 69% of cases (11/16) while maintaining 100% specificity and positive predictive value. Small/absent decreases in water : fat ratios accurately predicted final volume non-response in 50% of cases (3/6) while maintaining 100% sensitivity and negative predictive value. This level of accuracy might permit clinical application where early, accurate prediction of non-response would permit an early change to second-line treatment, thus sparing patients unnecessary toxicity, psychological morbidity and delay of initiation of effective treatment.

The intramolecular β-fluorine⋯ammonium interaction in 4- and 8-membered rings

The structures of 3-fluoroazetidinium hydrochloride and 3-fluoro-1,5-diazacyclooctane hydrobromide are explored both by X-ray diffraction analysis and DFT calculations, and the conformations of these molecules are shown to be significantly influenced by the through space C-F...N+ interaction.

Influence of Coulomb-attenuation on exchange–correlation functional quality

The dependence of functional quality on the attenuation parameters--which control the limiting (r12-->0, infinity) values and the rate of attenuation--is investigated for a Coulomb-attenuated exchange-correlation functional. For the attenuation and functional form considered, satisfaction of an exact long-range condition is detrimental for properties such as atomisation energies and bond lengths, but does improve classical reaction barriers and small molecule electronic excitation energies. The functionals considered can provide high quality valence, Rydberg, intramolecular and asymptotic intermolecular charge transfer (CT) excitations, but none are able to provide a simultaneously optimal description of all classes; CT excitations are not necessarily improved compared to those from conventional functionals. The study highlights the need for further development of Coulomb-attenuated functionals.

Assessment of a Coulomb-attenuated exchange–correlation energy functional

The recently proposed CAM-B3LYP exchange-correlation energy functional, based on a partitioning of the r operator in the exchange interaction into long- and short-range components, is assessed for the determination of molecular thermochemistry, structures, and second order response properties. Rydberg and charge transfer excitation energies and static electronic polarisabilities are notably improved over the standard B3LYP functional; classical reaction barriers also improve. Ionisation potentials, bond lengths, NMR shielding constants and indirect spin-spin coupling constants are comparable with the two functionals. CAM-B3LYP atomisation energies and diatomic harmonic vibrational wavenumbers are less accurate than those of B3LYP. Future research directions are outlined.

Magnetization transfer histograms in clinically isolated syndromes suggestive of multiple sclerosis

In established multiple sclerosis, magnetization transfer ratio (MTR) histograms reveal abnormalities of normal-appearing white matter (NAWM) and grey matter (NAGM). The aim of this study was to investigate for such abnormalities in a large cohort of patients presenting with clinically isolated syndromes suggestive of multiple sclerosis. Magnetization transfer imaging was performed on 100 patients (67 women, 33 men, median age 32 years) a mean of 19 weeks (SD 3.8, range 12-33 weeks) after symptom onset with a clinically isolated syndrome and in 50 healthy controls (34 women, 16 men, median age 32.5 years). SPM99 software was used to generate segmented NAWM and NAGM MTR maps. The volumes of T2 lesions, white matter and grey matter were calculated. Eighty-one patients were followed up clinically and with conventional MRI after 3 years (n = 61) or until they developed multiple sclerosis if this occurred sooner (n = 20). Multiple regression analysis was used to investigate differences between patients and controls with age, gender and volume measures as covariates to control for potential confounding effects. The MTR histograms for both NAWM and NAGM showed a reduction in the mean (NAWM, 38.14 versus 38.33, P = 0.001; NAGM 32.29 versus 32.50, P = 0.009; units in pu) and peak location, with a left shift in the histogram. Mean NAWM and NAGM MTR were also reduced in the patients who developed clinically definite multiple sclerosis and multiple sclerosis according to the McDonald criteria but not in the 24 patients with normal T2-weighted brain magnetic resonance imaging (MRI). MTR abnormalities occur in the NAWM and NAGM at the earliest clinical stages of multiple sclerosis.

Semiempirical hybrid functional with improved performance in an extensive chemical assessment

It is demonstrated that there is still scope for improvement in the quality of conventional, semiempirical hybrid exchange-correlation functionals in density-functional theory. A new functional, denoted B97-3, is determined from a fit to eight chemical properties (316 data points). For a series of 25 chemical assessments (850 data points) including 17 assessments and 10 chemical properties absent from the fitting data, B97-3 provides the lowest or joint-lowest mean absolute error on 15 occasions, compared to 6, 5, and 4 occasions for B3LYP, PBE0, and B97-2, respectively [A. D. Becke, J. Chem. Phys. 98, 5648 (1993); M. Ernzerhof and G. E. Scuseria, J. Chem. Phys. 110, 5029 (1999); C. Adamo and V. Barone, J. Chem. Phys. 110, 6158 (1999); P. J. Wilson, T. J. Bradley, and D. J. Tozer, J. Chem. Phys. 115, 9233 (2001)]. Mean absolute errors from B97-3 are, on average, 21%, 18%, and 12% smaller than from these three functionals. The most notable improvements are obtained for classical reaction barriers, where the error reductions are 60%, 54%, and 27%.

Computation of the Hardness and the Problem of Negative Electron Affinities in Density Functional Theory

The absolute hardness in density functional theory (DFT) is discussed, emphasizing the charge-transfer excitation interpretation. Direct evaluation from the computed ionization potential and electron affinity is intrinsically problematic when the affinity is negative; the calculated affinity exhibits a strong basis set dependence, becoming near zero as diffuse functions are added. An alternative Koopmans-based approximation using local functional eigenvalues uniformly and significantly underestimates the hardness. A simple correction to the Koopmans expression is highlighted on the basis of a consideration of the integer discontinuity. The resulting hardness expression does not require the explicit computation of the affinity and has a straightforward interpretation in terms of the electronegativity. The correction eliminates the underestimation and gives hardness values that do not degrade as the electron affinity becomes more negative. For systems with large negative affinities, the values are an improvement over those from the other approaches. The success can be traced to an implicit, unconventional approximation for the electron affinity, which outperforms the standard approach when the affinity is significantly negative and which does not break down as the basis set becomes more diffuse.