- Research article
- Open Access
Effect of backbone conformation and its defects on electronic properties and assessment of the stabilizing role of π–π interactions in aryl substituted polysilylenes studied by DFT on deca[methyl(phenyl)silylene]s
© Hanulikova et al. 2016
- Received: 23 November 2015
- Accepted: 25 April 2016
- Published: 5 May 2016
Recent efforts in the field of mesoscale effects on the structure and properties of thin polymer films call to revival interest in conformational structure and defects of a polymer backbone which has a crucial influence on electronic properties of the material. Oligo[methyl(phenyl)silylene]s (OMPSi) as exemplary molecules were studied theoretically by DFT in the form of optimal decamers and conformationally disrupted decamers (with a kink).
We proved that transoid backbone conformation is true energy minimum and that a kink in the backbone causes significant hypsochromic shift of the absorption maximum (λ max ), while backbone conformation altering from all-eclipsed to all-anti affects λ max in the opposite way. π–π stacking was investigated qualitatively through optimal geometry of OMPSi and mutual position of their phenyls along the backbone and also quantitatively by an evaluation of molecular energies obtained from single point calculations with functionals, which treat the dispersion effect in the varying range of interaction.
- Density functional calculations
- Stacking interaction
- UV/Vis spectroscopy
Silicon (Si) polymers with -Si–Si- backbones carry delocalized σ-electrons as their sp3 orbital lobes can overlap [1, 2]. From this point of view, polysilylenes substantially differ from single-bonded carbon analogues (e.g. polyethylene, polystyrene), especially in the area of optoelectronic properties . Electron delocalization origins in Si atoms arrangement and therefore it is highly dependent on the polysilylene secondary structure . Maximum of σ-conjugation is related with all-anti backbone conformation, which can be found in dialkylsilylenes with small side groups, for instance poly(dimethylsilylene) (PDMSi) [5, 6]. On the other hand, poly[methyl(phenyl)silylene] (PMPSi) is arranged into helix due to presence of bulky phenyl (Ph) groups and with them related deviant or transoid backbone conformation [6–8]. Polysilylene chains are not single rod-like, they form random coil in solutions. Similarly in solid phase, the most of polysilylenes is semi-crystalline and contains regular as well as amorphous phase. Recent efforts in the field of mesoscale effects on structure and properties of thin polymer films made from both π- and σ-conjugated conductive polymers call to revival interest in conformational structure and defects of a polymer backbone which has crucial influence on electronic properties of the material. It has been already shown by different groups that polymer conformational order/disorder shows strong dependence on the thin film thickness in order of hundredths nm and results into non-trivial effects on optoelectronic properties in terms of segment conjugation length, luminescence, photovoltaic effect, exciton diffusion length [9–12] and fine bandgap electronic structure (density of deep states) [13, 14]. Obviously, the polymer structure itself and other typical polymer related properties [15–17] are influenced too. Hence, various bends of backbones are needed for the creation of regular or irregular arrangements. Such bend can be regarded as conformational defect because it disrupts regular σ-delocalization and therefore influences final polysilylene properties [18, 19]. This defect was defined as a gauche-kink in the backbone and described on oligo-DMSin (ODMSi) and oligo-MPSin (OMPSi) with n = 1–10 by density functional theory (DFT) in our previous work, where the kink influence on the electronic properties of oligosilylenes was confirmed . The change has been clearly manifested in absorption spectra plots, where hypsochromic shift of the main absorption band had been detected. In addition, the shift is more strongly pronounced as the kink position altered closer the centre of a backbone. Another cause that is responsible for a rearrangement of the oligosilylene molecule can be identified as a charge carrier in its vicinity. From this reason, we have also investigated polaron quasiparticles of OMPSin with the introduced kink . In that research, a significant change has emerged in a dependence of the spin density on the conformation of a backbone and its shift to more regular part of a Si–Si chain, i.e. a shift from the kink.
The p orbitals are distributed on the Ph rings in PMPSi and it seems reasonable that π–π interactions are employed during geometry arrangement and stabilization. This type of non-bonding interaction was described in detail by Hunter or Gung in 1990s, however the interaction has already been known since the first half of 20th century [22–24]. These interactions play an important role in stabilization of double helix of nucleic acids or other biologically active substances and they have been abundantly studied in these areas, e.g. Ref. [25–27]. The character of the interaction (i.e. whether the interaction is attractive or repulsive) depends on the mutual position of involved aromatic rings (on their distance and angle between planes). Several positions were described and defined; they are sandwich, parallel displaced (offset of rings), T-shape and edge-to-face arrangements. The first is representative of repulsive interactions as the p orbitals, which carry delocalized π-electrons, are oriented to each other. The rest evince attractive interaction, whose intensity is dependent on the particular ring offset [28, 29]. Recent research, e.g. review , has suggested not to use only the term π-stacking for a description of all non-bonding interactions between aromatic groups as it could be related predominantly to a rarely observed face-to-face arrangement and regarded as insufficient for expression of other offset positions.
Contemporary theoretical research often uses DFT and time dependent-DFT (TD-DFT) that has been established by Kohn and Sham [31–33] and Runge and Gross [34, 35], respectively. B3LYP (Becke-3-Lee-Young-Parr) model has been confirmed as suitable for calculations on silicon compounds [32, 36]. Its use for geometry optimization is indisputable and in many cases, it is as well as sufficient for calculation of spectral or thermal properties [37, 38]. However, B3LYP functional is not able to clearly distinguish energy changes related with non-bonding interactions which are better covered in density functionals involving dispersion term in their definition . For π–π interaction energy evaluation are therefore usually used functionals such as M06 , ωB97X-D  or B3LYP-D , which are also able to characterise low- and long-range electron–electron interactions at various levels.
The present paper is another from the series of a computationally-led investigation of oligosilylenes and the purpose of this work is a determination of a mutual influence of silicon backbone conformation and conformational defect on the excitation properties of OMPSi10. Several constrained structures are here investigated to obtain a detailed and comprehensive view on the conformation issues as well as to confirm deviant or transoid conformation to be the global energy minimum. Description of π–π interactions of various conformations in the vicinity of the conformational defect is done through evaluation of phenyl angle-distance plot obtained from optimized geometries and molecular energy evaluation obtained from single point calculations with three different density functionals. We believe that results of this model study can be generalised and a useful lesson towards description of real polysilylene polymers can be learned from it.
PMPSi was obtained from Fluorochem Ltd. UK, GPC analysis revealed Mw = 27,600 g/mol and Mn = 8500 g/mol. Films for UV–Vis measurements were prepared by the spin coating method using spin coater Laurell WS-650-MZ-23NPP from the solution in toluene. Quartz glass was used as a substrate. The absorption spectrum was measured by Lambda 1050 UV/Vis/NIR spectrometer from Perkin Elmer.
Structures of OMPSi with ten repeated units (OMPSi10) were modelled with Spartan ´14 software (Wavefunction, Irvine, CA) . Optimal geometry of decamer (later in this text designed as 10_opt) was calculated with DFT on the level of B3LYP hybrid model and 6-31G(d) polarization basis set . The backbone end atoms were capped with methyl groups and calculation was set in vacuum with no constrained bonds or angles. OMPSi10 with approximately transoid conformation was obtained as can be also found in our previous work . This optimal structure was used for virtual preparation of other OMPSi10 analogues with a kink, which represents a conformational defect. The optimization of kinked decamers was performed with the same DFT model as described above and resulted in four OMPSi10 molecules. These structures differ in a position of the kink that adopted approximately gauche conformation. Geometry calculation of oligomers with a kink was described in detail in Ref. 11 these OMPSi10 were designed with A, B, C and D according to position of the kink and suffixed with opt as it is optimal structure with no constrained angles.
Single point energy calculations were performed for all 10A…10D OMPSi10 with M06 and ωB97X-D functionals, which are directly available in Spartan 14´ software. Although the absolute total energies obtained by these methods differ all three methods are known due to their low errors and variance of predicted values. Therefore, they can be used for prediction of trends and comparison of energy differences among series of conformers. The results calculated at higher levels of theory which includes non-bonding interactions were compared with molecular energy obtained with B3LYP which treats bonding interactions only. From the plots, which are given below, it was possible to determine the energy contribution to conformer stabilization caused by the weak phenyl– phenyl interactions because the Si backbone was constrained in all considered cases. The most energetically un-favourable conformation of the Si backbone with 120° dihedral angle was selected as the reference level. Hence, the contribution to the conformer stabilization due to σ-conjugation is predicted by B3LYP and the additional energy gain due to π-stacking is manifested as the difference between B3LYP and dispersion term including functionals.
An investigation of electronic properties was done through examination of absorption spectra and excitation energies, including distribution of molecular orbitals and their percentage involvement into the process. These features and UV–Vis spectra were calculated with TD-DFT energy calculation in the excited state of OMPSi10. Functional, basis set and virtual environment of molecules were set as described in geometry optimization part. Optimal geometries in the excited state were not calculated due to excessive computer requirements.
Backbone geometry and the kink
Figure 3 depicts MO distribution along Si backbones for all studied decamers. As can be found, the main difference is observable between symmetric (10 and 10D) and asymmetric structures (10A, 10B and 10C). The symmetry is here given by the position of the kink and the fact that in 10A, 10B and 10C is backbone divided into two unequally length parts–segments. HOMOs-1 are basically delocalized along whole Si backbone in 10 and D molecules. 10A OMPSi represents transition between symmetrical and asymmetrical structure as the kink is located in the very edge of a chain. HOMO-1 of 10A molecules is thus distributed almost symmetrically along the backbone, however a slight shift to a kink part is already observable. This shift of HOMO-1 towards the kink and its localization on the shorter segment is clearly visible in 10B and 10C decamers. Similarly as HOMOs-1, HOMOs of 10 and 10D decamers are distributed equally along Si–Si bonds and maximal values of c μi can be found on central Si atoms. On the other hand, in 10A–10C, HOMO orbitals are shifted from the kink part and maxima are kept in the middle of chains on Si4–Si6. The effect of a kink introduction on HOMOs seems to be of lower intensity than in case of HOMO-1 but this is only a semblance perception of the graph because the delocalization length over the longer segment is just longer, naturally. An influence of different ω is in both cases of HOMOs-1 and HOMOs distribution negligible.
Unoccupied MOs are more dependent on the overall backbone arrangement. As can be further seen in Fig. 3, LUMOs of all 10 structures are distributed along chain with higher values of coefficients in the central parts. This central gathering is particularly observable in 10_120. 10As, 10Bs and 10Cs carry LUMOs in longer parts of Si chain and this shift from kink part is especially observable in conformers with ω = 120°. 10Ds are the most influenced structures by ω value. Since the kink is located in the middle, the preference for LUMO delocalization is determined by the values of backbone dihedral angles. 10D_120–150 have LUMO orbitals located rather on one half of backbone and in 10D _ 160–180, the delocalization is again symmetrical almost along the whole chain. LUMO+1 orbitals are delocalized on Ph parts (described below) and they are presented on Si backbone in much less extent. There is no simple trend that could easily sum the kink and conformation influence up. Increasing ω causes variable shifts including opposite trends in dependence on the kink position. Images of all these Kohn–Sham orbitals that graphically express the bubble graphs are given in Additional file 2: Figures S1–S4.
Figure 4 reflects MO distribution on Ph rings attached along backbone. Rings are numbered according to the position of Si atom to which the ring is attached (e.g. a bubble on a position (1; 120) corresponds to sum of MO coefficients from six carbons that form the Ph ring attached to Si1 in conformer 120°). As can be observed, MO on Ph rings are much more localized in comparison with MO along Si backbone. HOMOs-1 are distributed on the edge phenyls while the phenyl groups attached to central Si5 and Si6 atoms remain practically not involved into the orbital delocalization. In no-kink structures of 10 delocalization is symmetrical and this characteristic splitting is also kept in other molecules but with a lesser extent of symmetry. HOMOs-1 of 10A–10C are preferentially localized on Ph groups adjacent to the kink and to the shorter segment of the decamer. In the case of 10D molecules, the symmetry is again restored, although to a lesser extent than in 10 oligomers. On the other hand, HOMOs seem to appear rather on the central Ph rings and on the longer segment up to Si1 (cases A, B, C). The more is the kink close to the centre of the decamer, the more these HOMOs are squeezed to that longer segment and kink-attached Ph groups are more involved in HOMO, which is an opposite effect than manifested for HOMOs-1. The population density of HOMOs on the two segments of symmetric 10D cases depends on ω. The optimized structure has the HOMO distributed more on the silicon chain than any other structure under investigation. The tested geometries have bigger population density located on phenyl groups. With increasing angle from 120° to 180°, the density becomes less symmetric and shifts from left to right (from lower number positions to higher number positions) having thus always quite densely populated Ph5 and Ph6. It must be stressed out that Ph rings adjacent to Si atoms forming the kink are involved in the MO delocalization. In both cases of HOMOs-1 and HOMOs, the overall distribution of occupied MOs is influenced by the presence of the kink and conformation of the backbone however it does not mean that Ph rings adjacent to the kink Si atoms are excluded from the delocalization.
It can be stated that LUMOs are present on Ph rings rarely. There are only a few Ph groups that carry LUMO in the considerable extent. Seemingly, the Ph group attributable portion of LUMOs in optimal conformations of OMPSi10 is located on that Ph group from the kink part in all kinked structures which is attached to the Si atom closer to the longer segment or in other cases the LUMO density is located on the two Ph groups attached to those two Si from the kink with lower position numbers, which means that these MOs are shifted from Ph7 to Ph5. 10D OMPSi10 carry LUMOs particularly on Ph5 and Ph6 irrespective of the dihedral angle of the backbone with exception of some population density located to the Ph9 for angles 130° and 140°. On the contrary, LUMO+1 delocalization is strongly related with Ph rings when compared with Si backbone orbitals. 180° conformations are the most symmetrical cases, which are affected by the kink presence. Generally, LUMOs+1 are significantly distributed on one or two Ph rings according to a kink position and backbone conformation. The ω has the largest effect on the distribution of LUMOs+1 among tested parameters as it evidently prevail over the importance of the kink position. This influence scatters the manifestation of kink-caused trends and makes the results less readable than in all previous cases. Images of Kohn–Sham orbitals distributed along phenyl rings are appended in the Additional file 2.
Summary of excitation process at λ max for all OMPSi10
H → L
H → L
H → L
H → L
H → L
H → L
H → L
H → L
H → L
H → L
H → L
H → L
H → L
H → L
H → L+4
H → L
H → L
H → L
H → L
H → L
H → L
H → L
H → L+1
H → L
H → L
H → L
H → L
H → L
H → L
H → L
H → L+3
H → L+1
H → L+1
H-1 → L
H → L
H → L
H → L
H → L
H → L
H → L
H → L
H → L+1
H → L+1
H → L+2
Calculated wavelengths are compared with experimentally measured UV–Vis spectra of PMPSi which is shown in Fig. 6. The spectrum contains peaks in the UV part of the spectrum since no sign of the absorption is manifested in Vis area. There are two absorption bands in UV range which can be also identified in calculated spectra, rather of coiled decamers with a non-centrally placed kink. This indicates that the real PMPSi backbone is not planar and straighten but it is rather in helical arrangement. This is in agreement with our optimal geometries with lowest potential energy. On the other hand, two band are observable in 180_B and 180_C OMPSi10 too. In these cases, the kink probably serves as a “helical mimic” structural element which delivers twisted-like conformation to the oligomer that causes similar spectral behaviour, which has been described for helical backbones. The difference between experiment and theory is, of course, observable predominantly due to comparison of experimental spectrum of polymer and theoretical spectrum of isolated decamer and therefore calculated spectral bands are energetically overestimated about several tenths of eV which is in accord with expectable eventual solvation effect of toluene. However, this drawback would not destroy the main trends referring to conformation and electronic behaviour of polysilylene and addition of solvent force field terms to calculations can neither significantly improve our virtual experiment nor clarify the role of phenyl–phenyl group interaction.
It is important to note that no states in the bandgap are formed by the investigated conformational defects, which means that no peaks are present in the Vis area of the absorption spectrum. This is in accordance with state-of-the-art interpretation of origin of such features which are normally manifested in luminescence spectra only .
π–π interactions between phenyl side groups
OMPSi10 served as model systems for the DFT study of overall backbone conformation with conformational defect (a kink), its influence on electronic properties and an investigation of the kink stability provided by π–π stacking interactions. Helical backbones with Si–Si–Si–Si angles equal to 150° and 160° have been determined as the most stable backbone arrangements. Conformations have been treated from 120° to 180° and together with the kink they significantly affect the distribution of Kohn–Sham orbitals along both Si backbone and Ph side groups. HOMO-1 orbitals are distributed along the backbone, while LUMO+1 orbitals are strictly kept on Ph groups. Further, HOMO and LUMO densities can be found delocalized over the whole molecule.
The main calculated absorption transition is assigned as σ–σ* and located at around 310 nm, in experimental UV–Vis spectrum at 336 nm. Second transition around 275 nm is probably of σ–π* character despite traditional assignment to π–π*. We presume that π–π* corresponds energetically to lower wavelengths below 200 nm. However, optimal geometries of excited states have not been successfully calculated due to too demanding computer requirements and at the same time these calculations could be a topic of the next research leading to specification of excitation transitions.
The analysis of angle-distance dependence between Ph planes determined from optimized geometries has revealed that even the molecule with a kink is stabilized by positive interactive mode of π–π stacking between pairs of Ph groups. Conformations with backbone dihedral angle of 160° are the most convenient for phenyl interactions, which was concluded from energy investigation with B3LYP, M06 and ωB97X-D models. There can be distinguished two principally different contributions to the PMPSi backbone geometry. First, it is the previously well-known σ-conjugation effect that has been estimated in order of approximately 1.2 eV Next, the long range π–π interaction contribution was found to be about 0.6 eV for linear chain and about 0.3–0.4 eV for kink defect containing chains. Since 160° conformation is close to the optimal geometry of OMPSi without constrained parts, it can be stated that the kink type of conformational defect is viable in real PMPSi chains.
BH proposed the research subject, carried out the computational studies, arranged the results and wrote the paper. IK assisted with results and discussion part and revised the final manuscript. PU carried out experimental measurement of UV–Vis spectrum. All authors read and approved the final manuscript.
This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic—Program NPU I (LO1504). This work was supported by Internal Grant Agency of Tomas Bata University in Zlin (reg. number IGA/CPS/2015/006).
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
- Mark JE, Allcock HR, West R (2003) Inorganic polymers. Oxford University Press, New YorkGoogle Scholar
- Karatsu T (2008) Photochemistry and photophysics of organomonosilane and oligosilanes: updating their studies on conformation and intramolecular interactions. J Photochem Photobiol, C 9:111–137View ArticleGoogle Scholar
- Nespurek S (2002) From one-dimensional organosilicon structures to polymeric semiconductors: optical and electrical properties. J Non-Cryts Sol 299–302:1033–1041View ArticleGoogle Scholar
- Fujiki M, Koe JR, Terao K, Sato T, Teramoto A, Watanabe J (2003) Optically active polysilanes. Ten years of progress and new polymer twist for nanoscience and nanotechnology. Polym J 35:297–344View ArticleGoogle Scholar
- Fukawa S, Ohta H (2003) Structure and orientation of vacuum-evaporated poly(di-methyl silane) film. Thin Sol Films 438–439:48–55View ArticleGoogle Scholar
- Fujiki MJ (2003) Switching handedness in optically active polysilanes. Organomet Film 685:15–34View ArticleGoogle Scholar
- Michl J, West R (2000) Conformations of linear chains. Systematics and suggestions for nomenclature. Acc Chem Res 33:821–823View ArticleGoogle Scholar
- Fogarty H-A, Ottoson C-H, Michl J (2000) The five favored backbone conformations of n-Si4Et10: cisoid, gauche, ortho, deviant, and transoid. J Mol Struc-Theochem 506:243–255View ArticleGoogle Scholar
- Nguyen TQ, Martini I, Liu J, Schwartz BJ (2000) Controlling interchain interactions in conjugated polymers: the effects of chain morphology on exciton-exciton annihilation and aggregation in MEH-PPV films. J Phys Chem B 104:237–255View ArticleGoogle Scholar
- Mirzov O, Scheblykin IG (2006) Photoluminescence spectra of a conjugated polymer: from films and solutions to single molecule. Phys Chem Chem Phys 8:5569–5576View ArticleGoogle Scholar
- Urbanek P, Kuritka I (2015) Thickness dependent structural ordering, degradation and metastability in polysilane thin films: a photoluminescence study on representative σ-conjugated polymers. J Lumin 168:261–268View ArticleGoogle Scholar
- Urbanek P, Kuritka I, Danis S, Touskova J, Tousek J (2014) Thickness threshold of structural ordering in thin MEH-PPV films. Polymer 55:4050–4056View ArticleGoogle Scholar
- Gmucova K, Nadazdy V, Schauer F, Kaiser M, Majkova E (2015) Electrochemical Spectroscopic Methods for the Fine Band Gap Electronic Structure Mapping in Organic Semiconductors. J Phys Chem C 119:15926–15934View ArticleGoogle Scholar
- Nadazdy V, Schauer F, Gmucova K (2014) Energy resolved electrochemical impedance spectroscopy for electronic structure mapping in organic semiconductors. Appl Phys Lett C 119:15926–15934Google Scholar
- Overney RM, Buenviaje C, Luginbuhl R, Dinelli F (2000) Glass and structural transitions measured at polymer surfaces on the nanoscale. J Therm Anal Cal 59:205–225View ArticleGoogle Scholar
- Benight SJ, Knorr DB Jr, Johnson LE, Sullivan PA, Lao D, Sun J, Kocherlakota LS, Elangovan A, Robinson BH, Overney RM, Dalton LR (2012) Nano-engineering lattice dimensionality for a soft matter organic functional material. Adv Mater 24:3263–3268View ArticleGoogle Scholar
- Despotopoulou MM, Frank CW, Miller RD, Rabolt JF (1995) Role of the restricted geometry on the morphology of ultrathin poly(di-n-hexylsilane) films. Macromolecules 28:6687–6688View ArticleGoogle Scholar
- Tsuji H, Michl J, Tamao K (2003) Recent experimental and theoretical aspects of the conformational dependence of UV absorption of short chain peralkylated oligosilanes. J Organomet Chem 685:9–14View ArticleGoogle Scholar
- Teramae H, Matsumoto N (1996) Theoretical study on gaucge-kink in polysilane polymer. Sol State Com 99:917–919View ArticleGoogle Scholar
- Hanulikova B, Kuritka I (2014) Manifestations of conformational defects in electronic spectra of polysilanes—a theoretical study. Macromol Symp 339:100–111View ArticleGoogle Scholar
- Hanulikova B, Kuritka I (2014) Theoretical study of polaron binding energy in conformationally disrupted oligosilanes. J Mol Model 20:2442–2450View ArticleGoogle Scholar
- Hunter CA, Sanders JKM (1990) The nature of π–π interactions. J Am Chem Soc 112:5525–5534View ArticleGoogle Scholar
- Chung SJ, Kim DH (1997) Intramolecular edge-to-face aromatic-aromatic ring interactionsin 3-(3-aryl-2-isopropylpropanoyl)-4-phenylmethyl-1,3-oxazolidin-2-ones prepared from Evans `chiral auxiliary. Bull Kor Chem 18:1324–1327Google Scholar
- Hunter CA, Singh J, Thornton JM (1991) π–π interactions: the geometry and energetics of phenylalanine-phenylalanine interactions in proteins. J Mol Biol 218:837–846View ArticleGoogle Scholar
- Meyer EA, Castellano RK, Diederich F (2003) Interactions with aromatic rings in chemical and biological recognition. Angew Chem Int Ed 42:1210–1250View ArticleGoogle Scholar
- Mignon P, Loverix S, De Proft F, Geerlings P (2004) Influence of stacking on hydrogen bonding: quantum chemical study on pyridine-benzene model complexes. J Phys Chem 108:6038–6044View ArticleGoogle Scholar
- Akher FB, Ebrahimi A (2015) π-stacking effects on the hydrogen bonding capacity of methyl 2-naphthoate. J Mol Graph Model 61:115–122View ArticleGoogle Scholar
- Hunter CA, Lawson KR, Perkins J, Urch CJ (2001) Aromatic interactions. J Chem Soc, Perkin Trans 2:651–669View ArticleGoogle Scholar
- Waters ML (2002) Aromatic interactions in model systems. Curr Opin Chem Biol 6:736–741View ArticleGoogle Scholar
- Martinez CR, Iverson BL (2012) Rethinking the term ‘‘pi-stacking’’. Chem Sci 3:2191–2201View ArticleGoogle Scholar
- Kohn W, Sham WL (1965) Self-consistent equations including exchange and correlation effect. Phys Rev 140:A1133–A1138View ArticleGoogle Scholar
- Biswas AK, Lo R, Ganguly B (2013) First principles studies toward the design of silylene superbases: a density functional theory study. J Phys Chem A 117:3109–3117View ArticleGoogle Scholar
- Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136:B864–B871View ArticleGoogle Scholar
- Runge E, Gross EKU (1964) Density-functional theory for time-dependent systems. Phys Rev Lett 52:997–1000View ArticleGoogle Scholar
- Pan X-Y, Sahni V (2008) New perspectives on the fundamental theorem of density functional theory. Int J Quantum Chem 108:2756–2762View ArticleGoogle Scholar
- Pichaandi KR, Mague JT, Fink MJ (2015) Synthesis, photochemical decomposition and DFT studies of 2,2,3,3-tetramethyl-1,1-bis(dimethylphenylsilyl)silacyclopropane. J Organomet Chem 791:163–168View ArticleGoogle Scholar
- Y-q Ding, Q-a Qiao, Wang P, Chen G-w, Han J-j, Xu Q, Feng S-y (2010) A DFT study of electronic structures of thiophene-based organosilicon compounds. Chem Phys 367:167–174View ArticleGoogle Scholar
- Boo BH, Im S, Lee S (2009) Ab initio and DFT studies of the thermal rearrangement of trimethylsilyl(methyl)silylene: remarkable rearrangements of silicon intermediates. J Comput Chem 31:154–163View ArticleGoogle Scholar
- Zhao Y, Truhlar DG (2006) A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions. J Chem Phys 125:194101View ArticleGoogle Scholar
- Walker M, Harvey AJA, Sen A, Dessent CEH (2013) Performance of M06, M06-2X, and M06-HF density functionals for conformationally flexible anionic clusters: M06 functionals perform better than B3LYP for a model system with dispersion and ionic hydrogen-bonding interactions. J Phys Chem A 117:12590–12600View ArticleGoogle Scholar
- Chai J-D, Head-Gordon M (2008) Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections. Phys Chem Chem Phys 10:6615–6620View ArticleGoogle Scholar
- Civalleri B, Zicovich-Wilson CM, Valenzano L, Ugliengo P (2008) B3LYP augmented with an empirical dispersion term (B3LYP-D*) as applied to molecular crystals. Cryst Eng Comm 10:405–410View ArticleGoogle Scholar
- Shao Y, Molnar LF, Jung Y, Kussmann J, Ochsenfeld C, Brown ST, Gilbert ATB, Slipchenko LV, Levchenko SV, O’Neill DP, DiStasio RA Jr, Lochan RC, Wang T, Beran GJO, Besley NA, Herbert JM, Lin CY, Van Voorhis T, Chien SH, Sodt A, Steele RP, Rassolov VA, Maslen PE, Korambath PP, Adamson RD, Austin B, Baker J, Byrd EFC, Dachsel H, Doerksen RJ, Dreuw A, Dunietz BD, Dutoi AD, Furlani TR, Gwaltney SR, Heyden A, Hirata S, Hsu C-P, Kedziora G, Khalliulin RZ, Klunzinger P, Lee AM, Lee MS, Liang W, Lotan I, Nair N, Peters B, Proynov EI, Pieniazek PA, Rhee YM, Ritchie J, Rosta E, Sherrill CD, Simmonett AC, Subotnik JE, Woodcock HL III, Zhang W, Bell AT, Chakraborty AK, Chipman DM, Keil FJ, Warshel A, Hehre WJ, Schaefer HF III, Kong J, Krylov AI, Gilla PMW, Head-Gordon M (2006) Advances in methods and algorithms in a modern quantum chemistry program package. Phys Chem Chem Phys 8:3172–3191View ArticleGoogle Scholar
- Frisch MJ, Pople JA, Binkley JS (1984) Self-consistent molecular orbital methods 25. Supplementary functions for Gaussian basis sets. J Chem Phys 80:3265–3269View ArticleGoogle Scholar
- Hehre WJ (2003) Guide to molecular mechanics and quantum chemical calculations. Wavefunction Inc., IrvineGoogle Scholar
- Nespurek S, Wang G, Yoshino K (2005) Polysilanes - Advanced materials for optoelectronics. J Optoelectron Adv M 7:223–230Google Scholar