UV Photoelectron Spectroscopy and Ab Initio Characterization of Valence Orbital Structures and Conformations of Neutral Phosphate Esters

Abstract

The Hel UV photoelectron spectrum of trimethyl phosphate (TMP) has been measured and interpreted with the aid of SCF molecular orbital calculations carried out with STO-3G, STO-3G* and 4–31G basis functions. The photoelectron spectrum of TMP is more accurately reproduced by results from 4–31G calculations than by results from STO-3G or STO-3G* calculations. However, all three basis sets yield results which predict the same assignment of the photoelectron spectrum. Results at the 4–31G level indicate that whether calculations are based on crystallographic bond angles and bond lengths or on STO-3G optimized geometries has little effect on the energetic ordering of the upper occupied orbitals. The energetic ordering of orbitals is also found to be only weakly dependent upon the torsional angle φ, describing rotation of ester groups about P-O bonds and upon the torsional angle ψ, describing rotation of methyl groups about C-O bonds. For trimethyl phosphate, with C₃ symmetry, the vertical ionization potentials of the upper occupied orbitals are 10.81 eV (8e), 11.4 eV (9a), 11.93 eV (7e), 12.6–12.9 eV (8a and 6e), 14.4 eV (7a) and 15.0–16.0 eV(5e and 6a). Calculations at the 4–31G level indicate that many of the highest occupied orbitals in neutral dimethyl phosphate and methyl phosphate have energies and electron distributions similar to orbitals in TMP.

For TMP, a search for optimized values of φ and ψ has been carried out at the STO-3G* level. In agreement with previous NMR studies and with classical potential calculations, the STO- 3G* results indicate that both the gauche φ= 53.1 °) and anticlinal (φ = 141.9°) conformations are thermally accessible. Also in agreement with the classical potential calculations, the STO-3G* results predict that in the all gauche conformation energy is minimized when the methyl groups assume a staggered geometry (ψ= 60° to 80°) and that an energy maximum occurs for an eclipsed geometry (ψ = 0° to 20°). A study of the dependence of optimized values of O-P-O ester bond angles on the torsional angles, φ, was carried out at the STO-3G, STO-3G* and 4–31G levels. The results demonstrate that for C₃ symmetry, the coupling of O-P-O angles to φ is influenced by repulsive steric interactions.     

UV photoelectron spectroscopy and ab initio characterization of valence orbital structures and conformations of neutral phosphate esters

The HeI UV photoelectron spectrum of trimethyl phosphate (TMP) has been measured and interpreted with the aid of SCF molecular orbital calculations carried out with STO-3G, STO-3G* and 4-31G basis functions. The photoelectron spectrum of TMP is more accurately reproduced by results from 4-31G calculations than by results from STO-3G or STO-3G* calculations. However, all three basis sets yield results which predict the same assignment of the photoelectron spectrum. Results at the 4-31G level indicate that whether calculations are based on crystallographic bond angles and bond lengths or on STO-3G optimized geometries has little effect on the energetic ordering of the upper occupied orbitals. The energetic ordering of orbitals is also found to be only weakly dependent upon the torsional angle phi, describing rotation of ester groups about P-O bonds and upon the torsional angle psi, describing rotation of methyl groups about C-O bonds. For trimethyl phosphate, with C3 symmetry, the vertical ionization potentials of the upper occupied orbitals are 10.81 eV (8e), 11.4 eV (9a), 11.93 eV (7e), 12.6-12.9 eV (8a and 6e), 14.4 eV (7a) and 15.0-16.0 eV (5e and 6a). Calculations at the 4-31G level indicate that many of the highest occupied orbitals in neutral dimethyl phosphate and methyl phosphate have energies and electron distributions similar to orbitals in TMP. For TMP, a search for optimized values of phi and psi has been carried out at the STO-3G*level. In agreement with previous NMR studies and with classical potential calculations, the STO-3G* results indicate that both the gauche (phi = 53.1 degrees) and anticlinal (phi = 141.9 degrees) conformations are thermally accessible. Also in agreement with the classical potential calculations, the STO-3G* results predict that in the all gauche conformation energy is minimized when the methyl groups assume a staggered geometry (psi = 60 degrees to 80 degrees) and that an energy maximum occurs for an eclipsed geometry (phi = 0 degrees to 20 degrees). A study of the dependence of optimized values of O-P-O ester bond angles on the torsional angles, phi, was carried out at the STO-3G, STO-3G* and 4-31G levels. The results demonstrate that for C3 symmetry, the coupling of O-P-O angles to phi is influence by repulsive steric interactions.     

The impact of Cu atoms on the reactivity of ZrO2 oligomers

A theoretical study on (ZrO₂) _n (n = 1–5) and Cu/ZrO₂ oligomers is presented, DFT/B3LYP/6-31G** calculations along with Lanl2DZ pseudopotentials on metallic centers have been used to predict ionization potentials and electron affinities, chemical potentials and bandgaps indicating that the reactivity reaches reasonably constant values at n = 5. The effect of copper atoms adsorbed on (ZrO₂) _n is discussed and the reactivity of oligomers of ZrO₂ and Cu/ZrO₂ are compared, results indicate that Cu activates the systems by localizing the specific nucleophilic and electrophilic reactivity.     

Density functional theory study on (LiNH<Subscript>2</Subscript>)<Subscript>n</Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1–5) clusters

Geometrical structures and relative stabilities of (LiNH₂)_n (n = 1–5) clusters were studied using density functional theory (DFT) at the B3LYP/6-31G* and B3LYP/6-31++G* levels. The electronic structures, vibrational properties, N–H bond dissociation energies (BDE), thermodynamic properties, bond properties and ionization potentials were analyzed for the most stable isomers. The calculated results show that the Li–N and Li–Li bonds can be formed more easily than those of the Li–H or N–H bonds in the clusters, in which NH₂ is bound to the framework of Li atomic clusters with fused rings. The average binding energies for each LiNH₂ unit increase gradually from 142 kJ mol⁻¹ up to about 180 kJ mol⁻¹ with increasing n. Natural bond orbital (NBO) analysis suggests that the bonds between Li and NH₂ are of strong ionicity. Three-center–two-electron Li–N–Li bonding exists in the (LiNH₂)₂ dimer. The N–H BDE values indicate that the change in N–H BDE values from the monomer a1 to the singlet-state clusters is small. The N–H bonds in singlet state clusters are stable, while the N–H bonds in triplet clusters dissociate easily. A study of their thermodynamic properties suggests that monomer a1 forms clusters (b1, c1, d2 and e1) easily at low temperature, and clusters with fewer numbers of rings tend to transfer to ones with more rings at low temperature. E _g, E _HOMO and E _av decrease gradually, and become constant. Ring-like (LiNH₂)_3,4 clusters possess higher ionization energy (VIE) and E _g, but lower values of E _HOMO. Ring-like (LiNH₂)_3,4 clusters are more stable than other types. A comparison of structures and spectra between clusters and crystal showed that the NH₂ moiety in clusters has a structure and spectral features similar to those of the crystal.     

Conformation and tautomerizm of the 2-methyl-4-pyridin-2′-yl-1,5-benzodiazepine molecule. An ab initio study

The protomeric tautomerizm and conformation of the 2-methyl-4-pyridin-2′-yl-1,5-benzodiazepine molecule were investigated, and its three neutral tautomers (B₁,B₂,B₃) and their rotamers (C₁,C₂,C₃) were considered. Full geometry optimizations were carried out at the HF/6-31G* and B3LYP/6-31G* levels in gas phase and in water. The tautomerization processes in water (ɛ = 78.54) were studied by using self-consistent reaction field theory. The calculation showed that the boat conformation is dominant for the seven-membered diazepine ring in all of the structures, even with different double bond positions. The calculated relative free energies (ΔG) showed that the tautomer C₁ was the most stable structure, and its conformer B₁ was the second most stable in the gas phase and in water. Figure 2-Methyl-4-pyridin-2′-yl-1,5-benzodiazepine     

Density functional theory study of the potassium complexation of an unsymmetrical 1,3-alternate calix[4]-crown-5-N-azacrown-5 bearing two different crown rings

Theoretical studies of an unsymmetrical calix[4]-crown-5-N-azacrown-5 (1) in a fixed 1,3-alternate conformation and the complexes 1·K⁺(a), 1·K⁺(b), 1·K⁺(c) and 1·K⁺K⁺ were performed using density functional theory (DFT) at the B3LYP/6-31G* level. The fully optimized geometric structures of the free macroligand and its 1:1 and 1:2 complexes, as obtained from DFT calculations, were used to perform natural bond orbital (NBO) analysis. The two main types of driving force metal–ligand and cation–π interactions were investigated. NBO analysis indicated that the stabilization interaction energies (E ₂) for O…K⁺ and N…K⁺ are larger than the other intermolecular interactions in each complex. The significant increase in electron density in the RY* or LP* orbitals of K⁺ results in strong host–guest interactions. In addition, the intermolecular interaction thermal energies (ΔE, ΔH, ΔG) were calculated by frequency analysis at the B3LYP/6-31G* level. For all structures, the most pronounced changes in the geometric parameters upon interaction are observed in the calix[4]arene molecule. The results indicate that both the intermolecular electrostatic interactions and the cation–π interactions between the metal ion and π orbitals of the two pairs that face the inverted benzene rings play a significant role.     

Are density functional theory predictions of the Raman spectra accurate enough to distinguish conformational transitions during amyloid formation?

We report density functional theory (DFT) calculations of the Raman spectra for hexapepetides of glutamic acid and lysine in three different conformations (α, β and PPII). The wave numbers of amide I, amide II and amide III bands of all three conformations predicted at B3LYP/6-31G and B3LYP/6-31G* are in good agreement with previously reported experimental values of polyglutamic acid and polylysine. Agreement with experiment improves when polarization functions are included in the basis set. Explicit water molecules, H-bonded to the backbone amide groups were found to be absolutely necessary to obtain this agreement. Our results indicate that DFT is a promising tool for assignment of the spectral data on kinetics of conformational changes for peptides during amyloid formation.     

Density functional studies of the substituent effect on absorption and emission properties of 1, 8-naphthalimide derivatives

Using TD-PBE1PBE/6-31G* and TD-B3LYP/6-31G* approaches, we calculated the absorption and emission spectra of 1,8-naphthalmide derivatives in gas-phase. The geometric structures optimized by HF/6-31G* and B3LYP/6-31G* models and the absorption and emission maxima were in good agreement with existed experimental measurements. It was also found that the lowest singlet states corresponded mainly to the electronic transition from the highest occupied orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO). Intramolecular charge transfer occurred between substituents and naphthalimic rings. Study also showed that most compounds with low absorption excitation energies had low vertical ionization potentials. Finally, the delocalization electronic energies between substituents and naphthalimic rings of isomers were investigated to obtain further sight into their stability.     

Azaguanine: A Theoretical Study of Its Tautomerism and Protonation in the Gas Phase and Aqueous Solution

The tautomerism and protonation of 8-azaguanine (azaG) have been studied by means of ab initio methods, both in the gas phase and in aqueous solution. An elimination procedure to choose the most stable tautomeric forms, based on AM1 and HF/6–31G* energies, has been applied. Tautomers azaG(1,9), azaG(1,7) and azaG(9,15) have been selected and their energies calculated at MP2/6–311++G**//HF/6–31G* level. Self-consistent reaction field IPCM, based on polarizable continuum model (PCM), has been applied to study the solvent effects. The stability order in the gas phase is azaG(1,7) = azag(1,9) > azaG(9,15), whereas in solution the order becomes azaG(1,7) > azaG(1,9) > azaG(9,15), the latter being just 0.76 kcal/mol over azaG(1,7). The calculations of proton affinities allowed to unambiguously determine the preferred sites of protonation of these species.     

Conformational stabilities, infrared, and vibrational dichroism spectroscopy studies of tris(ethylenediamine) zinc(II) chloride

The conformational stabilities of the transition metal complex of Zn (en)₃Cl₂ were studied using density functional theory (DFT). Deformational potential energy profiles (PEPs), and pathways between the different isomeric conformational energies were calculated using DFT/B3LYP/6–31G. The relative conformational energies of Δ(λλλ), Δ(λλδ), Δ(λδδ) and Δ(δδδ) are 10.48, 7.08, 3.56, and 0.0 kcal/mol, respectively, which are small compared to the barrier heights for reversible phase transitions (49.56, 49.55, 49.52 kcal/mol, respectively). Frequency assignment was carried out by decomposing Fourier transform infrared (FTIR) spectra using Gaussian and Gaussview. The theoretical IR and vibrational dichroism spectroscopy (VCD) absorption spectra are presented for all conformations within the range of 400–3,500 cm^-1.     

Optimization of parameters for semiempirical methods V: Modification of NDDO approximations and application to 70 elements

Several modifications that have been made to the NDDO core-core interaction term and to the method of parameter optimization are described. These changes have resulted in a more complete parameter optimization, called PM6, which has, in turn, allowed 70 elements to be parameterized. The average unsigned error (AUE) between calculated and reference heats of formation for 4,492 species was 8.0 kcal mol⁻¹. For the subset of 1,373 compounds involving only the elements H, C, N, O, F, P, S, Cl, and Br, the PM6 AUE was 4.4 kcal mol⁻¹. The equivalent AUE for other methods were: RM1: 5.0, B3LYP 6–31G*: 5.2, PM5: 5.7, PM3: 6.3, HF 6–31G*: 7.4, and AM1: 10.0 kcal mol⁻¹. Several long-standing faults in AM1 and PM3 have been corrected and significant improvements have been made in the prediction of geometries. Figure Calculated structure of the complex ion [Ta₆Cl₁₂]²⁺ (footnote): Reference value in parenthesis Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Ab initio calculation of the geometries, stabilities, and electronic properties for the bimetallic Be2Au(n) (n = 1-9) clusters: comparison with pure gold clusters

Ab initio methods based on density functional theory at BP86 level were applied to the study of the geometrical structures, relative stabilities, and electronic properties of small bimetallic Be₂Au _n (n = 1–9) clusters. The optimized geometries reveal that the most stable isomers have 3D structures at n = 3, 5, 7, 8, and 9. Here, the relative stabilities were investigated in terms of the averaged atomic binding energies, fragmentation energies and second-order difference of energies. The results show that the planar Be₂Au₄ structure is the most stable structure for Be₂Au _n clusters. The HOMO−LUMO gap, vertical ionization potential, vertical electron affinity and chemical hardness exhibit a pronounced even–odd alternating phenomenon. In addition, charge transfer and natural electron configuration were analyzed and compared.     

Ab initio and DFT study on the electrophilic addition reaction of bromine to tetracyclo[5.3.0.02,6.03,10]deca–4,8–diene

The electronic and geometric structures of tetracyclo[5.3.0.0^2,6.0^3,10]deca-4,8-diene (hypostrophene) have been investigated by ab initio and DFT/B3LYP methods using the 6-31G* and 6-311G* basis sets. The double bonds of hypostrophene are endo-pyramidalized. The cationic intermediates and products formed in the addition reaction have been investigated using the HF/6-311G*, HF/6-311G**, and B3LYP/6-311G* methods. The bridged bromonium cation was more stable than the U-type cation. Considering that the bridged cation does not isomerize to the less stable U-type cation, it is not possible for the U-type product to be obtained in the reaction. The bridged bromonium cation transformed into the more stable N-type cation and the N-type product was obtained via this cation. The thermodynamic stability of the exo, exo and exo, endo isomers of the N-type dibromide molecule were almost identical. The N-type product was 16.6 kcal mol⁻¹ more stable than the U-type product. Figure General energy diagram of the hypostrophene–bromine (HS–Br₂) system (kcal mol⁻¹) (MP2/6-311G*//HF/6-311G*)     

Molecular modeling studies of poly lactic acid initiation mechanisms

The two possible routes to synthesize poly (lactic acid) are polycondensation of the lactic acid and ring opening polymerization (ROP) of the lactide. This work involves molecular modeling of the polymerization initiation mechanisms using different initiators a) H₂SO₄ for polycondensation b) aluminum isopropoxide for coordination-insertion ROP c)methyl triflate for cationic ROP, and d) potassium methoxide for anionic ROP. For molecular modeling of PLA, we have benchmarked our approach using Ryner’s work on ROP of L-lactide using stannous (II) 2-ethylhexanoate (Sn(Oct)₂) and methanol as initiators. Our values of -15.2 kcal mol^-1 and -14.1 kcal mol^-1 for enthalpy changes in the two steps of activated complex formation match with Ryner’s. Geometric and frequency optimizations have been done on Gaussian’03 using B3LYP density functional theory along with the basis sets LANL2DZ for metal atoms and 6–31G* and 6–31G** for non metal atoms. The kinetic rate constant for each mechanism has been calculated using the values of energy of activation, change in enthalpy, Gibbs free energy, entropy and the partition functions from the Gaussian’03 output. Our polycondensation rate constant value of 1.07 × 10^–4 se^-1 compares well with 1.51 × 10^–4 se^-1 as reported by Wang. However, ROP rate constants could not be validated due to lack of experimental data. Figure Cationic Ring Opening Polymerization of L-Lactide

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Insight into the lithium/hydrogen bonding in (CH<Subscript>2</Subscript>)<Subscript>2</Subscript>X...LiY/HY (X: C=CH<Subscript>2</Subscript>, O,S; Y=F,Cl, Br) complexes

The nature of the lithium/hydrogen bonding between (CH₂)₂X(X: C=CH₂, O, S) and LiY/HY(Y=F, Cl, Br) have been theoretically investigated at MP2/6-311++G (d, p) level, using Bader’s “atoms in molecules (AIM)” theory and Weinhold’s “natural bond orbital (NBO)” methodology. The molecule formation density differences (MFDD) of the titled complexes are analyzed. Two kinds of geometries of the lithium/hydrogen bonded complexes are compared. As a whole, the nature of lithium bond and hydrogen bond are different. For the same electron donor and the same acceptor, lithium bond is stronger than hydrogen bond. For the same electron acceptor and different kind of donors, the interaction energies follows the n-type> π-type > pseudo-π-type order. For the same (CH₂)₂X, the interaction energy increases in the sequence of Y=F, Cl and Br for lithium bond systems while it decreases for hydrogen bond systems. Electron transfer plays an important role in the formation of lithium bond systems while it is less important in the hydrogen bond systems.     

Nucleation and mobility model of Ag<Subscript>n</Subscript> clusters adsorbed on perfect and oxygen vacancy MgO surfaces

The structures and energy properties for Ag_n (n = 1-8) metal clusters adsorbed on the perfect and oxygen vacancy MgO surfaces have been studied by using the DFT/UB3LYP method with an embedded cluster model. The nucleation and mobility model for the Ag_n (n = 1-8) clusters on the perfect and oxygen vacancy MgO(100) surfaces was investigated. The results show that the Ag atoms locate initially at the surface oxygen vacancy sites; then, with the growth of Ag cluster sizes, the large Ag clusters move possibly out of the vacancy sites by a rolling model, and diffuse on the MgO surface under a certain temperature condition. The relative energies needed for moving out of the oxygen vacancy region for the adsorbed Ag_n clusters with the rolling model have been predicted. The even-odd oscillation behaviors for the cohesive energies, nucleation energies, first ionization potentials and HOMO-LUMO gaps of the adsorbed Ag_n clusters with the variation of cluster sizes have also been discussed.     

Structure of a nonanucleotide duplex cross-linked by cisplatin at an ApG sequence

 The structure of the second major adduct formed by the antitumor drug cisplatin with DNA, the intrastand cis–Pt(NH₃)₂{d(ApG)N7–N7} chelate (A*G*), has been investigated using a double-stranded nonanucleotide, d(CTCA*G*CCTC)-d(GAGGCTGAG), by means of NMR and molecular modeling. The NMR data allow us to conclude that the oligonucleotide is kinked at the platinated site towards the major groove in a way similar to that observed elsewhere for the G*G*-crosslink in d(GCCG*G*ATCGC)-d(GCGATCCGGC). The main difference concerns the position of the thymine T(15) complementary to the platinated adenine A*(4). It remains stacked on its 5′-neighbor C(14), corresponding to the "model E" described previously, whereas in the G*G*-adduct, the cytosine facing the 5′-G* was found to oscillate between the 5′-branch ("model E") and the 3′-branch ("model C") of the complementary strand. Two "E-type" models are presented which account for the particular NOE connectivity and for two remarkable upfield NMR signals: those of the H2′ proton of the cytidine C(3) 5′ to the A*G* chelate, and of the H3 imino proton of T(15), the base complementary to A*(4). The former shift is attributed to shielding by the destacked A*(4) base, whereas the latter is accounted for by a swinging movement of the T(15) base between two positions where the imino Watson-Crick hydrogen bond with A*(4) remains intact and the amino hydrogen bond is disrupted, or vice versa. Possible implications of the structural difference between the AG and GG adducts of cisplatin in the mutagenic properties of the two adducts are discussed. Received: 19 August 1996 / Accepted: 4 November 1996     

Effect of alkyl substitution on H-bond strength of substituted amide-alcohol complexes

The effect of alkyl substitution (CH₃, C₂H₅, n-C₃H₇, i-C₃H₇, and t-C₄H₉) on the hydrogen bond strengths (H-bond) of substituted amide-alcohol complexes has been systematically explored. B3LYP/aug-cc-pVDZ method was applied to a total of 215 alkyl substituted amide-alcohol complexes to delineate the effect of substitution on the H-bond strength; formamide-water complex is taken as reference point. Complexes are classified into five types depending on the hydrogen donor, acceptor and the site of alkyl substitution (Type-IA, Type-IIA, Type-IB, Type-IIB and Type-III). The strength of H-bond was correlated with geometrical parameters such as proton-acceptor (H∙∙∙∙Y) distance, the length of proton donating bond (X–H). In all the complexes N–H and O–H stretching frequencies are red-shifted. The effect of alkyl substitution on N–H and O–H stretching frequencies were analyzed. Topological parameters like electron density at H∙∙∙∙Y and X–H bond critical points as derived from atom in molecules (AIM) theory was also evaluated. When C = O group is participating in H-bond, the strength of H-bond decreases with increasing size of alcohols except for methanol (Type-IA, Type-III and Type-IB complexes). But it increases with increasing size of alkyl groups on amide and decreases with bulky groups. In the case of N–H group as H-bond donor, the strength of H-bond increases with increasing size of alcohols (Type-IIA and Type-IIB complexes) whereas decreases with increasing size of alkyl groups on amide. Type-IA, IIA, IB and IIB complexes exhibit good correlations among IE, H-bond distance and electron density at bcp. In Type-III complexes, average H-bond distance and sum of electron densities shows better correlation with IEs than the corresponding individuals. The correlation of IE less with electron density at RCP compared to sum of electron densities.     

Density functional studies on the electron affinities of DNA and RNA bases

Influence of basis sets on electron affinities (EAs) of DNA and RNA bases has been investigated using density functional method (B3LYP functional) with different basis sets (6-31G, TZVP and 6-311+ + G**). Effect of some PBE functionals namely, PBEOP, PBELYP and PBEVWN, on EA values of the nucleobases was studied using basis set which predicted the most reliable values with B3LYP functional. Observation of the trends in the values of EA and dipole moment of the molecules enable us to identify the features of a basis set that shows the presence of dipole-bound state of some of the nucleobases. The vertical electron affinities with B3LYP and PBEOP functionals are close to the experimental values. The adiabatic electron affinities of uracil and thymine were found to be positive for basis set with diffuse functions using B3LYP functional. Adenine does not have a stable covalently bound anion at all levels of basis sets and functionals. The sign of adiabatic electron affinity value of cytosine is inconsistent with that of experimental value but in agreement with previous theoretical results. For guanine the adiabatic electron affinity value with 6-311+ + G** basis set was found to be very high as comparison with other two basis sets confirming the formation of mixed covalent-dipole character.     

Density functional study of the electronic and optical properties of fluorene-thieno[3,2-b]thiophene-based conjugated copolymers

Quantum mechanical techniques are applied to investigate a family of π-conjugated copolymers: poly(9,9′-dimethylfluorene-alt-thiophene) (PFT), poly(9,9′-dimethylfluorene-alt-thieno[3,2-b]-thiophene) (PFTT), poly(9,9′-dimethylfluorene-alt-bithiophene) (PFT2), and poly(9,9′-dimethylfluorene-alt-α,α′-bisthieno[3,2-b]-thiophene) (PFTT2). Linear extrapolation is employed to obtain polymers' properties from oligomer calculations. That is, the HOMO–LUMO gaps (Δ_H–Ls), band gaps (E _g s), ionisation potentials and electron affinities of the copolymers are obtained by plotting the corresponding quantities of the oligomers as a function of the inverse chain length (1/n) and extrapolating them to infinite chain length. The electronic properties of the neutral, positive and negative oligomers are determined using the density functional theory (DFT) at B3LYP/6-31G* approximation. The lowest singlet excitation energies of the oligomers of PFT, PFTT, PFT2, and PFTT2 are also determined with the use of the time-dependent DFT again at B3LYP/6-31G* approximation. Comparisons are made with experimental values when possible.