Determination of extremely localized molecular orbitals and their application to quantum mechanics/molecular mechanics methods and to the study of intramolecular hydrogen bonding

IGMPlot: A program to identify, characterize, and quantify molecular interactions

We describe the development and features of a program called IGMPlot, which is based on the independent gradient model (IGM) and its local descriptor δ g $$ \delta g $$ . The IGM approach analyzes the gradient of the electron density (ED) in a molecular system to identify regions of space where chemical interactions take place. IGMPlot is intended for use by both experimental scientists and theoretical chemists. It is standalone software written in C++, with versions available for multiple platforms. Some key features are: probing and quantifying interactions between two given molecular fragments, determining bond strength (IBSI), estimating the atomic contributions to an intermolecular interaction and preparing data to build 2D and 3D representations of interaction regions. The software has been updated to include new features: critical point analysis of the ED, assessing ED asymmetry of a given bond (PDA) and a new descriptor called q g $$ qg $$ designed to enhance the IGM- δ g $$ \delta g $$ analysis. The program can be found at: http://igmplot.univ-reims.fr.

Extracting Quantitative Information at Quantum Mechanical Level from Noncovalent Interaction Index Analyses

The noncovalent interaction (NCI) index is nowadays a well-known strategy to detect NCIs in molecular systems. Even though it initially provided only qualitative descriptions, the technique has been recently extended to also extract quantitative information. To accomplish this task, integrals of powers of the electron distribution were considered, with the requirement that the overall electron density can be clearly decomposed as sum of distinct fragment contributions to enable the definition of the (noncovalent) integration region. So far, this was done by only exploiting approximate promolecular electron densities, which are given by the sum of spherically averaged atomic electron distributions and thus represent too crude approximations. Therefore, to obtain more quantum mechanically (QM) rigorous results from NCI index analyses, in this work, we propose to use electron densities obtained through the transfer of extremely localized molecular orbitals (ELMOs) or through the recently developed QM/ELMO embedding technique. Although still approximate, the electron distributions resulting from the abovementioned methods are fully QM and, above all, are again partitionable into subunit contributions, which makes them completely suitable for the NCI integral approach. Therefore, we benchmarked the integrals resulting from NCI index analyses (both those based on the promolecular densities and those based on ELMO electron distributions) against interaction energies computed at a high quantum chemical level (in particular, at the coupled cluster level). The performed test calculations have indicated that the NCI integrals based on ELMO electron densities outperform the promolecular ones. Furthermore, it was observed that the novel quantitative NCI-(QM/)ELMO approach can be also profitably exploited both to characterize and evaluate the strength of specific interactions between ligand subunits and protein residues in protein-ligand complexes and to follow the evolution of NCIs along trajectories of molecular dynamics simulations. Although further methodological improvements are still possible, the new quantitative ELMO-based technique could be already exploited in situations in which fast and reliable assessments of NCIs are crucial, such as in computational high-throughput screenings for drug discovery.

Initial Maximum Overlap Method Embedded with Extremely Localized Molecular Orbitals for Core-Ionized States of Large Systems

Despite great advances in X-ray absorption spectroscopy for the investigation of small molecule electronic structure, the application to biosystems of experimental techniques developed within this research field remains a challenge. To partially circumvent the problem, users resort to theoretical methods to interpret or predict the X-ray absorption spectra of large molecules. To accomplish this task, only low-cost computational strategies can be exploited. For this reason, some of them are single Slater determinant wavefunction approaches coupled with multiscale embedding techniques designed to treat large systems of biological interest. Therefore, in this work, we propose to apply the recently developed IMOM/ELMO embedding method to the determination of core-ionized states. The IMOM/ELMO technique resulted from the combination of the single Slater determinant Δself-consistent-field-initial maximum overlap approach (ΔSCF-IMOM) with the QM/ELMO (quantum mechanics/extremely localized molecular orbital) embedding strategy, a method where only the chemically relevant region of the examined system is treated at fully quantum chemical level, while the rest is described through transferred and frozen extremely localized molecular orbitals (ELMOs). The IMOM/ELMO technique was initially validated by computing core-ionization energies for small molecules, and it was afterwards exploited to study larger biosystems. The obtained results are in line with those reported in previous studies that applied alternative ΔSCF approaches. This makes us envisage a possible future application of the proposed method to the interpretation of X-ray absorption spectra of large molecules.

Initial Maximum Overlap Method for Large Systems by the Quantum Mechanics/Extremely Localized Molecular Orbital Embedding Technique

Quantum chemistry offers a large variety of methods to treat excited states. Many of them are based on a multireference wave function ansatz and are therefore characterized by an intrinsic complexity and high computational costs. To overcome these drawbacks and also some limitations of simpler single-reference approaches (e.g., configuration interaction singles and time-dependent density functional theory), the single-determinant Δself-consistent field-initial maximum overlap method (ΔSCF-IMOM) has been proposed. This strategy substitutes the aufbau principle with a criterion that occupies molecular orbitals at successive SCF iterations on the basis of their maximum overlap with a proper set of guess orbitals for the target excited state. In this way, it prevents the SCF process to collapse to the ground state wave function and provides excited state single Slater determinant solutions to the SCF equations. Here, we propose to extend the applicability of the IMOM to the treatment of localized excited states of large systems. To accomplish this task, we coupled it with the QM/ELMO (quantum mechanics/extremely localized molecular orbitals) strategy, a quantum mechanical embedding method in which the most chemically relevant part of the system is treated with traditional quantum chemical approaches, while the rest is described by extremely localized molecular orbitals transferred from recently constructed libraries or proper model molecules. After presenting the theoretical foundations of the new IMOM/ELMO technique, in this paper, we will show and discuss the results of preliminary test calculations carried out on both model systems (i.e., decanoic acid, decene, decapentaene, and solvated acrolein) and a system of biological interest (flavin mononucleotide in the flavodoxin protein). We observed that, for localized excited states, the new IMOM/ELMO method provides reliable results, and it reproduces the outcomes of fully IMOM calculations within the chemical accuracy threshold (i.e., 0.043 eV) by including only a limited number of atoms in the QM region. Furthermore, the first application of our embedding technique to a larger biological system gave completely plausible results in line with those obtained through more traditional quantum mechanical methods, thus opening the possibility of using the new approach in future investigations of photobiology problems.

Three-Layer Multiscale Approach Based on Extremely Localized Molecular Orbitals to Investigate Enzyme Reactions

Quantum mechanics/molecular mechanics (QM/MM) calculations are widely used embedding techniques to computationally investigate enzyme reactions. In most QM/MM computations, the quantum mechanical region is treated through density functional theory (DFT), which offers the best compromise between chemical accuracy and computational cost. Nevertheless, to obtain more accurate results, one should resort to wave function-based methods, which however lead to a much larger computational cost already for relatively small QM subsystems. To overcome this drawback, we propose the coupling of our QM/ELMO (quantum mechanics/extremely localized molecular orbital) approach with molecular mechanics, thus introducing the three-layer QM/ELMO/MM technique. The QM/ELMO strategy is an embedding method in which the chemically relevant part of the system is treated at the quantum mechanical level, while the rest is described through frozen ELMOs. Since the QM/ELMO method reproduces results of fully QM computations within chemical accuracy and with a much lower computational effort, it can be considered a suitable strategy to extend the range of applicability and accuracy of the QM/MM scheme. In this paper, other than briefly presenting the theoretical bases of the QM/ELMO/MM technique, we will also discuss its validation on the well-tested deprotonation of acetyl coenzyme A by aspartate in citrate synthase.

Climbing Jacob's Ladder of Structural Refinement: Introduction of a Localized Molecular Orbital-Based Embedding for Accurate X-ray Determinations of Hydrogen Atom Positions

The positions of hydrogen atoms in molecules are fundamental in many aspects of chemistry. Nevertheless, most molecular structures are obtained from refinements of X-ray data exploiting the independent atom model (IAM), which uses spherical atomic densities and provides bond lengths involving hydrogen atoms that are too short compared to the neutron reference values. To overcome the IAM shortcomings, the wave function-based Hirshfeld atom refinement (HAR) method has been recently proposed, emerging as a promising strategy able to give element-hydrogen bond distances in excellent agreement with the neutron ones in terms of accuracy and precision. In this Letter, we propose a significant improvement of HAR based on the idea of describing the crystal environment explicitly in the underlying wave function calculation through a quantum mechanical embedding strategy that exploits extremely localized molecular orbitals. Test-bed refinements on a crystal structure characterized by strong intermolecular interactions are also discussed.

A Step toward the Quantification of Noncovalent Interactions in Large Biological Systems: The Independent Gradient Model-Extremely Localized Molecular Orbital Approach

The independent gradient model (IGM) is a recent electron density-based computational method that enables to detect and quantify covalent and noncovalent interactions. When applied to large systems, the original version of the technique still relies on promolecular electron densities given by the sum of spherically averaged atomic electron distributions, which leads to approximate evaluations of the inter- and intramolecular interactions occurring in systems of biological interest. To overcome this drawback and perform IGM analyses based on quantum mechanically rigorous electron densities also for macromolecular systems, we coupled the IGM approach with the recently constructed libraries of extremely localized molecular orbitals (ELMOs) that allow fast and reliable reconstructions of polypeptide and protein electron densities. The validation tests performed on small polypeptides and peptide dimers have shown that the novel IGM-ELMO strategy provides results that are systematically closer to the fully quantum mechanical ones and outperforms the IGM method based on the crude promolecular approximation, but still keeping a quite low computational cost. The results of the test calculations carried out on proteins have also confirmed the trends observed for the IGM analyses conducted on small systems. This makes us envisage the future application of the novel IGM-ELMO approach to unravel complicated noncovalent interaction networks (e.g., in protein-protein contacts) or to rationally design new drugs through molecular docking calculations and virtual high-throughput screenings.

Quantum Mechanics/Extremely Localized Molecular Orbital Embedding Strategy for Excited States: Coupling to Time-Dependent Density Functional Theory and Equation-of-Motion Coupled Cluster

The QM/ELMO (quantum mechanics/extremely localized molecular orbital) method is a recently developed embedding technique in which the most important region of the system under examination is treated at fully quantum mechanical level, while the rest is described by means of transferred and frozen extremely localized molecular orbitals. In this paper, we propose the first application of the QM/ELMO approach to the investigation of excited states, and, in particular, we present the coupling of the QM/ELMO philosophy with Time-Dependent Density Functional Theory (TDDFT) and Equation-of-Motion Coupled Cluster with single and double substitutions (EOM-CCSD). The proposed TDDFT/ELMO and EOM-CCSD/ELMO strategies underwent a series of preliminary tests that were already considered for the validation of other embedding methods for excited states. The obtained results showed that the novel techniques allow the accurate description of localized excitations in large systems by only including a relatively small number of atoms in the region treated at fully quantum chemical level. Furthermore, for TDDFT/ELMO, it was also observed that (i) the method enables to avoid the presence of artificial low-lying charge-transfer states that may affect traditional TDDFT calculations, even using functionals that do not take into account long-range corrections, and (ii) the novel approach can be also successfully exploited to investigate local electronic transitions in quite large systems (e.g., reduced model of the Green Fluorescent Protein), and the accuracy of the results can be improved by including a sufficient number of chemically crucial fragments/residues in the quantum mechanical region. Finally, concerning EOM-CCSD/ELMO, it was also seen that, despite the quite crude approximation of an embedding potential given by frozen extremely localized molecular orbitals, the new strategy is able to satisfactorily account for the effects of the environment. This work paves the way to further extensions of the QM/ELMO philosophy for the study of local excitations in extended systems, suggesting the coupling of the QM/ELMO approach with other quantum chemical strategies for excited states, from the simplest ΔSCF techniques to the most advanced and computationally expensive multireferences methods.

Quantum Crystallography in the Last Decade: Developments and Outlooks

In this review article, we report on the recent progresses in the field of quantum crystallography that has witnessed a massive increase of production coupled with a broadening of the scope in the last decade. It is shown that the early thoughts about extracting quantum mechanical information from crystallographic experiments are becoming reality, although a century after prediction. While in the past the focus was mainly on electron density and related quantities, the attention is now shifting toward determination of wavefunction from experiments, which enables an exhaustive determination of the quantum mechanical functions and properties of a system. Nonetheless, methods based on electron density modelling have evolved and are nowadays able to reconstruct tiny polarizations of core electrons, coupling charge and spin models, or determining the quantum behaviour at extreme conditions. Far from being routine, these experimental and computational results should be regarded with special attention by scientists for the wealth of information on a system that they actually contain.

Localized Molecular Orbital-Based Embedding Scheme for Correlated Methods

Embedding strategies currently provide the best compromise between accuracy and computational cost in modeling chemical properties and processes of large and complex systems. In this framework, different methods have been proposed all over the years, from the very popular QM/MM approaches to the more recent and very promising density matrix and density functional embedding techniques. Here, we present a further development of the quantum mechanics/extremely localized molecular orbital technique (QM/ELMO) method, a recently proposed multiscale embedding strategy in which the chemically active region of the investigated system is treated at a fully quantum mechanical level, while the rest is described by frozen extremely localized molecular orbitals previously transferred from proper libraries or tailor-made model molecules. In particular, in this work we discuss and assess in detail the extension of the QM/ELMO approach to density functional theory and post-Hartree-Fock techniques by evaluating its performances when it is used to describe chemical reactions, bond dissociations, and intermolecular interactions. The preliminary test calculations have shown that, in the investigated cases, the new embedding strategy enables the results of the corresponding fully quantum mechanical computations to be reproduced within chemical accuracy in almost all the cases but with a significantly reduced computational cost, especially when correlated post-Hartree-Fock strategies are used to describe the quantum mechanical subsystem. In light of the obtained results, we already envisage the future application of the new correlated QM/ELMO techniques to the investigation of more challenging problems, such as the modeling of enzyme catalysis, the study of excited states of biomolecules, and the refinement of macromolecular X-ray crystal structures.

Quantum Mechanics/Extremely Localized Molecular Orbital Method: A Fully Quantum Mechanical Embedding Approach for Macromolecules

The development of methods for the quantum mechanical study of macromolecules has always been an important challenge in theoretical chemistry. Nowadays, the techniques proposed in this context can be used to investigate very large systems and can be subdivided into two main categories: fragmentation and embedding strategies. In this paper, by modifying and improving the local self-consistent field approach originally proposed for quantum mechanics/molecular mechanics techniques, we introduce the new multiscale embedding quantum mechanics/extremely localized molecular orbital (QM/ELMO) method. The new strategy enables treatment of chemically relevant regions of large biological molecules through usual methods of quantum chemistry while describing the remaining parts of the systems by means of frozen extremely localized molecular orbitals transferred from properly constructed libraries. Test calculations have shown the correct functioning and the high reliability of the new approach, thus anticipating its possible applications to different fields of physical chemistry, such as rational drug design and structural refinements of proteins.

X-ray constrained spin-coupled technique: theoretical details and further assessment of the method

One of the well-established methods of modern quantum crystallography is undoubtedly the X-ray constrained wavefunction (XCW) approach, a technique that enables the determination of wavefunctions which not only minimize the energy of the system under examination, but also reproduce experimental X-ray diffraction data within the limit of the experimental errors. Initially proposed in the framework of the Hartree–Fock method, the strategy has been gradually extended to other techniques of quantum chemistry, but always remaining limited to a single-determinant ansatz for the wavefunction to extract. This limitation has been recently overcome through the development of the novel X-ray constrained spin-coupled (XCSC) approach [Genoni et al. (2018). Chem. Eur. J. 24, 15507–15511] which merges the XCW philosophy with the traditional spin-coupled strategy of valence bond theory. The main advantage of this new technique is the possibility of extracting traditional chemical descriptors (e.g. resonance structure weights) compatible with the experimental diffraction measurements, without the need to introduce information a priori or perform analyses a posteriori. This paper provides a detailed theoretical derivation of the fundamental equations at the basis of the XCSC method and also introduces a further advancement of its original version, mainly consisting in the use of molecular orbitals resulting from XCW calculations at the Hartree–Fock level to describe the inactive electrons in the XCSC computations. Furthermore, extensive test calculations, which have been performed by exploiting high-resolution X-ray diffraction data for salicylic acid and by adopting different basis sets, are presented and discussed. The computational tests have shown that the new technique does not suffer from particular convergence problems. Moreover, all the XCSC calculations provided resonance structure weights, spin-coupled orbitals and global electron densities slightly different from those resulting from the corresponding unconstrained computations. These discrepancies can be ascribed to the capability of the novel strategy to capture the information intrinsically contained in the experimental data used as external constraints.

Energy Decomposition Analysis for Metal Surface-Adsorbate Interactions by Block Localized Wave Functions

The energy decomposition analysis based on block localized wave functions (BLW-EDA) allows one to gain physical insight into the nature of chemical bonding, decomposing the interaction energy in (1) a "frozen" term, accounting for the attraction due to electrostatic and dispersion interactions, modulated by Pauli repulsion, (2) the variationally assessed polarization energy, and (3) the charge transfer. This method has so far been applied to gas- and condensed-phase molecular systems. However, its standard version is not compatible with fractionally occupied orbitals (i.e., electronic smearing) and, as a consequence, cannot be applied to metallic surfaces. In this work, we propose a simple and practical extension of BLW-EDA to fractionally occupied orbitals, termed Ensemble BLW-EDA. As illustrative examples, we have applied the developed method to analyze the nature of the interaction of various adsorbates on Pt(111), ranging from physisorbed water to strongly chemisorbed ethylene. Our results show that polarization and charge transfer both contribute significantly at the adsorption minimum for all studied systems. The energy decomposition analysis provides details with respect to competing adsorption sites (e.g., CO on atop vs hollow sites) and elucidates the respective importance of polarization and charge transfer for the increased adsorption energy of H₂S compared to H₂O. Our development will enable a deeper understanding of the impact of charge transfer on catalytic processes in general.

Libraries of Extremely Localized Molecular Orbitals. 3. Construction and Preliminary Assessment of the New Databanks

The fast and reliable determination of wave functions and electron densities of macromolecules has been one of the goals of theoretical chemistry for a long time, and in this context, several linear scaling techniques have been successfully devised over the years. Different approaches have been adopted to tackle this problem, and one of them exploits the fact that, according to the traditional chemical perception, molecules can be seen as constituted of recurring units (e.g., functional groups) with well-defined chemical features. This has led to the development of methods in which the global wave functions or electron densities of macromolecules are obtained by simply transferring density matrices or fuzzy electron densities associated with molecular fragments. In this context, we propose an alternative strategy that aims at quickly reconstructing wave functions and electron densities of proteins through the transfer of extremely localized molecular orbitals (ELMOs), which are orbitals strictly localized on small molecular units and, for this reason, easily transferable from molecule to molecule. To accomplish this task we have constructed original libraries of ELMOs that cover all the possible elementary fragments of the 20 natural amino acids in all their possible protonation states and forms. Our preliminary test calculations have shown that, compared to more traditional methods of quantum chemistry, the transfers from the novel ELMO databanks allow to obtain wave function and electron densities of large polypeptides and proteins at a significantly reduced computational cost. Furthermore, notwithstanding expected discrepancies, the obtained electron distributions and electrostatic potentials are in very good agreement with those obtained at Hartree-Fock and density functional theory (DFT) levels. Therefore, the results encourage to use the new libraries as alternatives to the popular pseudoatom-databases of crystallography in the refinement of crystallographic structures of macromolecules. In particular, in this context, we have already envisaged the coupling of the ELMO databanks with the promising Hirshfeld atom refinement technique to extend the applicability of the latter to very large systems.

Exploring charge density analysis in crystals at high pressure: data collection, data analysis and advanced modelling

The possibility to determine electron-density distribution in crystals has been an enormous breakthrough, stimulated by a favourable combination of equipment for X-ray and neutron diffraction at low temperature, by the development of simplified, though accurate, electron-density models refined from the experimental data and by the progress in charge density analysis often in combination with theoretical work. Many years after the first successful charge density determination and analysis, scientists face new challenges, for example: (i) determination of the finer details of the electron-density distribution in the atomic cores, (ii) simultaneous refinement of electron charge and spin density or (iii) measuring crystals under perturbation. In this context, the possibility of obtaining experimental charge density at high pressure has recently been demonstrated [Casatiet al.(2016).Nat. Commun.7, 10901]. This paper reports on the necessities and pitfalls of this new challenge, focusing on the speciessyn-1,6:8,13-biscarbonyl[14]annulene. The experimental requirements, the expected data quality and data corrections are discussed in detail, including warnings about possible shortcomings. At the same time, new modelling techniques are proposed, which could enable specific information to be extracted, from the limited and less accurate observations, like the degree of localization of double bonds, which is fundamental to the scientific case under examination.

Alternative definitions of the frozen energy in energy decomposition analysis of density functional theory calculations

In energy decomposition analysis (EDA) of intermolecular interactions calculated via density functional theory, the initial supersystem wavefunction defines the so-called "frozen energy" including contributions such as permanent electrostatics, steric repulsions, and dispersion. This work explores the consequences of the choices that must be made to define the frozen energy. The critical choice is whether the energy should be minimized subject to the constraint of fixed density. Numerical results for Ne2, (H2O)2, BH3-NH3, and ethane dissociation show that there can be a large energy lowering associated with constant density orbital relaxation. By far the most important contribution is constant density inter-fragment relaxation, corresponding to charge transfer (CT). This is unwanted in an EDA that attempts to separate CT effects, but it may be useful in other contexts such as force field development. An algorithm is presented for minimizing single determinant energies at constant density both with and without CT by employing a penalty function that approximately enforces the density constraint.

Libraries of Extremely Localized Molecular Orbitals. 1. Model Molecules Approximation and Molecular Orbitals Transferability

Despite more and more remarkable computational ab initio results are nowadays continuously obtained for large macromolecular systems, the development of new linear-scaling techniques is still an open and stimulating field of research in theoretical chemistry. In this family of methods, an important role is occupied by those strategies based on the observation that molecules are generally constituted by recurrent functional units with well-defined intrinsic features. In this context, we propose to exploit the notion of extremely localized molecular orbitals (ELMOs) that, due to their strict localization on small molecular fragments (e.g., atoms, bonds, or functional groups), are in principle transferable from one molecule to another. Accordingly, the construction of orbital libraries to almost instantaneously build up approximate wave functions and electron densities of very large systems becomes conceivable. In this work, the ELMOs transferability is further investigated in detail and, furthermore, suitable rules to construct model molecules for the computation of ELMOs to be stored in future databanks are also defined. The obtained results confirm the reliable transferability of the ELMOs and show that electron densities obtained from the transfer of extremely localized molecular orbitals are very close to the corresponding Hartree-Fock ones. These observations prompt us to construct new ELMOs databases that could represent an alternative/complement to the already popular pseudoatoms databanks both for determining electron densities and for refining crystallographic structures of very large molecules.

Libraries of Extremely Localized Molecular Orbitals. 2. Comparison with the Pseudoatoms Transferability

Due to both technical and methodological difficulties, determining and analyzing charge densities of very large molecular systems represents a serious challenge that, in the crystallographers community, has been mainly tackled by observing that the so-called pseudoatoms of the electron density multipole expansions are reliably transferable from molecule to molecule. This has led to the construction of pseudoatoms databanks that have allowed successful refinements of crystallographic structures of macromolecules, while taking into account their corresponding reconstructed electron distributions. A recent alternative/complement to the previous approach is represented by techniques based on extremely localized molecular orbitals (ELMOs) that, due to their strict localization on small molecular fragments (e.g., atoms, bonds, and functional groups), are also in principle exportable from system to system. The ELMOs transferability has been already tested in detail, and, in this work, it has been compared to the one of the pseudoatoms. To accomplish this task, electron distributions obtained both through the transfer of pseudoatoms and through the transfer of extremely localized molecular orbitals have been analyzed, especially taking into account topological properties and similarity indexes. The obtained results indicate that all the considered reconstruction methods give completely reasonable and similar charge densities, and, consequently, the new ELMOs libraries will probably represent new useful tools not only for refining crystal structures but also for computing approximate electronic properties of very large molecules.

Polarization contributions to intermolecular interactions revisited with fragment electric-field response functions

The polarization energy in intermolecular interactions treated by self-consistent field electronic structure theory is often evaluated using a constraint that the atomic orbital (AO) to molecular orbital transformation is blocked by fragments. This approach is tied to AO basis sets, overestimates polarization energies in the overlapping regime, particularly in large AO basis sets, and lacks a useful complete basis set limit. These problems are addressed by the construction of polarization subspaces based on the responses of isolated fragments to weak electric fields. These subspaces are spanned by fragment electric-field response functions, which can capture effects up to the dipole (D), or quadrupole (DQ) level, or beyond. Schemes are presented for the creation of both non-orthogonal and orthogonal fragment subspaces, and the basis set convergence of the polarization energies computed using these spaces is assessed. Numerical calculations for the water dimer, water-Na(+), water-Mg(2+), water-F(-), and water-Cl(-) show that the non-orthogonal DQ model is very satisfactory, with small differences relative to the orthogonalized model. Additionally, we prove a fundamental difference between the polarization degrees of freedom in the fragment-blocked approaches and in constrained density schemes. Only the former are capable of properly prohibiting charge delocalization during polarization.

Molecular Orbitals Strictly Localized on Small Molecular Fragments from X-ray Diffraction Data

Nowadays, the electron density is recognized as a fundamental property that contains most of the information concerning the electronic structure of molecules, and, therefore, its determination from high-resolution X-ray diffraction data is becoming more and more important. In this context, we propose a new strategy for the charge density analysis, strategy in which the chemical interpretability of the multipole model is combined with the quantum mechanical rigor of the wave function-based approaches. In particular, this novel technique aims at extracting molecular orbitals strictly localized on small molecular fragments (e.g., atoms, bonds, or functional groups) from a set of measured structure factors amplitudes. Preliminary tests have shown that their determination is really straightforward and, given their reliable transferability, we envisage the possibility of constructing new extremely localized molecular orbital databases as an alternative to the existing pseudoatom libraries.

Calculation of wave-functions with frozen orbitals in mixed quantum mechanics/molecular mechanics methods. II. Application of the local basis equation

The application of the local basis equation (Ferenczy and Adams, J. Chem. Phys. 2009, 130, 134108) in mixed quantum mechanics/molecular mechanics (QM/MM) and quantum mechanics/quantum mechanics (QM/QM) methods is investigated. This equation is suitable to derive local basis nonorthogonal orbitals that minimize the energy of the system and it exhibits good convergence properties in a self-consistent field solution. These features make the equation appropriate to be used in mixed QM/MM and QM/QM methods to optimize orbitals in the field of frozen localized orbitals connecting the subsystems. Calculations performed for several properties in divers systems show that the method is robust with various choices of the frozen orbitals and frontier atom properties. With appropriate basis set assignment, it gives results equivalent with those of a related approach [G. G. Ferenczy previous paper in this issue] using the Huzinaga equation. Thus, the local basis equation can be used in mixed QM/MM methods with small size quantum subsystems to calculate properties in good agreement with reference Hartree-Fock-Roothaan results. It is shown that bond charges are not necessary when the local basis equation is applied, although they are required for the self-consistent field solution of the Huzinaga equation based method. Conversely, the deformation of the wave-function near to the boundary is observed without bond charges and this has a significant effect on deprotonation energies but a less pronounced effect when the total charge of the system is conserved. The local basis equation can also be used to define a two layer quantum system with nonorthogonal localized orbitals surrounding the central delocalized quantum subsystem.

QM/MM methods for biomolecular systems

Combined quantum-mechanics/molecular-mechanics (QM/MM) approaches have become the method of choice for modeling reactions in biomolecular systems. Quantum-mechanical (QM) methods are required for describing chemical reactions and other electronic processes, such as charge transfer or electronic excitation. However, QM methods are restricted to systems of up to a few hundred atoms. However, the size and conformational complexity of biopolymers calls for methods capable of treating up to several 100,000 atoms and allowing for simulations over time scales of tens of nanoseconds. This is achieved by highly efficient, force-field-based molecular mechanics (MM) methods. Thus to model large biomolecules the logical approach is to combine the two techniques and to use a QM method for the chemically active region (e.g., substrates and co-factors in an enzymatic reaction) and an MM treatment for the surroundings (e.g., protein and solvent). The resulting schemes are commonly referred to as combined or hybrid QM/MM methods. They enable the modeling of reactive biomolecular systems at a reasonable computational effort while providing the necessary accuracy.

Role of the gauche effect and local 1,3-dipole–dipole interactions in stabilizing an unusual conformation of tartarodinitriles

This paper reports the synthesis, X-ray and NMR investigations of chiral and meso dinitriles of tartaric acid (tartarodinitriles) and their O,O′-diacetyl and O,O′-dibenzoyl derivatives. While in chiral tartaric acid its esters and NH amides the four-atom carbon chain is overwhelmingly trans, it is gauche in chiral tartarodinitriles. Conversely, meso-tartaric acid, its esters and amides display a tendency for the gauche conformation, but meso-tartarodinitriles usually have the trans conformation. The NMR studies of tartarodinitriles reveal the presence of a conformational equilibrium in solution with a preference for those conformers found in crystals. The gauche conformation of meso-tartarodinitriles seems to be stabilized by local dipolar interactions, intramolecular C—H...O hydrogen bonds and by a tendency for maximization of the gauche effect, the latter effect also operating in chiral tartarodinitriles. Stabilization of the trans conformers of tartarodinitriles in the crystals seems to originate from specific intermolecular interactions.

On the suitability of strictly localized orbitals for hybrid QM/MM calculations

In the QM/MM method we have developed (LSCF/MM), the QM and the MM parts are held together by means of strictly localized bonding orbitals (SLBOs). Generally these SLBOs are derived from localized bond orbitals (LBOs) that undergo tails deletion, resulting in a nonpredictable change of their properties. An alternative set of SLBOs is provided by the extremely localized molecular orbitals (ELMOs) approach, where the orbitals are rigorously localized on some prefixed atoms without tails on the other atoms of the molecule. A comparative study of SLBOs arising from various localization schemes and ELMOs is presented to test the reliability and the transferability of these functions within the Local Self-Consistent Field (LSCF) framework. Two types of chemical bonds were considered: C--C and C--O single bonds. The localized functions are obtained on the ethane and the methanol molecules, and are tested on beta-alanine and diethyl ether molecules. Moreover, the various protonation forms of beta-alanine have been investigated to illustrate how well the polarity variation of the chemical bond can be handled throughout a chemical process. At last, rotation energy profiles around C--C and C--O bonds are reproduced for butane and fluoromethanol. Energetic, geometric, as well as electronic factors all indicate that ELMO functions are much more transferable from one molecule to another, leading to results closer to the usual SCF reference than any other calculations involving any other localized orbitals. When the shape of the orbital is the most important factor then ELMO functions will perform as well as any other localized orbital.

A new scheme for determining the intramolecular seven-membered ring N–H⋯OC hydrogen-bonding energies of glycine and alanine peptides

In this paper a new scheme was proposed to calculate the intramolecular hydrogen-bonding energies in peptides and was applied to calculate the intramolecular seven-membered ring N-H...O=C hydrogen-bonding energies of the glycine and alanine peptides. The density-functional theory B3LYP6-31G(d) and B3LYP6-311G(d,p) methods and the second-order Moller-Plesset perturbation theory MP26-31G(d) method were used to calculate the optimal geometries and frequencies of glycine and alanine peptides and related structures. MP26-311++G(d,p), MP26-311++G(3df,2p), and MP2/aug-cc-pVTZ methods were then used to evaluate the single-point energies. It was found that the B3LYP6-31G(d), MP26-31G(d), and B3LYP6-311G(d,p) methods yield almost similar structural parameters for the conformers of the glycine and alanine dipeptides. MP2/aug-cc-pVTZ predicts that the intramolecular seven-membered ring N-H...O=C hydrogen-bonding strength has a value of 5.54 kcal/mol in glycine dipeptide and 5.73 and 5.19 kcal/mol in alanine dipeptides, while the steric repulsive interactions of the seven-membered ring conformers are 4.13 kcal/mol in glycine dipeptide and 6.62 and 3.71 kcal/mol in alanine dipeptides. It was also found that MP26-311++G(3df,2p) gives as accurate intramolecular N-H...O=C hydrogen-bonding energies and steric repulsive interactions as the much more costly MP2/aug-cc-pVTZ does.

Optimal virtual orbitals to relax wave functions built up with transferred extremely localized molecular orbitals

Extremely localized molecular orbitals (ELMOs), namely orbitals strictly localized on molecular fragments, are easily transferable from one molecule to another one. Hence, they provide a natural way to set up the electronic structure of large molecules using a data base of orbitals obtained from model molecules. However, this procedure obviously increases the energy with respect to a traditional MO calculation. To gain accuracy, it is important to introduce a partial electron delocalization. This can be carried out by defining proper optimal virtual orbitals that supply an efficient set for nonorthogonal configurations to be employed in VB-like expansions.