Insight into Substrate Recognition by Urea-Based Helical Foldamer Catalysts Using a DFT Global Optimization Approach.

Peptides and foldamers have recently gained increasing attention as chiral catalysts to achieve challenging (asymmetric) transformations. We previously reported that short helically folded aliphatic oligoureas in combination with achiral Brønsted bases are effective H-bonding catalysts for C-C bond-forming reactions─i.e., the conjugate addition of 1,3-dicarbonyl pronucleophiles to nitroalkenes─with high reactivity and selectivity and at remarkably low chiral catalyst/substrate molar ratios. This theoretical investigation at the density functional theory level of theory, aims to both analyze how the substrates of the reaction interact with the foldamer catalyst and rationalize a chain-length dependence effect on the catalytic properties. We confirm that the first two ureas are the only H-bond donors available to interact with external molecules. Moreover, each urea site interacts with one of the two reactants allowing a short distance between the two reacting carbons, thus facilitating the conjugated addition. Additionally, it was observed that the molecular recognition and catalyst-substrate interactions are mainly governed by electrostatic interactions but not orbital interactions (see from NBO if this is finally true). On these grounds, an electrostatic potential (ESP) analysis showed an important internal charge separation in the catalyst, the positive ESP region being concentrated around the first two ureas, with its area extending as the number of residues increases.

The CRYSTAL code, 1976-2020 and beyond, a long story.

CRYSTAL is a periodic ab initio code that uses a Gaussian-type basis set to express crystalline orbitals (i.e., Bloch functions). The use of atom-centered basis functions allows treating 3D (crystals), 2D (slabs), 1D (polymers), and 0D (molecules) systems on the same grounds. In turn, all-electron calculations are inherently permitted along with pseudopotential strategies. A variety of density functionals are implemented, including global and range-separated hybrids of various natures and, as an extreme case, Hartree-Fock (HF). The cost for HF or hybrids is only about 3-5 times higher than when using the local density approximation or the generalized gradient approximation. Symmetry is fully exploited at all steps of the calculation. Many tools are available to modify the structure as given in input and simplify the construction of complicated objects, such as slabs, nanotubes, molecules, and clusters. Many tensorial properties can be evaluated by using a single input keyword: elastic, piezoelectric, photoelastic, dielectric, first and second hyperpolarizabilities, etc. The calculation of infrared and Raman spectra is available, and the intensities are computed analytically. Automated tools are available for the generation of the relevant configurations of solid solutions and/or disordered systems. Three versions of the code exist: serial, parallel, and massive-parallel. In the second one, the most relevant matrices are duplicated on each core, whereas in the third one, the Fock matrix is distributed for diagonalization. All the relevant vectors are dynamically allocated and deallocated after use, making the code very agile. CRYSTAL can be used efficiently on high performance computing machines up to thousands of cores.

Anharmonic Vibrational States of Solids from DFT Calculations. Part I: Description of the Potential Energy Surface.

A computational approach is presented to compute anharmonic vibrational states of solids from quantum-mechanical DFT calculations by taking into explicit account phonon-phonon couplings via the vibrational configuration interaction (VCI) method. The Born-Oppenheimer potential energy surface (PES) is expanded in a Taylor's series in terms of harmonic normal coordinates, centered at the equilibrium nuclear configuration, is truncated to quartic order, and contains one-mode, two-mode, and three-mode interatomic force constants. The description of the anharmonic terms of the PES involves the numerical evaluation of high-order energy derivatives (cubic and quartic in our case) with respect to nuclear displacements and constitutes the most computationally demanding step in the characterization of anharmonic vibrational states of materials. Part I is devoted to the description of the PES. Four different numerical approaches are presented for the description of the potential, all based on a grid representation of the PES in the basis of the normal coordinates, that require different ingredients (energy and/or forces) to be evaluated at each point (i.e., nuclear configuration) of the grid. The numerical stability and relative computational efficiency of the various schemes for the description of the PES are discussed on two molecular systems (water and methane) and two extended solids (Ice-XI and MgH2). All the presented algorithms are implemented into a developmental version of the Crystal program.

Anharmonic Vibrational States of Solids from DFT Calculations. Part II: Implementation of the VSCF and VCI Methods.

Two methods are implemented in the Crystal program for the calculation of anharmonic vibrational states of solids: the vibrational self-consistent field (VSCF) and the vibrational configuration-interaction (VCI). While the former is a mean-field approach, where each vibrational mode interacts with the average potential of the others, the latter allows for an explicit and complete account of mode-mode correlation. Both schemes are based on the representation of the adiabatic potential energy surface (PES) discussed in Part I, where the PES is expanded in a Taylor's series so as to include up to cubic and quartic terms. The VSCF and VCI methods are formally presented and their numerical parameters discussed. In particular, the convergence of computed anharmonic vibrational states, within the VCI method, is investigated as a function of the truncation of the expansion of the nuclear wave function. The correctness and effectiveness of the implementation is discussed by comparing with available theoretical and experimental data on both molecular and periodic systems. The effect of the adopted basis set and exchange-correlation functional in the description of the PES on computed anharmonic vibrational states is also addressed.

The VN3H defect in diamond: a quantum-mechanical characterization.

The VN3H defect in diamond (a vacancy surrounded by three nitrogen and one carbon atoms, the latter being saturated by a hydrogen atom) is investigated quantum-mechanically by use of a periodic supercell approach, an all-electron Gaussian-type basis set, "hybrid" functionals of density functional theory, and the Crystal program. Three fully optimized structural models (supercells containing 32, 64, and 128 atoms) are considered to investigate the effect of defect concentration. The electronic configuration of the defect is reported along with a description of its structural features. In particular, the influence of the lone-pair electrons of the three nitrogen atoms on the C-H bond is discussed. A thorough characterization of the vibrational spectroscopic features of the VN3H defect is also presented, where the anharmonicity of the most relevant normal modes is discussed. The infrared and Raman spectra show specific peaks, which allow for the identification of this particular defect among the many defects that are commonly present in both natural and irradiation-damaged diamonds. In particular, the main feature of the spectral fingerprint of the defect (i.e. the C-H stretching mode), experimentally observed at 3107 cm-1, is here computed at 3094 cm-1 with the B3LYP "hybrid" functional (with an anharmonic redshift of 157 cm-1 with respect to its harmonic value). The role played by the three nitrogen atoms on the spectral features of the defect is clearly identified through the redshift due to the 14N → 15N isotopic substitution.

Vibrational Fingerprints of Low-Lying Pt(n)P(2n) (n = 1-5) Cluster Structures from Global Optimization Based on Density Functional Theory Potential Energy Surfaces.

Vibrational fingerprints of small Pt(n)P(2n) (n = 1-5) clusters were computed from their low-lying structures located from a global exploration of their DFT potential energy surfaces with the GSAM code. Five DFT methods were assessed from the CCSD(T) wavenumbers of PtP2 species and CCSD relative energies of Pt2P4 structures. The eight first Pt(n)P(2n) isomers found are reported. The vibrational computations reveal (i) the absence of clear signatures made by overtone or combination bands due to very weak mechanical and electrical anharmonicities and (ii) some significant and recurrent vibrational fingerprints in correlation with the different PP bonding situations in the Pt(n)P(2n) structures.

Intramolecular vibrational redistribution in the non-radiative excited state decay of uracil in the gas phase: an ab initio molecular dynamics study.

We report a study of intramolecular vibrational distribution (IVR) occurring in the electronic ground state of uracil (S0) in the gas phase, following photoexcitation in the lowest energy bright excited state (Sπ) and decay through the ethylene-like Sπ/S0 Conical Intersection (CI-0π). To this aim we have performed 20 independent ab initio molecular dynamics simulations starting from CI-0π (ten of them with 1 eV kinetic energy randomly distributed over the different molecular degrees of freedom) and 10 starting from the ground state minimum (Franck-Condon, FC, point), with the excess kinetic energy equal to the energy gap between CI-0π and the FC point. The simulations, exploiting PBE0/6-31G(d) calculations, were performed over an overall period of 10 ps. A thorough statistical analysis of the variation of the geometrical parameters of uracil during the simulation time and of the distribution of the kinetic energy among the different vibrational degrees of freedom provides a consistent picture of the IVR process. In the first 0-200 fs the structural dynamics involve mainly the recovery of the average planarity. In the 200-600 fs time range, a substantial activation of CO and NH degrees of freedom is observed. After 500-600 fs most of the geometrical parameters reach average values similar to those found after 10 ps, though the system cannot be considered to be in equilibrium yet.

Structural investigation of microhydrated thymine clusters and vibrational study of isolated and aqueous forms of thymine using DFT level of theory.

This theoretical study provides the physically reasonable structures of the microhydrated thymine clusters, from the mono- to the penta-hydrated species, by the exploration of their B3LYP and B3LYP-D potential energy surfaces using a global search algorithm of minima (GSAM). The anharmonic vibrational computations of the isolated and aqueous thymine are also reported. They were performed from B3LYP and B3LYP-D potential electronic surfaces followed by a second order perturbative treatment of the anharmonicity. On that point, the computational strategy to properly take into account the effect of the polar protic solvent consists in considering a micro-hydrated thymine cluster [T,nH2O] surrounded by a polarizable continuum model (PCM). The number of solvent molecules was chosen in such a way that the micro-hydrated cluster presents only one dominant stable conformer at 298 K. All the VPT2 fundamental transitions obtained from the B3LYP and B3LYP-D quartic force fields are reported for the isolated form ([T,0H2O]) and for the aqueous form ([T,nH2O + PCM]). The theoretical results are compared to the available experimental data, which are for some of them reassigned, in order to assess the reliability of the B3LYP and B3LYP-D methods for the anharmonic treatment of such organic species in a polar protic solvent.

The electronic structure of MgO nanotubes. An ab initio quantum mechanical investigation.

The structural, vibrational and response properties of the (n,0) and (m,m) MgO nanotubes are computed by using a Gaussian type basis set, a hybrid functional (B3LYP) and the CRYSTAL09 code. Tubes in the range 6 ≤ n ≤ 140 and 3 ≤ m ≤ 70 were considered, being n = 2 × m the number of MgO units in the unit cell (so, the maximum number of atoms is 280). Tubes are built by rolling up the fully relaxed 2-D conventional cell (2 MgO units, with oxygen atoms protruding from the Mg plane alternately up and down by 0.38 Å). The relative stability of the (n,0) with respect to the (m,m) family, the relaxation energy and equilibrium geometry, the band gap, the IR vibrational frequencies and intensities, and the electronic and ionic contributions to the polarizability are reported. All these properties are shown to converge smoothly to the monolayer values. Absence of negative vibrational frequencies confirms that the tubes have a stable structure. The parallel component of the polarizability α(∥) converges very rapidly to the monolayer value, whereas α(⊥) is still changing at n = 140; however, when extrapolated to very large n values, it coincides with the monolayer value to within 1%. The electronic contribution to α is in all cases (α(∥) and α(⊥); 6 ≤ n ≤ 140) smaller than the vibrational contribution by about a factor of three, at variance with respect to more covalent tubes such as the BN ones, for which the ratio between the two contributions is reversed.

The use of the GSAM approach for the structural investigation of low-lying isomers of molecular clusters from density-functional-theory-based potential energy surfaces: the structures of microhydrated nucleic acid bases.

This study presents structural properties of microhydrated nucleic acid bases (NABs) - uracil (U), thymine (T), guanine (G), adenine (A), and cytosine (C) - investigated by theoretical computations at the B3LYP level of theory. To obtain the different representations of these microhydrated species, we applied the GSAM procedure: the most stable conformers labeled X,nH2O (X = U, T, G, A and n = 1...5) for which the Boltzmann population is higher than 2% at 298K are calculated at the B3LYP and B3LYP-D levels of theory. At the B3LYP level, our calculated geometries are compared with those obtained in the literature. New physically relevant isomers are found with the GSAM algorithm, especially for the tetra- and pentahydrated species. The use of DFT-D functional does not strongly modify the relative energies of the isomers for the monohydrated species. When the number of water molecules increases, the results become extremely sensitive to the consideration of dispersion contributions.

Theoretical strategy to build structural models of microhydrated inorganic systems for the knowledge of their vibrational properties: the case of the hydrated nitrate aerosols.

This study provides theoretical anharmonic calculations for microhydrated NaNO3-labeled (NaNO3, nH2O)x with a water-to-solute ratio (n) ranging from 1 to 3. A representative geometrical model of these forms was first investigated by simulating the molecular clusters as (NaNO3,1H2O)x with x = 1 to 4. The comparison between the calculated time independent anharmonic frequencies using the B3LYP-D/6-311+G(d,p) method and their experimental counterparts led to the choice of a supercluster model. The most probable structures of (NaNO3,nH2O)3 molecular system were investigated by using our global search algorithm we developed recently (GSAM code) both at the B3LYP/6-311+G(d,p) and the B3LYP-D/6-311+G(d,p) levels of theory. The quality of the structural model is illustrated by comparing the B3LYP/6-311+G(d,p) and B3LYP-D/6-311+G(d,p) anharmonic vibrational signatures with those obtained from IR experiments. While an average deviation of 16 cm(-1) is observed in the case of the B3LYP computations, the deviation is reduced to 7 cm(-1) for the B3LYP-D computations.

Doping-enhanced hyperpolarizabilities of silicon clusters: a global ab initio and density functional theory study of Si10 (Li, Na, K)n (n=1, 2) clusters.

A global theoretical study of the (hyper)polarizabilities of alkali doped Si(10) is presented and discussed. First, a detailed picture about the low lying isomers of Si(10)Li, Si(10)Na, Si(10)K, Si(10)Li(2), Si(10)Na(2), and Si(10)K(2) has been obtained in a global manner. Then, the microscopic first (hyper)polarizabilities of the most stable configurations have been determined by means of ab initio methods of high predictive capability such as those based on the Møller-Plesset perturbation and coupled cluster theory, paying extra attention to the (hyper)polarizabilities of the open shell mono-doped systems Si(10)Li, Si(10)Na, Si(10)K, and the influence of spin contamination. These results were used to assess the performance of methods of low computational cost based on density functional theory (DFT) in the reliable computation of these properties in order to proceed with an in-depth study of their evolution as a function of the alkali metal, the cluster composition, and the cluster structure. The most interesting outcomes of the performed (hyper)polarizability study indicate that while alkali doping leaves the per atom polarizability practically unaffected, influences dramatically the hyperpolarizabilities of Si(10). The lowest energy structures of the mono-doped clusters are characterized by significantly enhanced hyperpolarizabilities as compared to the analogue neutral or charged bare silicon clusters Si(10) and Si(11), while, certain patterns governed by the type and the number of the doping agents are followed. The observed hyperpolarizability increase is found to be in close connection with specific cluster to alkali metal charge transfer excited states and to the cluster structures. Moreover, an interesting correlation between the anisotropy of the electron density, and the hyperpolarizabilities of these systems has been observed. Finally, it is important to note that the presented method assessment points out that among the various DFT functionals used in this work, (B3LYP, B3PW91, BhandHLYP, PBE0, CAM-B3LYP, LC-BLYP, LC-BPW91) only B3PW91 and PBE0 out of the seven provided a consistent quantitative performance for both polarizabilities and hyperpolarizabilities with respect to the ab initio methods utilized here. On the other hand, the long range corrected functionals LC-(U)BLYP and LC-(U)BPW91 (µ = 0.47) failed to supply quantitatively accurate hyperpolarizability results in all the studied clusters while the CAM-(U)B3LYP functional performs satisfactory only in the case of the Na and K doped systems.

A global search algorithm of minima exploration for the investigation of low lying isomers of clusters from density functional theory-based potential energy surfaces: The example of Si(n) (n=3,15) as a test case.

Using an effective generation algorithm coupled with a PBE0/LANL2DZdp level of theory, 905 stable structures of Si(n) (n=3,15) have been found. This global search algorithm of minima exploration includes two original parts: the spheroidal generation, allowing the generation of rings, sphericals, m rings cylinders, and planar structures, and the raking optimization, which discards step by step the conformations that become physically unreasonable during the optimization process. The 142 isomers lying below 1 eV are reported and include the 28 structures reported in the literature. Conformational energies are well reproduced with respect to the values previously published (DeltaE=0,00+/-0,09 eV).

Vibrational analysis of glycine radical: a comparative ab initio static and dynamic study.

We present quantum mechanical (QM) vibrational computations beyond the harmonic approximation for an organic molecule that exhibits both torsional and NH(2) out of plane type modes: the glycine radical. The effective second order perturbative, variational and variation-perturbation treatments-defined as static approaches-as well as vibrational analysis from ab initio molecular dynamics trajectories at 300 K and 600 K were performed using the B3LYP/6-31+G(d,p) description of the electronic structure. Theses schemes are compared in terms of prediction of fundamental transitions, simulation of the corresponding medium infrared (MIR) spectrum and extraction of substantial information for the understanding of chemical problems. The validity of the analyses is checked for a similar molecule, formamide, for which experimental data are available.

Fermi resonances of borohydrides in a crystalline environment of alkali metals.

Vibrational spectra of BH(4)(-) and its isotopic analogues in a crystalline environment of alkali metals cations (K(+), Rb(+), Cs(+)) have been investigated beyond the harmonic approximation using a variational approach supported by computations of B3LYP type anharmonic force fields. From the comparison of the observed and simulated IR spectra, the influence of the anharmonic couplings on the band position and on the relative intensity of the allowed vibrational transitions is discussed. Here, the effect of the crystalline environment induces a blue shift of about 50 and 100 cm(-1) respectively for the bending and stretching modes of BH(4)(-). Furthermore, anharmonic effects, which are exclusively well reproduced by a variational approach, are needed to yield reliable positions and relative amplitudes of IR allowed combination and overtone transitions. This leads to theoretical results fitting their experimental counterpart between 6 and 30 cm(-1) in the investigated series.

Accurate vibrational spectra and magnetic properties of organic free radicals: the case of H2CN.

We present the structural, magnetic, and vibrational properties of H2CN computed using a second-order perturbative approach in which equilibrium values and harmonic frequencies evaluated at the coupled-cluster level are combined with anharmonic and vibrational averaging contributions obtained by hybrid Hartree-Fock/Kohn-Sham methods. Our computations lead to remarkably accurate results and suggest some revision of the experimental vibrational assignments.

Vibrational computations beyond the harmonic approximation: performances of the B3LYP density functional for semirigid molecules.

The performances of the B3LYP density functional in the computation of harmonic and anharmonic frequencies were tested using 14 standard basis sets of double and triple zeta quality for a set of semirigid molecules containing from 4 to 12 atoms. The quality of the results is assessed by comparison with the most reliable computations available in the literature. The study reveals that the relatively cheap 6-31+G(d,p) basis set performs a very good job for harmonic frequency calculations and that B3LYP anharmonicities are in close agreement with the reference values irrespective of the basis set used. On these grounds "hybrid force fields" are proposed to achieve the best compromise between computer time and quality of the results.