Critical test of some computational methods for prediction of NMR <Superscript>1</Superscript>H and <Superscript>13</Superscript>C chemical shifts

Performance of 18 DFT functionals (B1B95, B3LYP, B3PW91, B97D, BHandHLYP, BMK, CAM-B3LYP, HSEh1PBE, M06-L, mPW1PW91, O3LYP, OLYP, OPBE, PBE1PBE, tHCTHhyb, TPSSh, wB97xD, VSXC) in combinations with six basis sets (cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, aug-cc-pVTZ, IGLO-II, and IGLO-III) and three methods for calculating magnetic shieldings (GIAO, CSGT, IGAIM) was tested for predicting ¹H and ¹³C chemical shifts for 25 organic compounds, for altogether 86 H and 88 C atoms. Proton shifts varied between 1.03 ppm to 12.00 ppm and carbon shifts between 7.87 ppm to 209.28 ppm. It was found that the best method for calculating ¹³C shifts is PBE1PBE/aug-cc-pVDZ with CSGT or IGAIM approaches (mae?=?1.66 ppm), for ¹H the best results were obtained with HSEh1PBE, mPW1PW91, PBE1PBE, CAM-B3LYP, and B3PW91 functionals with cc-pVTZ basis set and with CSGT or IGAIM approaches (mae?=?0.28 ppm). We found that often larger basis sets do not give better results for chemical shifts. The best basis sets for calculating ¹H and ¹³C chemical shifts were cc-pVTZ and aug-cc-pVDZ, respectively. CSGT and IGAIM NMR approaches can perform really well and are in most cases better than popular GIAO approach.

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Graphical Abstract Mean absolute errors for ¹H and ¹³C chemical shifts and computational times of neutral toluene molecule with aug-cc-pVDZ basis set and CSGT approach

     

DFT tests for group 8 transition metal carbonyl complexes

The applicability of several popular density functionals in predicting the geometrical parameters and energetics of transition metal carbonyl complexes of iron, ruthenium and osmium has been studied. The methods tested include pure GGA functionals (BLYP, BP86, OPBE, HCTH, PBE, VSXC) and hybrid GGA functionals (B3PW91, B3LYP, PBE1PBE, MPW1K, B97-2, B1B95, PBE1KCIS). The effect of changing the metal basis set from Huzinaga’s all-electron basis to SDD scECP basis was also studied. The results show, that hybrid functionals are needed in order to describe the back-bonding ability of the carbonyl ligands as well as to deal with metal-metal bonds. The best general performance, when also the computational cost was considered, was obtained with hybrid functionals B3PW91 and PBE1PBE, which therefore provide an efficient tool for solving problems involving large or medium sized transition metal carbonyl compounds. Figure Optimized structure for one of the test molecules, the Ru₃(CO)₁₂ cluster, showing the staggered conformation of the carbonyl ligands     

DFT/TDDFT computational study of the structural,electronic and optical properties of rhodium (III) and iridium (III) complexes based on tris-picolinate bidentate ligands

The electronic structures and spectroscopic properties of two complexes [M(pic)₃] (M = Ir, Rh) containing picolinate as bidentate ligands have been calculated by means density functional theory (DFT) and time-dependent DFT/TD-DFT using three hybrid functionals B3LYP, PBE0 and mPW1PW91. The PBE0 and mPW1PW91 functionals, which have the same HF exchange fraction (25%), give similar results and do not differ drastically from B3LYP results. Calculated geometric parameters of the complexes are in good agreement with the available experimental data. The UV absorptions observed in acetonitrile were assigned on the basis of singlet state transitions. The most intense band observed in the UV-C region corresponds to ligand-to-ligand charge transfer states (LLCT) in both complexes. The theoretical spectrum of the rhodium complex is characterized by a large degree of mixing between metal-to-ligand-charge-transfer (MLCT), LLCT and metal centered (MC) states in the UV-A region. The presence of low-lying excited states with MC character affects the absorption spectrum under spin-orbit coupling (SOC) effects and play important roles in the photochemical properties.

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Graphical abstract Frontier molecular orbital diagram of mer-M(pic)₃ (M=Ir, Rh).

     

Synthesis,electronic, and spectral properties of novel geranylated chalcone derivatives: a theoretical and experimental study

Novel chalcone derivatives with different substituents attached to A and B-rings: hydroxyl, methoxyl, geranyl, and prenyl groups were synthesized. The obtained compounds were characterized by NMR, HRMS, UV-Vis, IR, and MS. The theoretical analysis was carried out in all the compounds using density functional theory (DFT) with the B3LYP, PBE0, and M06-2X functionals in combination with the 6-311G(d,p) Pople-type basis set. The excited state properties were calculated by time dependent density functional theory (TD-DFT) using the same methodology applied for the ground state properties. The calculated vertical absorption wavelengths (λ_max) in gas phase and in ethanol as a solvent are consistent with the experimental ones, being the TD-DFT:B3LYP/6-311G(d,p) and PCM-TD-DFT:PBE0/6-311G(d,p) the best methodologies for these calculations with good approximation to the experimental values. The calculated reorganization energies indicated that, the four chalcone derivatives present an electron transfer character due to the smaller registered values. From these parameters it is proposed that these show an n-type semiconductor character. The localization of the frontier orbitals (HOMO and LUMO) shows that only the compound containing a hydroxyl group on the A-ring displays a marked delocalization favoring the charge-transfer process in this system. The HOMO-LUMO gap energies indicate that the inclusion of different donor groups in the rings does not improve the obtained values for this property.

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Graphical Abstract Relationship between spectroscopic and geometrical properties of chalcones were carried out using quantum-chemical calculations and compared with experimental values.

     

Structures of the neutral and positively charged forms of the 4,4′,4″-tris(<Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>-phenyl-3-methylphenylamino)triphenylamine (m-MTDATA) molecule and its dimer,and charge localization in the corresponding cationic species

The structures of the 4,4′,4″-tris(N,N-phenyl-3-methylphenylamino)triphenylamine (m-MTDATA) molecule and its dimer in their neutral and positively charged forms were studied by performing quantum-chemical calculations at the Hartree?Fock (HF) and density functional theory (DFT) levels of theory using several exchange-correlation functionals (PBE, PBE0, BHANDHLYP, and M06-HF) with different percentages of HF exchange. It was found that there are at least four possible isomeric structures of m-MTDATA with different (planar or perpendicular) arrangements of the peripheral diphenylamino groups. The charge localization in the monomeric and dimeric cationic species was also determined. The results indicated that the charge on the dimeric cation is localized on the central region or on the side fragment of the cationic part of the dimer, depending on the dimer structure. DFT calculations showed a tendency to overestimate the charge delocalization over the molecule, irrespective of the percentage of HF exchange applied.

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Graphical abstract Structure of an m-MTDATA dimer cation.

     

Benchmark,DFT assessments,cooperativity, and energy decomposition analysis of the hydrogen bonds in HCN/HNC oligomeric complexes

Hydrogen cyanide (HCN) and its tautomer hydrogen isocyanide (HNC) are relevant for extraterrestrial chemistry and possible relation to the origin of biomolecules. Several processes and reactions involving these molecules depend on their intermolecular interactions that can lead to aggregates and liquids especially due to the hydrogen bonds. It is thus important to comprehend, to describe, and to quantify their hydrogen bonds, mainly their nature and the cooperativity effects. A systematic study of all linear complexes up to pentamers of HCN and HNC is presented. CCSD(T)/CBS energy calculations, with and without basis set superposition error (BSSE) corrections for energies and geometries, provided a suitable set of benchmarks. Approximated methods based on the density functional theory (DFT) such as BP86, PBE, TPSS, B3LYP, CAM-B3LYP with and without dispersion corrections and long-range corrections, were assessed to describe the interaction energies and cooperativity effects. These assessments are relevant to select DFT functionals for liquid simulations. Energy decomposition analysis was performed at the PBE/STO-TZ2P level and provided insights into the nature of the hydrogen bonds, which are dominated by the electrostatic component. In addition, several linear relationships between the various energy components and the interaction energy were obtained. The cooperativity energy was also found to be practically linear with respect to the interaction energy, which may be relevant for designing and/or correcting empirical force fields.

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Graphical Abstract Hydrogen bonds in HCN/HNC oligomeric complexes?

     

Effects of shape,size, and pyrene doping on electronic properties of graphene nanoflakes

Effects of size, shape, and pyrene doping on electronic properties of graphene nanoflakes (GNFs) were theoretically investigated using density functional theory method with PBE, B3PW91, and M06-2X functionals and cc-pVDZ basis set. Two shapes of zigzag GNFs, hexagonal (HGN) and rhomboidal (RGN), were considered. The energy band gap of GNF depends on shape and decreases with size. The HGN has larger band gap energy (1.23–3.96 eV) than the RGN (0.13–2.12 eV). The doping of pyrene and pyrene derivatives on both HGN and RGN was also studied. The adsorption energy of pyrene and pyrene derivatives on GNF does not depend on the shape of GNFs with energies between 21 and 27 kcal mol^?1. The substituent on pyrene enhances the binding to GNF but the strength does not depend on electron withdrawing or donating capability. The doping by pyrene and pyrene derivatives also shifts the HOMO and LUMO energies of GNFs. Both positive (destabilizing) and negative (stabilizing) shifts on HOMO and LUMO of GNFs were seen. The direction and magnitude of the shift do not follow the electron withdrawing and donating capability of pyrene substituents. However, only a slight shift was observed for doped RGN. A shift of 0.19 eV was noticed for HOMO of HGN doped with 1-aminopyrene (pyNH₂) and of 0.04 eV for LUMO of HGN doped with 1-pyrenecarboxylic acid (pyCOOH).

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Graphical Abstract HOMO and LUMO Energies of pyrene/pyrene derivatives doped Graphene Nanoflakes

     

How do halogen bonds (S–O⋯I,N–O⋯I and C–O⋯I) and halogen–halogen contacts (C–I⋯I–C,C–F⋯F–C) subsist in crystal structures? A quantum chemical insight

Thirteen X-ray crystal structures containing various non-covalent interactions such as halogen bonds, halogen–halogen contacts and hydrogen bonds (I?N, I?F, I?I, F?F, I?H and F?H) were considered and investigated using the DFT-D3 method (B97D/def2-QZVP). The interaction energies were calculated at MO62X/def2-QZVP and MP2/aug-cc-pvDZ level of theories. The higher interaction and dispersion energies (2nd crystal) of ?9.58 kcal mol^?1 and ?7.10 kcal mol^?1 observed for 1,4-di-iodotetrafluorobenzene bis [bis (2-phenylethyl) sulfoxide] structure indicates the most stable geometrical arrangement in the crystal packing. The electrostatic potential values calculated for all crystal structures have a positive σ-hole, which aids understanding of the nature of σ-hole bonds. The significance of the existence of halogen bonds in crystal packing environments was authenticated by replacing iodine atoms by bromine and chlorine atoms. Nucleus independent chemical shift analysis reported on the resonance contribution to the interaction energies of halogen bonds and halogen–halogen contacts. Hirshfeld surface analysis and topological analysis (atoms in molecules) were carried out to analyze the occurrence and strength of all non-covalent interactions. These analyses revealed that halogen bond interactions were more dominant than hydrogen bonding interactions in these crystal structures.

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Graphical Abstract Molecluar structure of 1,4-Di-iodotetrafluorobenzene bis(thianthrene 5-oxide) moelcule and its corresponding molecular electrostatic potential map for the view of σ-hole.

     

Accurate predictions of the EPR parameters in planar cobalt(II) complexes by hybrid density functional theory

The hybrid density functional theory is applied to calculate the electron paramagnetic resonance parameters, i.e, the g- and A-tensors of some planar Cobalt(II) complexes with a C_2v symmetry. Calculations were done for four systems: Co(acacen), Co(tacacen), Co(seacacen) and Co(sacsac)₂. The following hybrid functionals were employed: B3LYP, B3PW91, mPW1PW91 and PBE0. The expected large deviation of the g- and A-tensors is well reproduced, and is in very good agreement with the experimental observations. Comparative study shows that the PBE0 hybrid model yields the best agreement with experimental data.     

Performance of wave function and density functional methods for water hydrogen bond spin–spin coupling constants

Spin–spin coupling constants in water monomer and dimer have been calculated using several wave function and density functional-based methods. CCSD, MCSCF, and SOPPA wave functions methods yield similar results, specially when an additive approach is used with the MCSCF. Several functionals have been used to analyze their performance with the Jacob’s ladder and a set of functionals with different HF exchange were tested. Functionals with large HF exchange appropriately predict ¹ J _{O H} , ² J _{H H} and ^2h J _{O O} couplings, while ^1h J _{O H} is better calculated with functionals that include a reduced fraction of HF exchange. Accurate functionals for ¹ J _{O H} and ² J _{H H} have been tested in a tetramer water model. The hydrogen bond effects on these intramolecular couplings are additive when they are calculated by SOPPA(CCSD) wave function and DFT methods.

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Graphical Abstract Evaluation of the additive effect of the hydrogen bond on spin-spin coupling constants of water using WF and DFT methods.

     

DFT studies on the structural and vibrational properties of polyenes

Detailed density functional theory (DFT) calculations on the structure and harmonic frequencies of model all-trans and all-cis polyenes were undertaken. For the first time, we report on the convergence of selected B3LYP/6-311++G** and BLYP/6-311++G** calculated structural parameters resulting from a systematic increase in polyene size (chains containing 2 to 14 C?=?C units). The limiting values of the structural parameters for very long chains were estimated using simple three-parameter empirical formulae. BLYP/6-311++G** calculated ν(C?=?C) and ν(C–C) frequencies for all-trans and all-cis polyenes containing up to 14 carbon–carbon double bonds were used to estimate these values for very long chains. Correction of raw, unscaled vibrational data was performed by comparing theoretical and experimental wavenumbers for polyenes chains containing 3 to 12 conjugated C?=?C units with both ends substituted by tert-butyl groups. The corrected ν(C?=?C) and ν(C–C) wavenumbers for all-trans molecules were used to estimate the presence of 9 – 12 C?=?C units in all-trans polyene pigment in red coral.

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Graphical abstract Detailed density functional theory (DFT) calculations on the structure and harmonic frequencies of model all-trans and all-cis polyenes were undertaken. For the first time, we report on the convergence of selected B3LYP/6-311++G** and BLYP/6-311++G** calculated structural parameters resulting from a systematic increase in polyene size (chains containing 2 to 14 C=C units). The limiting values of the structural parameters for very long chains were estimated using simple three-parameter empirical formulae.

     

Choice of a spin singlet or triplet: electronic properties of Bis-Co(II), Bis-Ni(II), Bis-Cu(II) and Bis-Zn(II) oxygen doubly N-confused hexaphyrin (1.1.1.1.1.1)

Fused hexaphyrins have many physical and chemical properties and can coordinate transition metal ions. In this study, we investigated the geometric structure, charge decomposition analysis (CDA), spin density, frontier molecular orbital (FMO) compositions and absorption spectra of four oxygen doubly N-confused hexaphyrin (1.1.1.1.1.1) (ONCP) complexes with the metal ions Co(II), Ni(II), Cu(II) and Zn(II) (designated ONCP-d-Co, ONCP-d-Ni, ONCP-d-Cu and ONCP-d-Zn). Based on their energies, geometric structures, FMO characteristics and comparison to experiments, ONCP-d-Co and ONCP-d-Cu have the mix-states of the triplet state and broken-symmetry state (antiferromagnetic state) rather than the spin singlet of a closed shell as previously reported. Moreover, based on analyses of the spin density and spin population of the spin triplet ONCP-d-Co and ONCP-d-Cu complexes, the charge transfer in ONCP-d-Cu is greater than that in ONCP-d-Co because the spin density in ONCP-d-Cu is concentrated not only on the Cu ion but also on the ONCP ligand. Thus, the CDA value for ONCP-d-Cu is larger. Finally, through comparative analysis of the FMO compositions and absorption spectra, the complexes and ligand are shown to have very similar absorption spectra with characteristics that arise mainly from π?→?π* transitions both in the B-band and the Q-band, which is due to the FMO compositions being dominated by the highly delocalized conjugated system, rather than by the metal ions. The absorption maxima of the Q-band are ONCP-d-Co (1020 nm)?>?ONCP-d-Zn (1012 nm)?>?ONCP-d-Ni (997 nm)?>?ONCP-d-Cu (988 nm), which is inversely proportional to the energy gap in their FMOs.

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Graphical Abstract The present work investigates the geometric structure, charge decomposition analysis (CDA), spin density, frontier molecular orbital (FMO) compositions and absorption spectra of four oxygen doubly N-confused hexaphyrin (1.1.1.1.1.1) (ONCP) complexes with the metal ions Co(II), Ni(II), Cu(II) and Zn(II) (designated ONCP-d-Co, ONCP-d-Ni, ONCP-d-Cu and ONCP-d-Zn). Based on their energies, geometric structures, FMO characteristics and comparison to experiments, ONCP-d-Co and ONCP-d-Cu have the mix-state of the triplet state and broken-symmetry state (antiferromagnetic state) rather than the spin singlet of a close shell as were previously reported. Meanwhile, ONCP-d-Ni and ONCP-d-Zn show spin singlet structure. The calculated CDA shows the following order: ONCP-d-Cu (1.487)?>?ONCP-d-Ni (1.255)?>?ONCP-d-Co (1.211)?>?ONCP-d-Zn (1.201). Through comparisons of spin density and spin populations of ONCP-d-Co and ONCP-d-Cu, charge transfer between Cu and ligand ONCP is greater than that of Co and ONCP, which makes the CDA value of ONCP-d-Cu obviously larger than that of the other complexes

     

QM/MM theoretical study of the pentacoordinate Mn(III) and resting states of manganese-reconstituted cytochrome P450<Subscript>cam</Subscript>

Quantum mechanical/molecular mechanical (QM/MM) theoretical calculations were performed for the pentacoordinate Mn(III) and water-bound resting states of the Mn-reconstituted mutant of cytochrome P450_cam (Mn-P450_cam) in order to obtain insights into their characters, especially, their spin state ordering. The QM/MM study was carried out by use of the B3LYP and BLYP density functional theory (DFT) methods coupled to the CHARMM force field. Although the relative energies of possible spin states for the Mn-P450_cam species varied depending on the functional, this dependence was less significant compared with previous calculations on the corresponding intermediates of wild-type P450_cam. The results suggested that both Mn-P450_cam intermediates have quintet ground states. Additional time-dependent DFT (TDDFT) calculations were carried out for the quintet states of these species using the B3LYP and BP86 functionals with the electrostatic environmental effect included. The TDDFT results enabled us to assign the origins of the peaks observed in optical absorption spectra (Makris et al. in J. Inorg. Biochem. 100:507–518, 2006). Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Capturing the spin state diversity of iron(III)-aryl porphyrins: OLYP is better than TPSSh

DFT calculations with a variety of exchange-correlation functionals, including PW91, OLYP, TPSSh, B3LYP and B3LYP*, have been carried out on the low-energy spin states of chloroiron(III) porphyrin and four aryliron(III) porphyrins, viz. Fe^III(P)Ph (S = 1/2), Fe^III(P)C₆F₅ (S = 5/2), Fe^III(P)(3,4,5-C₆F₃H₂) (S = 1/2), Fe^III(P)(2,4,6-C₆F₃H₂) (S = 5/2), where the expected spin states have been indicated within parentheses. Qualitatively, OLYP reproduces all the expected ground spin states. B3LYP appears to have some difficulty yielding the observed sextet ground states. B3LYP*, TPSSh and PW91 all fail to reproduce the sextet ground states, the latter two by rather large margins of energy. As far as this study is concerned, the overall performance of the functionals appears to be OLYP/OPBE > B3LYP > B3LYP* >> TPSSh > PW91/BLYP/BP86/TPSS.     

Metal–metal bonding in 1st, 2nd and 3rd row transition metal complexes: a topological analysis

A topological analysis based on density functional electronic and spin densities of the bonding characteristics in a series of Fe, Ru, Os, Tc and Rh dimers and trimers bridged, respectively, by μ-1,8-naphthyridine (nap) and μ-2,2′-dipyridylamine (dpa) is presented. By this simple qualitative analysis, we were able to determine the electronic ground state and correlated bonding order for a number of complexes potentially involved in extended metal atom chains (EMAC). Furthermore, we showed in the Ru dimer that it was possible to control the spin state simply by changing the bonded counter-anion.

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Graphical Abstract Electron localization analysis of the bonding properties in [M₂(nap)₄Cl₂]²⁺ and [M₃(dpa)₄(Cl₂] complexes

     

Calculations of hyperfine coupling constant of copper(II) in aqueous environment. Finite temperature molecular dynamics and relativistic effects

The presented paper is focused on the calculation of hyperfine coupling constants (HFCC) of Cu ²⁺ ion in water environment. To simulate the conditions of the electron paramagnetic resonance (EPR) experiment in aqueous phase, molecular dynamics using the density functional theory (DFT) was employed. In total three different functionals (BLYP, B3LYP, M06) were employed for studying their suitability in describing coordination of Cu ²⁺ by water molecules. The system of our interest was composed of one Cu ²⁺ cation surrounded by a selected number (between thirty and fifty) of water molecules. Besides the non-relativistic HFCCs (Fermi contact terms) of Cu ²⁺ also the four-component relativistic HFCC calculations are presented. The importance of the proper evaluation of HFCCs, the inclusion of spin-orbit term, for Cu ²⁺ containing systems (Neese, J. Chem. Phys. 118, 3939 2003; Almeida et al., Chem. Phys. 332, 176 2007) is confirmed at the relativistic four-component level of theory.

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Graphical Abstract Five and six coordinated copper dication is solvated by adding extra water molecules to simulate conditions in aqueous solution. Molecular dynamics study is performed and nonrelativistic and relativistic hyperfine coupling constants are calculated subsequently.

     

Benchmark of different charges for prediction of the partitioning coefficient through the hydrophilic/lipophilic index

A few different theoretical methods for assigning the partial atomic charges were benchmarked for calculation of the hydrophilic/lipophilic index (HLI). The coefficients were selected to produce the best correlation of the HLI values with the experimental octanol-water partition. Different parameters were checked in calculations of partial charges to get the best performance of the HLI values obtained. Thus, four partitioning schemes (Coulson, Mulliken, Merz-Kollman, Ford-Wang) were benchmarked for calculations of atomic charges with six semiempirical methods (AM1, PM3, RM1, PM6, PM6-D3H4, PM7). Moreover, five distinct types of partial atomic charges (Mulliken, Hirshfeld, Löwdin, CHELPG, NPA), obtained at the Hartree–Fock and DFT levels of theory with three basis sets, were tested for their ability to produce the HLI values with the best correlation to experimental logP coefficients of 50 mono-charged organic anions. In the case of the semiempirical methods, the best correlation between the HLI and logP values (the correlation coefficient r?=?0.9216) was obtained with the AM1 Ford–Wang parametric electrostatic potential charges. The Mulliken and Coulson charges calculated with the PM7 method can be used as an alternative to AM1, with the r values of 0.9107 and 0.8984, respectively. In the case of the DFT, the PBE/def2-TZVP natural population analysis charges produce the best correlation (r?=?0.9220). Nevertheless, in spite of a marginally lower performance (r?=?0.9159), the NPA charges computed at the PBE/def2-SVP level are more robust and can be regarded as the optimum choice for calculating the HLI values.

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Graphical abstract The hydrophilic/lipophilic index (HLI)

     

Predicting the structure and vibrational frequencies of ethylene using harmonic and anharmonic approaches at the Kohn–Sham complete basis set limit

In this work, regular convergence patterns of the structural, harmonic, and VPT2-calculated anharmonic vibrational parameters of ethylene towards the Kohn–Sham complete basis set (KS CBS) limit are demonstrated for the first time. The performance of the VPT2 scheme implemented using density functional theory (DFT-BLYP and DFT-B3LYP) in combination with two Pople basis sets (6-311++G** and 6-311++G(3df,2pd)), the polarization-consistent basis sets pc-n, aug-pc-n, and pcseg-n (n?=?0, 1, 2, 3, 4), and the correlation-consistent basis sets cc-pVXZ and aug-cc-pVXZ (X?=?D, T, Q, 5, 6) was tested.The BLYP-calculated harmonic frequencies were found to be markedly closer than the B3LYP-calculated harmonic frequencies to the experimentally derived values, while the calculated anharmonic frequencies consistently underestimated the observed wavenumbers. The different basis set families gave very similar estimated values for the CBS parameters. The anharmonic frequencies calculated with B3LYP/aug-pc-3 were consistently significantly higher than those obtained with the pc-3 basis set; applying the aug-pcseg-n basis set family alleviated this problem. Utilization of B3LYP/aug-pcseg-n basis sets instead of B3LYP/aug-cc-pVXZ, which is computationally less expensive, is suggested for medium-sized molecules. Harmonic BLYP/pc-2 calculations produced fairly accurate ethylene frequencies.

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Graphical Abstract In this study, the performance of the VPT2 scheme implemented using density functional theory (DFT-BLYP and DFT-B3LYP) in combination with the polarization-consistent basis sets pc-n, aug-pc-n, and pcseg-n (n?=?0, 1, 2, 3, 4), and the correlation-consistent basis sets cc-pVXZ and aug-cc-pVXZ (X?=?D, T, Q, 5, and 6) was tested. For the first time, we demonstrated regular convergence patterns of the structural, harmonic, and VPT2-calculated anharmonic vibrational parameters of ethylene towards the Kohn–Sham complete basis set (KS CBS) limit

     

Experimental and theoretical investigations of spectroscopic properties of azobenzene derivatives in solution

The UV-Vis spectra of series of polymethylmethacrylate (PMMA) copolymers with attached trans-azobenzene derivatives were measured in 1,1,2-trichloroethane. In order to gain some insight into the recorded spectra, the quantum chemical calculations were performed for the substituted azobenzenes using both configuration interaction with single excitations method (CIS) as well as density functional theory (DFT) with B3LYP and PBE0 functionals. The calculations were performed in solvent. In particular, we found that the PBE0 excitation energies are in very good agreement with the experimental data. Figure The plots of orbital contour surfaces for molecule II. The molecular orbitals were calculated at the PBE0/6-311++G(d,p) level of theory. The upper plot presents contour surface of HOMO and the lower presents contour surface of LUMO. Shown are the contour surfaces of orbital amplitude 0.04 (red) and -0.04 (blue)