cc-pVDZ Basis Set Research Articles

DFT calculations of metal-organic I-III-VI semiconductor clusters: Benchmark of exchange-correlation functionals and localized basis sets

The primary objective of this work was to find the numerical methods suitable for DFT calculations of ternary I-III-VI semiconductor quantum dots emerging as new functional materials which demonstrate an increasing need to comprehend their complex physicochemical properties. The benchmarking analysis of 8 exchange-correlation functionals and 11 basis sets including all-electron and effective core potential ones was performed. Four metal-organic molecules, widely used as a single-precursor in the synthesis of A-In-X2 semiconductor quantum dots (A = Cu, Ag; X = S, Se) were considered as simple representatives of ternary semiconductor quantum dots. The geometrical parameters of the optimized structures were compared to the X-ray diffraction data. The hybrid PBE0 and B3PW91 functionals were found to be the best performing methods especially when connected with cc-PVDZ or Def2-SVP basis sets. The methods widely used in the previous calculations of II-VI semiconductor quantum dots, namely B3LYP functional and LANL2DZ or SBKJC basis sets, in this case resulted in lower agreement with the experimental data.

Quantitative and qualitative analyses of intermolecular interactions in neutral/deprotonated aspirin@β-CD inclusion complexes: QTAIM and NBO analyses

Most of the researches in supramolecular chemistry area are focused on the conventional hydrogen bonds without taking into account unconventional intermolecular interactions. The nature and strength of the conventional and unconventional interactions in inclusion complexes formed between neutral aspirin (ASA) and its deprotonated form (ASA−) with β-cyclodextrin (β-CD) have been studied. It was conducted through combining atoms in molecules (AIM) theoretical criteria suggested by Koch and Popelier and natural bond orbital (NBO) analyses by means of dispersion-corrected density functional theory (DFT-D3) with the functional B3LYP using cc-pvdz basis set in the gas phase. We have found five intermolecular closed-shell interaction groups responsible for neutral ASA:β-CD and deprotonated ASA−:β-CD inclusion complexes stability: One is conventional O–H···O bond group. The four C–H···O, C–H···C, O–H···H–C and C–H···H–C groups are nonconventional. Also, with respect to the Koch and Popelier criteria, some of them present the properties of a hydrogen bond, while others do not. The non-covalent interaction energies are calculated using Espinosa approach. Finally, according to the AIM and NBO analyses, the topological parameters (electron density ρb and its Laplacian ∇2ρb), estimated interaction energies (Eint), and the stabilization energy E(2) of both complexes were correlated with the intermolecular bond lengths.

DFT-Based Molecular Conformational Analysis of a Diarylethylene Cyano-Derivative

Structural stability and conformational behavior of trans-4,4′-methoxycyanostilbene are studied theoretically within the method of density functional theory using the B3LYP functional and 6-31G(d) and cc-pVDZ split-valence basis sets. According to quantum chemical calculations performed for the molecule in its ground state, two possible conformations of the molecule differ in energies so that the configuration with triple conjugation (p,π-, π,π-, and direct polar conjugation of substituents) is energetically preferable. First- and second-order saddle points are found by scanning the three-dimensional potential energy surface. Vibrational analysis is used to find stationary points.

Stabilizing influence of silicon substitution on dibenzene and its isomers

The stabilizing effect of silicon substitution on sixteen different isomers of dibenzene $$(\hbox {C}_{{12}}\hbox {H}_{12})$$ has been investigated using second-order Moller-Plesset perturbation (MP2) theory and the cc-pVDZ basis set. While the most stable isomers of $$\hbox {Si}_{{12}}\hbox {H}_{12 }$$ have only Si–Si bonds, some of the stable isomers have isolated $$\hbox {Si}{=}\hbox {Si}$$ bonds and may be amenable to experimental observation. Vibrational frequencies were calculated for the optimized geometries at the Hartree-Fock level of theory to ensure that they corresponded to true minima on the potential energy landscape. Natural bonding orbital analysis confirms the existence of isolated $$\hbox {Si}{=}\hbox {Si}$$ double bonds in some of the isomers. Dipole moment values were determined to check for the presence of centre of symmetry in certain geometries. Ab initio calculations suggest that silicon analogs of several isomers of unstable dibenzene moiety are stable. While the most stable isomers of $$\hbox {Si}_{{12}}\hbox {H}_{{12}}$$ have all tetrahedral silicon atoms, some of the stable isomers do contain $$\hbox {Si}{=}\hbox {Si}$$ bonds, suggesting that they may be amenable to experimental observation.

The s‐homodesmotic method for the computation of conventional strain energies of bicyclic systems and individual rings within these systems

AbstractThe s‐homodesmotic method for computing conventional strain energies (CSE) has been extended for the first time to bicyclic systems and to individual rings within these systems. Unique isodesmic, homodesmotic, and hyperhomodesmotic reactions originate from the s‐homodesmotic method. These are used to investigate 12 bicyclic systems comprising cyclopropane and cyclobutane and how the CSE of each system compares to the sum of the individual rings within each. Equilibrium geometries, harmonic vibrational frequencies, and the corresponding electronic energies and zero point vibrational energy corrections are computed for all relevant molecules using second‐order perturbation theory and density functional theory (B3LYP) with the correlation consistent basis sets cc‐pVDZ and cc‐pVTZ. Single‐point CCSD(T) energies are computed at the MP2/cc‐pVTZ optimized geometries to ascertain the importance of higher order correlation effects. Results indicate that CSEs are additive when the two rings are separated by one or two bonds and somewhat additive in other cases.

DFT studies of camptothecin aggregation in solutions

The structures of camptothecin (CPT) lactone head-to-tail π-aggregates up to tetramers were optimized in DMSO and aqueous solutions using various DFT functionals with cc-pVDZ basis sets. Solvent effects were estimated using the Integral Equation Formalism Polarizable Continuum Model. The calculated reaction equilibria indicate that the higher π-aggregates formation is more preferred in DMSO than in aqueous solutions. TD-B3LYP calculated electron transitions ascribe two strong peaks over 300 nm in UV–Vis spectra to the CPT monomer (at lower wavelength) and to higher CPT head-to-tail π-aggregates (at higher wavelengths). Only B3LYP with D2 dispersion correction of Grimme and ωB97XD functionals are able to produce reliable results.

Theoretical Study of the Histidine-catalyzed Asymmetric Aldol Reaction of Acetone and Benzaldehyde.

The mechanism of histidine-catalyzed asymmetrical aldol reaction of acetone with benzaldehyde was studied by using B3LYP method of density functional theory at the levels of 6-31G(d,p) and cc-pvdz basis sets. The calculation results showed that the reaction mechanism included four steps: (I) nucleophilic attack of histidine on acetone to form alcohol intermediate Inter-A through the transition state TS1 (considered a rate control step because the activation energy (49.95 kcal/mol) was relatively high); (II) dehydration of the alcohol intermediate to form the cis- or trans-enamine through the transition states TS3 and TS4 with the energy barriers of 36.12 and 38.15 kcal/mol; (III) electrophilic addition of cis-enamine or trans-enamine with benzaldehyde to form imine Inter-C or Inter-E through the transition states TS8, TS9, TS10, and TS11 (energy barriers 18.43, 22.34, 13.24, and 13.24 kcal/mol, respectively); (IV) after combination of the imine intermediate with water through the transition states TS12, TS13, TS14, and TS15 (energy barriers 22.79, 34.6, 28.2, 25.12 kcal/mol, respectively), removal of the histidine catalys to obtain the final S or R aldol product. Through analyzing the potential energy profile of reaction, we found that the histidine-catalyzed reaction of acetone with benzaldehyde was more energetically favorable to obtain the R-product (ee value >99%). Solvent effects computed with a polarizable continuum model (PCM) indicated that the DMSO and water can reduce the reaction energy barrier.

Antioxidant activity of some khellin derivatives: a density functional theory study

Background The antioxidant activity of some benzofuran and 2H-pyran-2-one derivatives of naturally occurring khellin and visnagin was theoretically investigated using a quantum chemical method, density functional theory. These molecules possess a variety of biological and pharmacological activities including antioxidant activity. Materials and methods The calculations were carried out using Gaussian 03 computational package in gas phase with the purpose of obtaining the intrinsic properties of the molecules studied, free of any interaction. The geometries of neutral species and their respective radicals and radical cations were optimized using PM3 and density functional theory/B3LYP calculations with cc-pVDZ basis set. Results As they possess O-H, N-H, or both O-H and N-H bonds, we chose to investigate theoretically their antioxidant activity via H-atom transfer or single electron transfer pathway. In the gas phase, the ionization potential, the highest occupied molecular orbital (HOMO), bond dissociation energies of hydroxyl group O-H and N-H [bond-dissociation enthalpy (BDE)O-H–BDEN-H], and spin density distribution are carried out. Molecule 14 showed potential antioxidant activity as BDE for the N-H bond was found to be 84.71 and for the O-H bond was 85.32, whereas the ionization potential was 6.26 and the EHOMO was 5.39. Conclusion Based on the antioxidant activities of 15 derivatives of naturally occurring khellin and visnagin, they were found to be potent antioxidant compounds comparable to quercetin or vitamin C.

Post-CCSD(T) contributions to total atomization energies in multireference systems.

We examine the magnitude and the basis set convergence of post-coupled-cluster with single, double, and perturbative triple excitations (CCSD(T)) contributions (up to CCSDTQ567) for a wide and diverse set of 21 first- and second-row molecules with up to four non-hydrogen atoms. We focus on multireference systems for which post-CCSD(T) effects are particularly pronounced. The considered molecules are BN(1∑+), C2(1∑+), O2, FO, P2, S2, ClO, N2O, NO2, O3, FNO, FO2, F2O, S2O, S3, ClNO, ClOO, Cl2O, N2C2, P4, and S4. This set spans the gamut from molecules dominated by moderate nondynamical correlation (e.g., FO, ClO, NO2, S2O, N2C2, and P4) to systems dominated by strong nondynamical correlation (e.g., BN, C2, FO2, O3, ClOO, and S4). We examine the basis set convergence of the CCSDT, CCSDT(Q), CCSDTQ, CCSDTQ(5), CCSDTQ5, CCSDTQ5(6), CCSDTQ56, CCSDTQ56(7), and CCSDTQ567 methods. The largest basis sets employed in each category are cc-pV6Z (CCSDT(Q)), cc-pV5Z (CCSDTQ), cc-pVTZ (CCSDTQ5(6)), and cc-pVDZ (CCSDTQ567). Apart from examining the basis-set convergence of post-CCSD(T) contributions near the one-particle basis-set limit, this work explores cost-effective approaches for obtaining these contributions from fairly small basis sets. We consider both effective basis-set extrapolations and scaling factors. An important finding is that extrapolating the perturbative connected quadruples, (Q), from the cc-pVDZ(4s3p1d) and cc-pVTZ basis sets yields near basis-set limit results and represents a significant improvement relative to cc-pV{D,T}Z extrapolation at no additional computational cost (where cc-pVDZ(4s3p1d) is an extended version of the cc-pVDZ basis set). Combining the (Q)/cc-pV{D(4s3p1d),T}Z extrapolations with the fully iterative connected quadruples, Q-(Q), contribution calculated with the cc-pVDZ (or even the cc-pVDZ(3s2p)) basis set is a cost-effective way for obtaining the connected quadruples component close to the basis-set limit (where cc-pVDZ(3s2p) is a truncated version of the cc-pVDZ basis set). In addition, we show that the (5)/cc-pVDZ(3s2p) and (6)/cc-pVDZ(3s2p) components provide reasonable approximations for the connected quintuple and sextuple components close to the basis-set limit, respectively.

Conformational and electronic properties of hydroquinone adsorption on C60 fullerenes: Doping atom, solvent and basis set effects

Hydroquinone (HQ) is widely used as a reducing agent with well-known antioxidant properties. The interaction with pristine and doped fullerenes seems to have a promising research field particularly for the drug delivery and sensor applications. In this research, sensitivity of silicon or boron doped and undoped fullerenes to the HQ molecule and adsorption energies of HQ interacted fullerene cages and dopant effect on the electronic properties were mainly examined with density functional theory (DFT).M06-2X and B3LYP functionals were used for the gas phase and water media. The effect on the basis sets for the investigated systems was also searched by using 6-31G(d) and ccpvdz basis sets.

Carbon dioxide capture using covalent organic frameworks (COFs) type material—a theoretical investigation

The present work deals with a density functional theory (DFT) study of porous organic framework materials containing - groups for CO2 capture. In this study, first principle calculations were performed for CO2 adsorption using N-containing covalent organic framework (COFs) models. Ab initio and DFT-based methods were used to characterize the N-containing porous model system based on their interaction energies upon complexing with CO2 and nitrogen gas. Binding energies (BEs) of CO2 and N2 molecules with the polymer framework were calculated with DFT methods. Hybrid B3LYP and second order MP2 methods combined with of Pople 6-31G(d,p) and correlation consistent basis sets cc-pVDZ, cc-pVTZ and aug-ccVDZ were used to calculate BEs. The effect of linker groups in the designed covalent organic framework model system on the CO2 and N2 interactions was studied using quantum calculations.

Conformational study of melamine crosslinkers and spectroscopical comparison of HMMM molecules by practical measurements and quantum chemical calculations

To understand and improve network formation processes and performance properties makes structural molecular studies critically important for the coil-coating industry. Crosslinking agents such as hexamethoxymethylmelamine (HMMM) or less methylated derivatives, e.g. methoxymethylmelamine (MMM), are often added to industrial coating formulations. For molecules with considerably fewer atoms and accordingly less rotational freedom (such as MMM) it is readily accessible to identify principal conformations. Thus, an MMM conformer study is straightforward and serves as orientation concerning HMMM conformer studies. For HMMM molecules an extensive computation method was developed to investigate the conformational distribution average and probably most likely molecular structures. Using the density functional theory (DFT) B3LYP-D3BJ method with Dunning's correlation basis set, calculations were performed to investigate the three-dimensional structural geometries of HMMM (basis set cc-pVDZ) and MMM (basis set cc-pVTZ). Beginning with 1500 conformations for HMMM and using various cut-off filters we focused on final residual 22 conformers for solvent phase calculations and 16 conformers for gas phase calculations. To the best of our knowledge, this is the first time that chemical properties for melamine crosslinkers were presented under consideration of conformational population distribution. Thus, computations of fully optimized structural geometries, energies and vibrational states indicate that preferred structural alignments for the methoxymethyl (MM) group in melamine molecules exist. Nevertheless, we suppose that as a matter of principle the MM group of MMM molecules can easily perform rotations by itself and all conformational structure geometries of MMM will exist. Concerning the MM groups position compared to triazine plane HMMM molecules have two main configurations,”3up-3down” and “4up-2down”, as dominant conformer species. Computations of weighted and averaged IR and Raman spectra of final conformations for HMMM monomers, dimers and trimers at ambient temperature are novel and in good agreement with experiment. Prediction of a final UV–Vis spectrum of top ten Boltzmann-weight and averaged monomeric HMMM conformers is in perfect agreement with practical measurement of commercially available HMMM.

Effect of three-body transformed Hamiltonian ( $$\tilde{H} _3 $$ H ~ 3 ) using full connected triple excitation coupled cluster operators on valence ionisation potentials of $$\hbox {Cl}_{2}$$ Cl 2 and $$\hbox {F}_{2}$$ F 2 computed via EIP-VUMRCCSD $$\uptau $$ τ scheme

Valence universal multireference coupled cluster (VUMRCC) method via eigenvalue independent partitioning has been applied to estimate the effect of three-body transformed Hamiltonian (\(\widetilde{{H}}_3\)) on ionisation potentials through full connected triple excitations \(S_{3}^{(1,0) }\). \(\widetilde{H}_3 \) is constructed using CCSDT1-A model of Bartlett et al for the ground-state calculation. Contribution of transformed Hamiltonian through full connected triples \(\overline{\widetilde{H}_3 S_3^{\left( {1,0} \right) }}\) involves huge amount of computational operations that is time-consuming. Investigation on \(\hbox {Cl}_{2}\) and \(\hbox {F}_{2}\) molecules using cc-pVDZ and cc-pVTZ basis sets shows that the above effect varies from 0.001 eV to around 0.5 eV, suggesting that inclusion of \(\overline{\widetilde{H} _3 S_3^{\left( {1,0} \right) } }\) is essential for highly accurate calculations.

Structure, Spectroscopic and Quantum Chemical Investigations of 4-Amino-2-Methyl-8-(Trifluoromethyl)Quinoline

This work deals with the spectroscopic properties (FT-IR, FT-Raman and NMR), structural and some electronic properties as well as theoretical calculations of 4-amino-2-methyl-8-(trifluoromethyl) quinoline (AMTQ) molecule. T he vibrational, structural and some electronic properties observations of the AMTQ were reported, which is investigated using some spectral methods and DFT calculations. FT-IR and FT-Raman spectra were obtained for AMTQ at room temperature in the region 4000 cm -1 - 400 cm -1 and 3500-50 cm -1 , respectively. In the DFT calculations, the B3LYP functional with cc-pVDZ, cc-pVTZ and cc-pVQZ basis sets was applied to carry out the quantum mechanical calculations of the spectroscopic, structural and some electronic properties of AMTQ. FT-IR and FT-Raman spectra were interpreted with the by using of normal coordinate analysis based on scaled quantum mechanical force field. The present work expands our understanding of the both the vibrational and structural properties as well as some electronic properties of the AMTQ by means of the theoretical and experimental methods.

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 (1.23-3.96eV) than the RGN (0.13-2.12eV). 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 27kcal 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 0.19eV was noticed for HOMO of HGN doped with 1-aminopyrene (pyNH2) and of 0.04eV for LUMO of HGN doped with 1-pyrenecarboxylic acid (pyCOOH). Graphical Abstract HOMO and LUMO Energies of pyrene/pyrene derivatives doped Graphene Nanoflakes.

Prediction of electronic structure, dielectric and thermodynamical properties of flurbiprofen by density functional theory calculation

The molecular structure of the pain killer drug Flurbiprofen has been fully optimized using Berny's optimization algorithm in Gaussian 09, using redundant internal coordinates. The dipole moments, polarizability tensors, average polarizability, anisotropy, first molecular hyperpolarizability, thermodynamics properties, dielectric constant, refractive index, dielectric susceptibility, molar refractivity, IR and Raman spectra have also been studied. A tentative assignment of the IR vibration frequencies was equally carried out. This was done by using Density functional theory calculations with three different functional B3LYB, X3LYP and BPBE by employing cc-pVDZ basis set. The calculated energy band gap (Egap) of the molecule obtained by using HOMO and LUMO molecular orbitals show that the molecule has an Egap value of 0.195 eV, 0.201 eV and 0.244 eV at the BPBE, B3LYP and X3LYP levels respectively. The first molecular hyperpolarizability value obtained by using the BPBE (6.79187 × 10−30 esu), B3LYP (5.07308 × 10−30 esu) and (2.74471 × 10−30 esu) methods are very large compared to that of Urea (0.1947 × 10−30 esu) reported in literature. The results also show that the molecule has a dielectric constant of 2.85 × 10−11, 3.03 × 10−11 and 2.99 × 10−11 obtained at the PBPE, B3LYP and X3LYP levels respectively. Equally, our IR and Raman spectra were in the same range as those reported in literature.

Electronic structure, physico-chemical, linear and non linear optical properties analysis of coronene, 6B-, 6N-, 3B3N- substituted C24H12 using RHF, B3LYP and wB97XD methods

In this work we have investigated the effects of substituting carbon atoms with B, N and BN on the electronic structure, physico-chemical, linear and non linear optical properties of Coronene (C24H12) using HF and DFT methods. We have calculated total electronic energy E0, zero point vibrational energy ZPVE, the enthalpy H, entropy S, molar heat capacity at constant volume Cv, ionization potential IP, electron affinity EA, hardness $$\kappa$$ , softness $$\vartheta$$ , electronegativity EN, dipole moment µ, average polarizability $$ $$ , anisotropy $$\Delta \alpha$$ , the first molecular hyperpolarizability βmol, second order hyperpolarizability $$\gamma_{av}$$ , HOMO–LUMO Energy gap Egap, work function EF, refractive index n, susceptibility χ, dielectric constant e and molar refractivity MR of coronene (C24H12), the 6B-, 6N- and 3B3N- substitute-doped C24H12 C18B6H12 C18N6H12 and C18B3N3H12. The Egap values of the molecules are between 0.91 and 2.36 eV. We observed that βmol changes slightly when C24H12 is doped with either 6B or 6N even though their βmol values are too small. However, by doping C24H12 with both 3B and 3N, creating a strong donor–acceptor system, a very large increase in µ and βmol was found for C18B3N3H12. This study was done using RHF, B3LYP and wB97XD methods with the cc-pVDZ basis set. The studies have shown that doping decreases some of the above properties significantly while some increases significantly compared to pure coronene, suggesting that 6B-, 6N-, and 3B3N-doped Coronene as serious candidates for electronics, optoelectronics and photonic devices.

Quantifying the Performances of DFT for Predicting Vibrationally Resolved Optical Spectra: Asymmetric Fluoroborate Dyes as Working Examples.

This article aims at a quantitative assessment of the performances of a panel of exchange-correlation functionals, including semilocal (BLYP and PBE), global hybrids (B3LYP, PBE0, M06, BHandHLYP, M06-2X, and M06-HF), and range-separated hybrids (CAM-B3LYP, LC-ωPBE, LC-BLYP, ωB97X, and ωB97X-D), in predicting the vibrationally resolved absorption spectra of BF2-carrying compounds. To this end, for 19 difluoroborates as examples, we use, as a metric, the vibrational reorganization energy (λvib) that can be determined based on the computationally efficient linear coupling model (a.k.a. vertical gradient method). The reference values of λvib were determined by employing the CC2 method combined with the cc-pVTZ basis set for a representative subset of molecules. To validate the performances of CC2, comparisons with experimental data have been carried out as well. This study shows that the vibrational reorganization energy, involving Huang-Rhys factors and normal-mode frequencies, can indeed be used to quantify the reliability of functionals in the calculations of the vibrational fine structure of absorption bands, i.e., an accurate prediction of the vibrational reorganization energy leads to absorption band shapes better fitting the selected reference. The CAM-B3LYP, M06-2X, ωB97X-D, ωB97X, and BHandHLYP functionals all deliver vibrational reorganization energies with absolute relative errors smaller than 20% compared to CC2, whereas 10% accuracy can be achieved with the first three functionals. Indeed, the set of examined exchange-correlation functionals can be divided into three groups: (i) BLYP, B3LYP, PBE, PBE0, and M06 yield inaccurate band shapes (λvib,TDDFT < λvib,CC2), (ii) BHandHLYP, CAM-B3LYP, M06-2X, ωB97X, and ωB97X-D provide accurate band shapes (λvib,TDDFT ≈ λvib,CC2), and (iii) LC-ωPBE, LC-BLYP, and M06-HF deliver rather poor band topologies (λvib,TDDFT > λvib,CC2). This study also demonstrates that λvib can be reliably estimated using the CC2 model and the relatively small cc-pVDZ basis set. Therefore, the linear coupling model combined with the CC2/cc-pVDZ level of theory can be used as a very efficient approach to determine λvib values that can be used to select the most adequate functional for more accurate vibronic calculations, e.g., including more refined models and environmental effects.

Analytic Energy Gradients for Variational Two-Electron Reduced-Density-Matrix-Driven Complete Active Space Self-Consistent Field Theory.

Analytic energy gradients are presented for a variational two-electron reduced-density-matrix (2-RDM)-driven complete active space self-consistent field (CASSCF) method. The active-space 2-RDM is determined using a semidefinite programing (SDP) algorithm built upon an augmented Lagrangian formalism. Expressions for analytic gradients are simplified by the fact that the Lagrangian is stationary with respect to variations in both the primal and the dual solutions to the SDP problem. Orbital response contributions to the gradient are identical to those that arise in conventional CASSCF methods in which the electronic structure of the active space is described by a full configuration interaction (CI) wave function. We explore the relative performance of variational 2-RDM (v2RDM)- and CI-driven CASSCF for the equilibrium geometries of 20 small molecules. When enforcing two-particle N-representability conditions, full-valence v2RDM-CASSCF-optimized bond lengths display a mean unsigned error of 0.0060 Å and a maximum unsigned error of 0.0265 Å, relative to those obtained from full-valence CI-CASSCF. When enforcing partial three-particle N-representability conditions, the mean and maximum unsigned errors are reduced to only 0.0006 and 0.0054 Å, respectively. For these same molecules, full-valence v2RDM-CASSCF bond lengths computed in the cc-pVQZ basis set deviate from experimentally determined ones on average by 0.017 and 0.011 Å when enforcing two- and three-particle conditions, respectively, whereas CI-CASSCF displays an average deviation of 0.010 Å. The v2RDM-CASSCF approach with two-particle conditions is also applied to the equilibrium geometry of pentacene; optimized bond lengths deviate from those derived from experiment, on average, by 0.015 Å when using a cc-pVDZ basis set and a (22e,22o) active space.

Stabilisation of the [6]-prismane structure by silicon substitution

Using the second-order Moller–Plesset perturbation (MP2) theoretic method and the cc-pVDZ basis set, it is shown that with an increase in the number of carbon atoms substituted by silicon, the [6]-prismane structure becomes increasingly more stable, relative to the two isolated benzene (like) structures. A similar trend is observed for germanium substituted prismanes as well. Extending this investigation, the stability of benzene-capped fullerene ( $$\hbox {C}_{60}$$ fused with benzene) is also investigated. Synopsis: Ab initio calculations show that the stability of the [6]-prismane structure increases with an increase in the substitution of carbon atoms in the individual benzene rings by silicon or germanium atoms.