X-ray restrained extremely localized molecular orbitals for the embedding of quantum mechanical calculations

The X-ray restrained wavefunction (XRW) method is a quantum crystallographic technique that allows the calculation of molecular wavefunctions adapted to minimize the difference between computed and reference structure factor amplitudes. The latter result from experimental measurements on crystals or from advanced theoretical calculations with periodic boundary conditions, and are used as external restraints in a traditional least-squares structural refinement. Detailed investigations have shown that the technique is able to reliably capture the effects of the crystal field on the molecular electron density. In a recent application, electron distributions obtained from preliminary X-ray restrained wavefunction calculations have been employed in the framework of frozen density embedding theory to embed excited state computations of well defined subsystems. Inspired by these results, it was decided to test, for the first time, the X-ray restrained extremely localized molecular orbitals (XR-ELMOs) along with the recently developed quantum mechanics/extremely localized molecular orbital multiscale embedding approach. By exploiting XR-ELMOs obtained through XRW calculations that used structure factor amplitudes resulting from periodic ab initio computations, excited state calculations of acrylamide in an environment mimicking the one of the crystal structure were performed. In all these computations, the QM region coincides with the crystal asymmetric unit and the ELMO subsystem consisted of two other acrylamide molecules involved in direct hydrogen bonds with the reference unit. The shifts of the excitation energies with respect to the corresponding gas-phase values were evaluated as a function of different parameters on which the computations with XR-ELMOs depend. For instance, the dependence on the resolution of the sets of structure factors that were used to determine the embedding XR-ELMOs were assessed in particular. The results have shown that the use of XR-ELMOs slightly (but not negligibly) improves the description of excited states compared to the gas-phase ELMOs. Once again, these results demonstrate the efficiency of the XRW approach in incorporating environment effects into the calculated molecular orbitals and, hence, into the corresponding electron densities.

lamaGOET: an interface for quantum crystallography

In quantum crystallography, theoretical calculations and crystallographic refinements are closely intertwined. This means that the employed software must be able to perform both quantum-mechanical calculations and crystallographic least-squares refinements. So far, the program Tonto is the only one able to do that. The lamaGOET interface described herein deals with this issue since it interfaces dedicated quantum-chemical software (the widely used Gaussian package and the specialized ELMOdb program) with the refinement capabilities of Tonto. Three different flavours of quantum-crystallographic refinements of the dipetide glycyl-L-threonine dihydrate are presented to showcase the capabilities of lamaGOET: Hirshfeld atom refinement (HAR), HAR-ELMO, namely HAR coupled with extremely localized molecular orbitals, and X-ray constrained wavefunction fitting.

The advanced treatment of hydrogen bonding in quantum crystallography

Although hydrogen bonding is one of the most important motifs in chemistry and biology, H-atom parameters are especially problematic to refine against X-ray diffraction data. New developments in quantum crystallography offer a remedy. This article reports how hydrogen bonds are treated in three different quantum-crystallographic methods: Hirshfeld atom refinement (HAR), HAR coupled to extremely localized molecular orbitals and X-ray wavefunction refinement. Three different compound classes that form strong intra- or intermolecular hydrogen bonds are used as test cases: hydrogen maleates, the tripeptide L-alanyl-glycyl-L-alanine co-crystallized with water, and xylitol. The differences in the quantum-mechanical electron densities underlying all the used methods are analysed, as well as how these differences impact on the refinement results.

Extending Libraries of Extremely Localized Molecular Orbitals to Metal Organic Frameworks: A Preliminary Investigation

Libraries of extremely localized molecular orbitals (ELMOs) have been recently assembled to reconstruct approximate wavefunctions of very large biological systems, such as polypeptides and proteins. In this paper, we investigate for the first time the possibility of using ELMO transferability to also quickly obtain wavefunctions, electron densities, and electrostatic potentials of three-dimensional coordination polymers such as metal organic frameworks (MOFs). To accomplish this task, we propose a protocol that, in addition to exploiting the usual exportability of extremely localized molecular orbitals, also takes advantage of the novel QM/ELMO (quantum mechanics/extremely localized molecular orbital) approach to properly describe the secondary building units of MOFs. As a benchmark test, our technique has been applied to the well-known metal organic framework HKUST-1 ({Cu3(BTC)2}n, with BTC=1,3,5-benzenetricarboxylate) to quickly calculate electrostatic potential maps in the small and large cavities inside the network. On the basis of the obtained results, we envisage further improvements and applications of this strategy, which can be also seen as a starting point to perform less computationally expensive quantum mechanical calculations on metal organic frameworks with the goal of investigating transformation phenomena such as chemisorption.

Energy Decomposition Analysis Method for Metallic Systems

In this work, we present the first extension of an energy decomposition analysis (EDA) method to metallic systems. We extend the theory of our Hybrid Absolutely Localized Molecular Orbitals (HALMO)...

Consistent Inclusion of Continuum Solvation in Energy Decomposition Analysis: Theory and Application to Molecular CO2 Reduction Catalysts

<p>To facilitate computational investigation of intermolecular interactions in the solution phase, we report the development of ALMO-EDA(solv), a scheme that allows the application of continuum solvent models within the framework of energy decomposition analysis (EDA) based on absolutely localized molecular orbitals (ALMOs). In this scheme, all the quantum mechanical states involved in the variational EDA procedure are computed with the presence of solvent environment so that solvation effects are incorporated in the evaluation of all its energy components. After validation on several model complexes, we employ ALMO-EDA(solv) to investigate substituent effects on two classes of complexes that are related to electrochemical CO₂ reduction catalysis. For [FeTPP(CO₂−κC)]²⁻ (TPP = tetraphenylporphyrin), we reveal that two ortho substituents which yield most favorable CO2 binding, −N(CH₃)₃⁺ (TMA) and −OH, stabilize the complex via through-structure and through-space mechanisms, respectively. The Coulombic interaction between the positively charged TMA group and activated CO₂ is found to be largely attenuated by the polar solvent. Furthermore, we also provide computational support for the design strategy of utilizing bulky, flexible ligands to stabilize activated CO₂ via long-range Coulomb interactions, which creates biomimetic solvent-inaccessible “pockets” in that electrostatics is unscreened. For the reactant and product complexes associated with the electron transfer from the <i>p</i>-terphenyl radical anion to CO₂ , we demonstrate that the double terminal substitution of <i>p</i>-terphenyl by electron-withdrawing groups considerably strengthens the binding in the product state while moderately weakens that in the reactant state, which are both dominated by the substituent tuning of the electrostatics component. These applications illustrate that this new extension of ALMO-EDA provides a valuable means to unravel the nature of intermolecular interactions and quantify their impacts on chemical reactivity in solution.<br></p>

Consistent Inclusion of Continuum Solvation in Energy Decomposition Analysis: Theory and Application to Molecular CO2 Reduction Catalysts

<p>To facilitate computational investigation of intermolecular interactions in the solution phase, we report the development of ALMO-EDA(solv), a scheme that allows the application of continuum solvent models within the framework of energy decomposition analysis (EDA) based on absolutely localized molecular orbitals (ALMOs). In this scheme, all the quantum mechanical states involved in the variational EDA procedure are computed with the presence of solvent environment so that solvation effects are incorporated in the evaluation of all its energy components. After validation on several model complexes, we employ ALMO-EDA(solv) to investigate substituent effects on two classes of complexes that are related to electrochemical CO₂ reduction catalysis. For [FeTPP(CO₂−κC)]²⁻ (TPP = tetraphenylporphyrin), we reveal that two ortho substituents which yield most favorable CO2 binding, −N(CH₃)₃⁺ (TMA) and −OH, stabilize the complex via through-structure and through-space mechanisms, respectively. The Coulombic interaction between the positively charged TMA group and activated CO₂ is found to be largely attenuated by the polar solvent. Furthermore, we also provide computational support for the design strategy of utilizing bulky, flexible ligands to stabilize activated CO₂ via long-range Coulomb interactions, which creates biomimetic solvent-inaccessible “pockets” in that electrostatics is unscreened. For the reactant and product complexes associated with the electron transfer from the <i>p</i>-terphenyl radical anion to CO₂ , we demonstrate that the double terminal substitution of <i>p</i>-terphenyl by electron-withdrawing groups considerably strengthens the binding in the product state while moderately weakens that in the reactant state, which are both dominated by the substituent tuning of the electrostatics component. These applications illustrate that this new extension of ALMO-EDA provides a valuable means to unravel the nature of intermolecular interactions and quantify their impacts on chemical reactivity in solution.<br></p>