Spatially-optimized urban greening for reduction of population exposure to land surface temperature extremes.

The population experiencing high temperatures in cities is rising due to anthropogenic climate change, settlement expansion, and population growth. Yet, efficient tools to evaluate potential intervention strategies to reduce population exposure to Land Surface Temperature (LST) extremes are still lacking. Here, we implement a spatial regression model based on remote sensing data that is able to assess the population exposure to LST extremes in urban environments across 200 cities based on surface properties like vegetation cover and distance to water bodies. We define exposure as the number of days per year where LST exceeds a given threshold multiplied by the total urban population exposed, in person ⋅ day. Our findings reveal that urban vegetation plays a considerable role in decreasing the exposure of the urban population to LST extremes. We show that targeting high-exposure areas reduces vegetation needed for the same decrease in exposure compared to uniform treatment.

Ab initio non-covalent crystal field theory for lanthanide complexes: a multiconfigurational non-orthogonal group function approach.

We present a multiconfigurational ab initio methodology based on non-orthogonal fragments for the calculation of crystal field energy levels and magnetic properties of lanthanide complexes, implementing a systematic description of non-covalent contributions to metal-ligand bonding. The approach consists of two steps. In the first step, appropriate ab initio wave functions for the various ionic fragments (lanthanide ions and coordinating ligands) are optimized separately, accounting for the influence of the surrounding environment within various approximations. In the second and final step, the scalar relativistic (DKH2) electrostatic Hamiltonian of the whole molecule is represented on the basis of the optimized metal-ligand multiconfigurational non-orthogonal group functions (MC-NOGFs), and reduced to an effective (2J + 1)-dimensional non-orthogonal configuration interaction (CI) problem via Löwdin-partitioning. Within the proposed formalism, the projected non-orthogonal CI Hamiltonian can be expanded to any desired order of perturbation theory in the fragment-localised excitations out of the degenerate space, and its eigenvalues and eigenfunctions provide systematic approximations to the crystal field energies and wave functions. We present here a preliminary implementation of the proposed MC-NOGF method developed for first-order degenerate perturbation theory within our own ab initio code CERES, and compare its performance both with the simpler non-covalent orthogonal ab initio approach, Fragment Ab Initio Model Potential (FAIMP) approximation, and the full CAHF/CASCI-SO method, accounting for metal-ligand covalency in a mean-field manner. We found that the energies and magnetic properties of 44 complexes obtained via an iteratively optimized version of our MC-NOGF first-order non-covalent method compare remarkably well with those obtained using the full CAHF/CASCI-SO method including metal-ligand covalency, thus exposing the predominantly electrostatic character of the metal-ligand interactions, and are superior to those obtained using the FAIMP approach, which in its iteratively optimised variant was believed to date to be the best ab initio description of non-covalent metal-ligand interactions.

Elucidation of LMCT Excited States for Lanthanoid Complexes: A Theoretical and Solid-State Experimental Framework.

Photophysical and magnetic properties arising from both ground and excited states of lanthanoid ions are relevant for numerous applications. These properties can be substantially affected, both adversely and beneficially, by ligand-to-metal charge-transfer (LMCT) states. However, probing LMCT states remains a significant challenge in f-block chemistry, particularly in the solid state. Intriguingly, the europium compounds [EuIII(18-c-6)(X4Cat)(NO3)]·MeCN (18-c-6 = 18-crown-6; X = Cl (tetrachlorocatecholate, 1-Eu) or Br (tetrabromocatecholate, 2-Eu) are distinctly darkly-colored, in marked contrast to the analogues with other lanthanoid ions in the 1-Ln and 2-Ln series (Ln = La, Ce, Nd, Gd, Tb, and Dy). Herein, we report a multi-technique investigation of these compounds that has allowed elucidation of the LMCT character of the relevant absorption bands using magnetometry, absorption and emission spectroscopies, and solid-state electrochemistry. To support experimental observations, we present a semi-quantitative multireference ab initio model that (i) captures the anomalously low-lying LMCT excited state observed in the visible spectrum of 1-Eu (and its absence in the other 1-Ln analogues); (ii) elucidates the contribution of the LMCT excitation to the crystal field split 7FJ ground-state wave functions; and (iii) identifies the crucial role played by radial dynamical correlation of the EuIII 4f electrons in the description of the LMCT excited state, modeled by the inclusion of 4f → 5f excitations in the optimized wave function. By providing a set of experimental and theoretical tools, this work establishes a framework for the elucidation of LMCT excited states in lanthanoid compounds in the solid state.

Study of the most relevant spin-orbit coupling descriptions of magnetic excitations in a series of lanthanide complexes.

We present a number of computationally cost-effective approaches to calculate magnetic excitations (i.e. crystal field energies and magnetic anisotropies in the lowest spin-orbit multiplet) in lanthanide complexes. In particular, we focus on the representation of the spin-orbit coupling term of the molecular Hamiltonian, which has been implemented within the quantum chemistry package CERES using various approximations to the Breit-Pauli Hamiltonian. The approximations include the (i) bare one-electron approximation, (ii) atomic mean field and molecular mean field approximations of the two-electron term, (iii) full representation of the Breit-Pauli Hamiltonian. Within the framework of the CERES implementation, the spin-orbit Hamiltonian is always fully diagonalized together with the electron repulsion Hamiltonian (CASCI-SO) on the full basis of Slater determinants arising within the 4f ligand field space. For the first time, we make full use of the Cholesky decomposition of two-electron spin-orbit integrals to speed up the calculation of the two-electron spin-orbit operator. We perform an extensive comparison of the different approximations on a set of lanthanide complexes varying both the lanthanide ion and the ligands. Surprisingly, while our results confirm the need of at least a mean field approach to accurately describe the spin-orbit coupling interaction within the ground Russell-Saunders term, we find that the simple bare one-electron spin-orbit Hamiltonian performs reasonably well to describe the crystal field split energies and g tensors within the ground spin-orbit multiplet, which characterize all the magnetic excitations responsible for lanthanide-based single-molecule magnetism.

Design of annulene-within-an-annulene systems by the altanisation approach. A study of altan-[n]annulenes.

The altanisation strategy, devised to design molecules with large and paratropic perimeter circulations, is applied to the family of [n]annulenes to give, altan-[n]annulenes, i.e. [n,5]coronenes. Analytical expressions are obtained for the eigenvalues of the Hückel Hamiltonian for altan-[n]annulenes, and used in conjunction with selection rules derived from the ipsocentric approach to predict patterns of global ring current in these systems. Density-functional calculations performed on seven altan-[n]annulenes, three neutral and four charged, give current-density maps in essential agreement with the predictions obtained at the unperturbed Hückel level. All but one of the systems show patterns with the tropicities expected for isolated annulenes, in line with the altanisation concept. The apparent exception is altan-[11]annulene-, the only singlet system with a well defined open-shell character in the studied set. The key role of open-shell character can be accommodated by appropriate choice of the occupation numbers of the initial Hückel molecular orbitals, where the anion altan-[11]annulene- is considered as an [11]annulene inside the [22]annulene anion.

Slow Magnetic Relaxation in Lanthanoid Crown Ether Complexes: Interplay of Raman and Anomalous Phonon Bottleneck Processes.

The combination of lanthanoid nitrates with 18-crown-6 (18-c-6) and tetrahalocatecholate (X4 Cat2- , X=Cl, Br) ligands has afforded two compound series [Ln(18-c-6)(X4 Cat)(NO3 )]⋅MeCN (X=Cl, 1-Ln; X=Br, 2-Ln; Ln=La, Ce, Nd, Gd, Tb, Dy). The 18-c-6 ligands occupy equatorial positions of a distorted sphenocorona geometry, whereas the charged ligands occupy the axial positions. The analogues of both series with Ln=Ce, Nd, Tb and Dy exhibit out-of-phase ac magnetic susceptibility signals in the presence of an applied magnetic field, indicative of slow magnetization relaxation. When diluted into a diamagnetic La host to reduce dipolar interactions, the Dy analogue exhibits slow relaxation up to 20 K in the absence of an applied dc field. Concerted magnetic measurements, EPR spectroscopy, and ab initio calculations have allowed elucidation of the mechanisms responsible for slow magnetic relaxation. A consistent approach has been applied to quantitatively model the relaxation data for different lanthanoid analogues, suggesting that the spin dynamics are governed by Raman processes at higher temperatures, transitioning to a dominant phonon bottleneck process as the temperature is decreased, with an observed T-6 rather than the usual T-2 dependence (T is temperature). This anomalous thermal dependence of the phonon bottleneck relaxation is consistent with anharmonic effects in the lattice dynamics, which was predicted by Van Vleck more than 70 years ago.

CERES: An ab initio code dedicated to the calculation of the electronic structure and magnetic properties of lanthanide complexes.

We have developed and implemented a new ab initio code, Ceres (Computational Emulator of Rare Earth Systems), completely written in C++11, which is dedicated to the efficient calculation of the electronic structure and magnetic properties of the crystal field states arising from the splitting of the ground state spin-orbit multiplet in lanthanide complexes. The new code gains efficiency via an optimized implementation of a direct configurational averaged Hartree-Fock (CAHF) algorithm for the determination of 4f quasi-atomic active orbitals common to all multi-electron spin manifolds contributing to the ground spin-orbit multiplet of the lanthanide ion. The new CAHF implementation is based on quasi-Newton convergence acceleration techniques coupled to an efficient library for the direct evaluation of molecular integrals, and problem-specific density matrix guess strategies. After describing the main features of the new code, we compare its efficiency with the current state-of-the-art ab initio strategy to determine crystal field levels and properties, and show that our methodology, as implemented in Ceres, represents a more time-efficient computational strategy for the evaluation of the magnetic properties of lanthanide complexes, also allowing a full representation of non-perturbative spin-orbit coupling effects. © 2017 Wiley Periodicals, Inc.

A full-pivoting algorithm for the Cholesky decomposition of two-electron repulsion and spin-orbit coupling integrals.

A significant reduction in the computational effort for the evaluation of the electronic repulsion integrals (ERI) in ab initio quantum chemistry calculations is obtained by using Cholesky decomposition (CD), a numerical procedure that can remove the zero or small eigenvalues of the ERI positive (semi)definite matrix, while avoiding the calculation of the entire matrix. Conversely, due to its antisymmetric character, CD cannot be directly applied to the matrix representation of the spatial part of the two-electron spin-orbit coupling (2e-SOC) integrals. Here, we present a computational strategy to achieve a Cholesky representation of the spatial part of the 2e-SOC integrals, and propose a new efficient CD algorithm for both ERI and 2e-SOC integrals. The proposed algorithm differs from previous CD implementations by the extensive use of a full-pivoting design, which allows a univocal definition of the Cholesky basis, once the CD δ threshold is made explicit. We show that 2δ is the upper limit for the errors affecting the reconstructed 2e-SOC integrals. The proposed strategy was implemented in the ab initio program Computational Emulator of Rare Earth Systems (CERES), and tested for computational performance on both the ERI and 2e-SOC integrals evaluation. © 2017 Wiley Periodicals, Inc.

Semiexperimental equilibrium structures for building blocks of organic and biological molecules: the B2PLYP route.

The B2PLYP double hybrid functional, coupled with the correlation-consistent triple-ζ cc-pVTZ (VTZ) basis set, has been validated in the framework of the semiexperimental (SE) approach for deriving accurate equilibrium structures of molecules containing up to 15 atoms. A systematic comparison between new B2PLYP/VTZ results and several equilibrium SE structures previously determined at other levels, in particular B3LYP/SNSD and CCSD(T) with various basis sets, has put in evidence the accuracy and the remarkable stability of such model chemistry for both equilibrium structures and vibrational corrections. New SE equilibrium structures for phenylacetylene, pyruvic acid, peroxyformic acid, and phenyl radical are discussed and compared with literature data. Particular attention has been devoted to the discussion of systems for which lack of sufficient experimental data prevents a complete SE determination. In order to obtain an accurate equilibrium SE structure for these situations, the so-called templating molecule approach is discussed and generalized with respect to our previous work. Important applications are those involving biological building blocks, like uracil and thiouracil. In addition, for more general situations the linear regression approach has been proposed and validated.

Generalized Vibrational Perturbation Theory for Rotovibrational Energies of Linear, Symmetric and Asymmetric Tops: Theory, Approximations, and Automated Approaches to Deal with Medium-to-Large Molecular Systems.

Models going beyond the rigid-rotor and the harmonic oscillator levels are mandatory for providing accurate theoretical predictions for several spectroscopic properties. Different strategies have been devised for this purpose. Among them, the treatment by perturbation theory of the molecular Hamiltonian after its expansion in power series of products of vibrational and rotational operators, also referred to as vibrational perturbation theory (VPT), is particularly appealing for its computational efficiency to treat medium-to-large systems. Moreover, generalized (GVPT) strategies combining the use of perturbative and variational formalisms can be adopted to further improve the accuracy of the results, with the first approach used for weakly coupled terms, and the second one to handle tightly coupled ones. In this context, the GVPT formulation for asymmetric, symmetric, and linear tops is revisited and fully generalized to both minima and first-order saddle points of the molecular potential energy surface. The computational strategies and approximations that can be adopted in dealing with GVPT computations are pointed out, with a particular attention devoted to the treatment of symmetry and degeneracies. A number of tests and applications are discussed, to show the possibilities of the developments, as regards both the variety of treatable systems and eligible methods.

Semi-experimental equilibrium structure determinations by employing B3LYP/SNSD anharmonic force fields: validation and application to semirigid organic molecules.

This work aims at extending the semi-experimental (SE) approach for deriving accurate equilibrium structures to large molecular systems of organic and biological interest. SE equilibrium structures are derived by a least-squares fit of the structural parameters to the experimental ground-state rotational constants of several isotopic species corrected by vibrational contributions computed by quantum mechanical (QM) methods. A systematic benchmark study on 21 small molecules (CCse set) is carried out to evaluate the performance of hybrid density functionals (in particular B3LYP) in the derivation of vibrational corrections to rotational constants. The resulting SE equilibrium structures show a very good agreement with the corresponding geometries obtained employing post-Hartree-Fock vibrational corrections. The use of B3LYP in conjunction with the double-ζ SNSD basis set strongly reduces the computational costs, thus allowing for the evaluation of accurate SE equilibrium structures for medium-sized molecular systems. On these grounds, an additional set of 26 SE equilibrium structures including the most common organic moieties has been set up by collecting the most accurate geometries available in the literature together with new determinations from the present work. The overall set of 47 SE equilibrium structures determined using B3LYP/SNSD vibrational corrections (B3se set) provides a high quality benchmark for validating the structural predictions of other experimental and/or computational approaches. Finally, we present a new strategy (referred to as the template approach) to deal with the cases for which it is not possible to fit all geometrical parameters due to the lack of experimental data.

Ultrafast resonance energy transfer in the umbelliferone-alizarin bichromophore.

In this work we present the synthesis, time-resolved spectroscopic characterization and computational analysis of a bichromophore composed of two very well-known naturally occurring dyes: 7-hydroxycoumarin (umbelliferone) and 1,2-dihydroxyanthraquinone (alizarin). The umbelliferone donor (Dn) and alizarin acceptor (Ac) moieties are linked to a triazole ring viaσ bonds, providing a flexible structure. By measuring the fluorescence quantum yields and the ultrafast transient absorption spectra we demonstrate the high efficiency (∼85%) and the fast nature (∼1.5 ps) of the energy transfer in this compound. Quantum chemical calculations, within the density functional theory (DFT) approach, are used to characterize the electronic structure of the bichromophore (Bi) in the ground and excited states. We simulate the absorption and fluorescence spectra using the TD-DFT methods and the vertical gradient approach (VG), and include the solvent effects by adopting the conductor-like polarizable continuum model (CPCM). The calculated electronic structure suggests the occurrence of weak interactions between the electron densities of Dn and Ac in the excited state, indicating that the Förster-type transfer is the appropriate model for describing the energy transfer in this system. The average distance between Dn and Ac moieties calculated from the conformational analysis (12 Å) is in very good agreement with the value estimated from the Förster equation (∼11 Å). At the same time, the calculated rate constant for energy transfer, averaged over multiple conformations of the system (3.6 ps), is in reasonable agreement with the experimental value (1.6 ps) estimated by transient absorption spectroscopy. The agreement between experimental results and computational data leads us to conclude that the energy transfer in Bi is well described by the Förster mechanism.

Stereo-electronic, vibrational, and environmental contributions to polarizabilities of large molecular systems: a feasible anharmonic protocol.

Reliable computations of linear and non-linear optical properties of molecular systems in condensed phases require a proper account of stereo-electronic, vibrational, and environmental effects. In the framework of density functional theory, these effects can be accurately introduced using second-order vibrational perturbation theory in conjunction with polarizable continuum models. We illustrate the combination of an anharmonic description of the ground-state potential energy surface with solvation effects treated with the polarizable continuum model (PCM) in the calculation of the electronic, zero-point, and pure vibrational polarizabilities of selected systems. The description of the solvation environment is enriched by taking into account the dynamical aspects of the solute-solvent interactions through the inclusion of both electronic and vibrational non-equilbrium effects, as well as the direct effect of the solvent on the electric field that generates the molecular response (local field effect). This treatment yields accurate results which can be directly compared with experimental findings without the need of empirical corrections.

Tuning the photophysical properties of pyrene-based systems: a theoretical study.

Recently new molecular systems based on the pyrene moiety were developed for photovoltaic applications. Here we present the results of a quantum chemical study focused on the effects induced by some different substituents on the electronic properties of pyrene, to obtain general hints for the molecular design of new pyrene-based systems. In particular, a series of electron-donating (hydroxy, amino, acetylamino) and electron-withdrawing (cyano, carbamoyl, formyl, ethynyl, ethenyl) groups were considered. Furthermore, in addition to the single pyrene molecule, two pyrene units linked by ethenylene, ethynylene, 2,5-thienylene, and ethynylene-p-phenylene containing chains of different lengths were taken into account. For all of the model structures presented, the ground state geometries have been optimized using the density functional approach, while the vertical transition energies were calculated using the time-dependent density functional theory. We will show that the tuning of the lowest electronic excitation energy (i.e., the HOMO-LUMO energy gap) as well as the localization of the spatial distributions of the frontier molecular orbitals (i.e., the nature of the electron-hole pair, generated by photon absorption) can be obtained through the analysis of the pyrene frontier molecular orbitals. This approach allows to evaluate the most suitable position of the substituents on the pyrene moiety giving rise to enhanced electronic effects also in function of their electronic nature. In this way, pyrene-structures with tailored electronic properties could be modeled. Our screening shows that promising candidates for photovoltaic applications could be molecular structures formed by two pyrene units joined/linked by a short conjugated bridge containing double or triple bonds (henceforth pyrene-linked dimers). As far as the single pyrene units are considered, the most significant reduction of the transition energy of the lowest optical electronic excitation is obtained with disubstituted pyrenes with push-pull character.