The Ziegler–Rauk–Baerends multiplet sum method (MSM) assumes that density functional theory (DFT) provides a good description of states dominated by a single determinant. It then uses symmetry to add static correlation to DFT. In our previous article (Article I) [J. Chem. Phys.159, 244306 (2023)], we introduced diagrammatic MSM-DFT as a tool to aid in extending MSM-DFT to include the nondynamic correlation needed for making and breaking bonds even in the absence of symmetry. An attractive feature of this approach is that no functional-dependent parameters need to be introduced, although choices are needed in making correspondences between wave function theory and MSM-DFT diagrams. The preliminary examples in Article I used the two-orbital two-electron model (TOTEM) less completely than could have been the case as we wanted to limit calculations to diagonalizing 2 × 2 matrices, which can be done by solving a simple quadratic equation. Diagrammatic MSM-DFT is extended here to treat the full TOTEM, and it is shown that the unsymmetric lithium hydride molecule dissociates into neutral atoms when diagrammatic MSM-DFT techniques are used to introduce a proper description of the avoided crossing between ionic bonding and covalent bonding states. This involves diagonalizing a 3 × 3 matrix, which requires going beyond solving a quadratic equation but is still trivial these days. The method is tested for Hartree–Fock and for three functionals (LDA, PW91, and B3LYP). All the functionals yield similar results as should be expected for a properly formulated parameter-free theory. Agreement with available estimates show that the magnitude of the coupling element introduced here is excellent. However, more work will be needed to obtain quantitative agreement between our diagrammatic MSM-DFT ground-state potential energy curve and that found from high-quality ab initio calculations.

Ruthenium(II) polypyridine compounds often have a relatively long lived triplet metalligand charge transfer (3MLCT) state, making these complexes useful as chromophores for photoactivated electron transfer in photomolecular devices (PMDs). As different PMDs typically require different ligands and as the luminescence lifetime of the 3MLCT is sensitive to the structure of the ligand, it is important to understand this state and what types of photoprocesses can lead to its quenching. Recent work has increasingly emphasized that there are likely multiple competing pathways involved which should be explored in order to fully comprehend the 3MLCT state. However the lowest barrier that needs to be crossed to pass over to the nonluminescent triplet metal-centered (3MC) state has been repeatedly found to be a trans dissociation of the complex, at least in the simpler cases studied. This is the fourth in a series of articles investigating the possibility of an orbital based luminescence index (LI3, because it was the most successful of three) for predicting luminescence lifetimes. In an earlier study of bidentate (N N) ligands, we showed that the gas-phase 3MLCT to 3MC mechanism proceeded via an initial charge transfer to a single N N ligand which moves symmetrically away from the central ruthenium atom, followed by a bifurcation pathway to one of two 3MC enantiomers. The actual transition state barrier was quite small and independent, to within the limits of our calculations, to the choice of ligand studied. Here we investigate the same reaction in acetonitrile, CH3CN, solution and find that the mechanism differs from that in the gas phase in that the reaction passes directly via a trans mechanism. This has implications for the interpretation of LI3 via the Bell-Evans Polanyi principle.

Buckminsterfullerene, C60, has not only a beautiful truncated icosahedral (soccer ball) shape but also simple Hückel calculations that predict a 3-fold degenerate lowest unoccupied molecular orbital, which can accommodate up to six electrons, making it a good electron acceptor. Experiments have confirmed that C60 is a radical sponge, and it is now sold for use in topical cosmetics. Further medical uses require functionalization of C60 to make it soluble, and one of the simplest functionalizations is to make C60(OH)n fullerenols. A previous article [Adv. Quantum Chem. 88, 351 (2023)] studied reactivity indices for the successive addition of the •OH radical to (•)C60(OH)n in the gas phase [(•)C60(OH)n is a radical only when n is an odd number]. This present article extends this previous work by examining various aspects of how the reaction, •C60OH + •OH → C60(OH)2 (R1) changes in aqueous solution. One obvious difference between C60 and their various isomers of C60(OH)2 is the presence of a dipole. As fullerendiols are nearly spherical, their change in dipole moment in going from the gas to aqueous phase may be estimated using back-of-the-envelope calculations with the Onsager model. The result is remarkably similar to what is obtained using density functional theory (DFT) with an implicit solvation model (surface molecular density, SMD). Calculation of fullerendiol C-O bond energies and reactivity indices using the SMD approach confirms that the general conclusions from the earlier work regarding gas-phase reactivity still hold in the aqueous phase. A major difference between the present work and the earlier work is the calculation of potential energy curves (PECs) for reaction R1 in the gas and aqueous phases. This is done in exploratory work for all 59 possible fullerendiols in both the gas phase and in aqueous solution with the SMD approach using spin-unrestricted DFT calculations with symmetry breaking. Surprisingly little change is found between the gas- and aqueous-phase PECs. However, it was discovered that the majority of C60(OH)2 shows radicaloid character, as might have been expected from trying to draw resonance structures. Spin-contamination curves are also remarkably similar for gas- and aqueous-phase results. Although our calculations do not include a dispersion correction, it was noticed that all calculated PECs have a 1/R6 behavior over a significant R = R(C-O) distance, underlying the need to be careful of double counting when including dispersion corrections in DFT. A shortcoming of our SMD approach is the lack of explicit water molecules, which can form hydrogen bonds with the OH groups and dissociating radicals.

Ruthenium(II) polypyridine compounds often luminesce, with ligand-dependant lifetimes. This is the third in a series of papers devoted to finding orbital-based luminescence indices (LI) for predicting luminescence lifetimes. The third attempt (LI3) was based upon a frontier molecular orbital (FMO) like estimate of the height of the barrier to conversion from an initial phosophorescent triplet metal-ligand charge transfer (3MLCT) state to a nonluminescent triplet metal-centered (3MC) state which decays nonradiatively. A linear correlation was found between LI3 and extracted empirical average 3MLCT → 3MC transition state (TS) barrier heights (Eaves) which were not believed to be quantitative but which were believed to capture the trends in the true barrier heights correctly. As it is known that Eave is a large underestimate of the true 3MLCT → 3MC TS barrier height in the case of the trisbipyridine ruthenium(II) cation { [Ru(bpy)3]2+ }, but accurate TS barrier heights are difficult to obtain experimentally, it was judged useful to verify the ideas used to derive the LI3 index in the present work by calculating the energetics of the gas-phase 3MLCT → 3MC reaction for a series of ruthenium(II) tris bipyridine complexes using the same density functional and basis sets used in calculating LI3. Specifically, four closely-related bipyridine complexes { [Ru(N∧N)3]2+ with N∧N = bpy (6), 4,4’-dm-bpy (70), 4,4’-dph-bpy (73), and 4,4’-DTB-bpy (74) } were used for these calculations. In the process, we examined the gas-phase trans dissociation mechanism in greater detail than has been previously done and uncovered a two part mechanism. In the first part, the electron is transferred to a single ligand rather than symmetrically to all three ligands. It is the two Ru-N bonds to this ligand which are equally elongated in the transition state. The intrinsic reaction coordinate then continues down a ridge in hyperspace and bifurcates into one of two symmetry-equivalent 3MC structures with elongated trans bonds. Interestingly, no significant difference is found for the TS barriers for the four complexes treated here. Instead, LI3 is linearly correlated with the energy difference ΔE=E(3MLCT)−E(3MC), different from what was originally intended but still consistent with the FMO arguments underlying the derivation of LI3.

Luminescence lifetimes of Ruthenium (II) polypyridine compounds is thought to be controlled by the barrier to conversion of triplet metal-ligand charge transfer ($^{3}$MLCT) state to a non-luminescent triplet metal-centered ($^{3}$MC) state. This work builds on earlier work [J. Photochem. Photobiol. A 276, 8 (2014)] and [J. Photochem. Photobiol. A 348, 305 (2017)] that derived several orbital-based luminescence indices of which the third (LI3) was based upon frontier-molecular-orbital-like ideas and correlated linearly with values of $E_{ave}$. $E_{ave}$ is a large underestimate of the true $^3$MLCT$\rightarrow$ $^3$MC TS barrier height in the case of the tris bipyridine ruthenium(II) cation {[Ru(bpy)$_3]^{2+}$}, but accurate TS barrier heights are difficult to obtain experimentally, it was judged useful to verify the ideas used to derive the LI3 index by calculating the energetics of the gas-phase $^{3}$MLCT $\rightarrow$ $^{3}$MC reaction for four complexes $\{$[Ru(N$^\wedge$N)$_3$]$^{2+}$ with N$^\wedge$N = bpy ({6}), 4,4'-dm-bpy ({70}), 4,4'-dph-bpy ({73}), and 4,4'-DTB-bpy ({74}) $\}$ using the same density functional and basis sets used in calculating LI3. We examine the trans dissociation mechanism in detail at the B3LYP/6-31G+LANLDZ(Ru) level and uncover a two-part mechanism. In the first part, the electron is transferred to a single ligand rather than symmetrically to all three ligands. It is the two Ru-N bonds to this ligand which are equally elongated in the transition state. The intrinsic reaction coordinate then continues down a ridge in hyperspace and bifurcates into one of two symmetry-equivalent $^3$MC structures with elongated trans bonds. Interestingly, no significant difference is found for the TS barriers for the four complexes treated here. Instead, LI3 is linearly correlated with the energy difference $\Delta$ E = E($^{3}$MLCT) - E($^{3}$MC).

Static correlation is a difficult problem for density-functional theory (DFT) as it arises in cases of degenerate or quasi-degenerate states where a multideterminantal wave function provides the simplest reasonable first approximation to the true interacting wave function. This is also where Kohn-Sham DFT may also fail to be noninteracting v-representible (NVR). In contrast, Kohn-Sham DFT typically works well for describing the missing dynamic correlation when a single-determinantal reference wave function provides a good first approximation to the true interacting wave function. Multiplet sum method (MSM) DFT [Theor. Chim. Acta 4, 877 (1977)] provides one of the earliest and simplest ways to include static correlation in DFT. MSM-DFT assumes that DFT provides a good description of single-determant energies and uses symmetry and simple ansatzes to include the effects of static correlation. This is equivalent to determining the off-diagonal matrix elements in a small configuration interaction (CI) eigenvalue problem. We have developed a diagrammatic approach to MS-DFT facilitates comparison with wave function CI and so allows educated guesses of off-diagonal CI matrix elements even in the absence of symmetry. In every case, an additional exchange-only ansatz (EXAN) allows the MSM-DFT formulae to be transformed into wave function formulae. This EXAN also works for transforming time-dependent DFT into time-dependent Hartree-Fock. Although not enough to uniquely guess DFT formulae from wave function formulae, the diagrammatic approach and the EXAN provide important constraints on any guesses that might be used. Some alternative guesses are tried out for problems concerning the ground and excited states of H2 , LiH, and O2 in order to assess how much difference might be involved for different DFT guesses for off-diagonal matrix elements.

As emphasized in a recent review article [Chem. Rev. 122, 14180 (2022)], organic solar cell (OSC) photoconversion efficiency has been rapidly evolving with results increasingly comparable to those of traditional inorganic solar cells. Historically, OSC performance improvement focused first on the morphology of P3HT:PC61BM solar cells then went through different stages to shift lately interest towards nonfullerene acceptors (NFAs) as a replacement of PC61BM acceptor (ACC) molecule. Here, we use density-functional theory (DFT) and time-dependent (TD) DFT to investigate four novel NFAs of A-D-A (acceptor-donor-acceptor) form derived from the recently synthesized IDIC-4Cl [Dyes and Pigments 166, 196 (2019)]. Our level of theory is carefully evaluted for IDIC-4Cl and then applied to the four novel NFAs in order to understand how chemical modifications lead to physical changes in cyclic voltammetry (CV) frontier molecular orbital (FMO) energies and absorption spectra in solution.Finally we design and apply a new type of Scharber plot for NFAs based upon some simple but we think reasonable assumptions. Unlike the original Scharber plots where a larger DON band gap favors a larger PCE, our modified Scharber plot reflects the fact that a smaller ACC band gap may favor PCE by filling in gaps in the DON acceptor spectrum. We predict that only the candidate molecule with the least good acceptor A, with the highest frontier molecular orbital energies, and one of the larger CV lowest unoccupied molecular orbital (LUMO) highest unoccupied molecular orbital (HOMO) gaps, will yield a PM6:ACC PCE exceeding that of the parent IDIC-4Cl ACC. This candidate also shows the largest oscillator strength for the primary 1 (HOMO,LUMO) charge-transfer transition and the largest degree of delocalization of charge transfer of any of the ACC molecules investigated here.

One of us (MEC) developed a hands-on workbook for density-functional theory (DFT) during the summer of 2020. The idea was to have something that could be used to provide practical teaching for students at the Masters or advanced undergraduate level that would be free, could be used on a student's own personal computer, and would complement formal course work. The workbook is also very much intended to encourage students to explore program options, discover theory limitations, puzzle out what to do when the program does not work as expected, and to help students transition to thinking and using quantum chemistry programs as a researcher might do. After describing the structure of the workbook, we describe how the workbook has been used thus far as a teaching tool and as a useful step towards research-level problems.

We study the successive addition reaction of .OH on fullerene C60. We confirm that the lowest energy isomers of C60(OH)n form a belt of hydroxyl groups around the equator of C60, but ask the question of what governs the relative stability of subtitutions at different carbons? Factors concerning regioselectivity are analyzed in terms of conceptual density-functional theory, frontier molecular orbital theory, charge and spin densities, based upon Mulliken population analysis. We confirm that .OH is an electrophilic radical whose successive reaction with C60 is under both charge and orbital control. This is seen to be especially the case for addition to odd .C60(OH)2m+1 fullerenols, but is also seen from a Fukui function and dual descriptor analysis for even C60(OH)2m fullerenols. Of particular interest is the ability of the condensed radical Fukui function f0 to provide information about the reactivity of even C60(OH)2m fullerenols with .OH also when the spin density is zero, and the observation that the interpretation of the sign of the dual descriptor changes depending upon whether a spin-restricted calculation is being performed for even C60(OH)2m fullerenols or a spin-unrestricted calculation is being performed for odd .C60(OH)2m+1 fullerenols.

The energy sciences attempt to meet the increasing world-wide need for energy, as well as sustainability goals, by cleaner sources of energy, by new alternative sources of energy, and by more efficient uses of available energy. These goals are entirely consistent with the principles of green chemistry. This chapter concerns devices for creating electricity from light and for creating light from electricity. The major focus is on the photoproperties of ruthenium and iridium complexes, which have been proven to be a rich source of inspiration for conceiving photoactivated devices, including organic photovoltaic (OPV) cells and organic light emitting diodes (OLEDs). The chapter reviews important already-in-use and potential applications of ruthenium and iridium complex-based photodevices, including the underlying mechanism behind their functioning and its investigation through computational chemistry approaches. It highlights the role of the information obtained from computational studies for the design of more efficient photodevices. The final part complements the discourse with a review of the progress on greener alternatives for OPVs and OLEDs.

The dominant majority of the hundreds of available spin-crossover compounds, including the technologically most promising ones, are based on the Earth-abundant metal iron, making these switches particularly appealing in terms of sustainable technology. Furthermore, it has recently been established that these materials may be synthesized using the techniques of Green Chemistry. Spin crossover in transition metal complexes can be induced by a change of temperature, by the application of an external pressure, or a magnetic field, and also by photoexcitation. Given the wide variety of functionalities to which these bistable photomagnetic systems could give access, they may be viewed as the prototypes of molecular-scale optomagnetic switches. Hence, in response to the growing demand for storing and treating increasingly-dense information, much effort has been devoted over several decades to the design of transition metal materials exhibiting spin crossover in technologically-accessible temperature ranges. The cornerstone for designing new efficient photoactive spin-crossover materials remains the ability to predict the magnetic behaviour and the photoresponse of any first-row transition complex, and the manner in which its properties are influenced by its environment. This is a challenge for the inorganic chemist and also, most notably, for the theoretical and the computational chemist. This chapter gives an overview of the issues tied to the application of DFT and TD-DFT to the characterisation of transition metal complexes in the framework of spin-crossover and related phenomena.

Singlet oxygen ( $$^1$$ O $$_2$$ ) comes in two flavors—namely the dominant lower-energy $$a \,^1\Delta _g$$ state and the higher-energy shorter-lived $$b \,^1\Sigma _g^+$$ state—and plays a key role in many photochemical and photobiological reactions. For this reason, and because of the large size of the systems treated, many papers have appeared with density-functional theory (DFT) treatments of the reactions of $$^1$$ O $$_2$$ with different chemical species. The present work serves as a reminder that the common assumption that it is enough to fix the spin multiplicity as unity is not enough to insure a correct treatment of singlet oxygen. We review the correct group theoretical treatment of the three lowest energy electronic states of O $$_2$$ which, in the case of $$^1$$ O $$_2$$ is often so badly explained in the relevant photochemical literature that the explanation borders on being incorrect and prevents, rather than encourages, a correct treatment of this interesting and important photochemical species. We then show how many electronic structure programs, such as a freely downloadable and personal-computer compatible Linux version of deMon2k, may be used, together with the multiplet sum method (MSM), to obtain a more accurate estimation of the potential energy curves (PECs) of the two $$^1$$ O $$_2$$ states. Applications of the MSM DFT method to $$^1$$ O $$_2$$ appear to be extremely rare as we were only able to find one correct application of the DFT MSM (or rather a very similar approach) to $$^1$$ O $$_2$$ in our literature search. Here we treat both the $$a \,^1\Delta _g$$ and $$b \,^1\Sigma _g^+$$ state with a wide variety of density-functional approximations (DFAs). Various strengths and weaknesses of different DFAs emerge through our application of the MSM method. In particular, the quality of the $$a \,^1\Delta _g$$ excitation energy reflects how well functionals are able to describe the spin-flip energy in DFT while the quality of the $$b \,^1\Sigma _g^+$$ excitation energy reflects how well functionals are able to describe the spin-pairing energy in DFT. Finally, we note that improvements in DFT-based excited-state methods will be needed to describe the full PECs of $$^1$$ O $$_2$$ including both the equilibrium bond lengths and dissociation behavior.

Atomistic modeling of energy and charge transfer at the heterojunction of organic solar cells is an active field with many remaining outstanding questions owing, in part, to the difficulties in performing reliable photodynamics calculations on very large systems. One approach to being able to overcome these difficulties is to design and apply an appropriate simplified method. Density-functional tight binding (DFTB) has become a popular form of approximate density-functional theory based on a minimal valence basis set and neglect of all but two center integrals. We report the results of our tests of a recent long-range correction (lc) [A. Humeniuk and R. Mitrić, J. Chem. Phys. 143, 134120 (2015)] for time-dependent (TD) lc-DFTB by carrying out TD-lc-DFTB fewest switches surface hopping calculations of energy and charge transfer times using the relatively new DFTBABY [A. Humeniuk and R. Mitrić, Comput. Phys. Commun. 221, 174 (2017)] program. An advantage of this method is the ability to run enough trajectories to get meaningful ensemble averages. Our interest in the present work is less in determining exact energy and charge transfer rates than in understanding how the results of these calculations vary with the value of the range-separation parameter (Rlc = 1/μ) for a model organic solar cell heterojunction consisting of a gas-phase van der Waals complex P/F made up of a single pentacene (P) molecule together with a single buckminsterfullerene (F) molecule. The default value of Rlc = 3.03 a0 is found to be much too small as neither energy nor charge transfer is observed until Rlc ≈ 10 a0. Tests at a single geometry show that the best agreement with high-quality ab initio spectra is obtained in the limit of no lc (i.e., very large Rlc). A plot of energy and charge transfer rates as a function of Rlc is provided, which suggests that a value of Rlc ≈ 15 a0 yields the typical literature (condensed-phase) charge transfer time of about 100 fs. However, energy and charge transfer times become as high as ∼300 fs for Rlc ≈ 25 a0. A closer examination of the charge transfer process P*/F → P+/F- shows that the initial electron transfer is accompanied by a partial delocalization of the P hole onto F, which then relocalizes back onto P, consistent with a polaron-like picture in which the nuclei relax to stabilize the resultant redistribution of charges.

In this work, we focus on designing a donor copolymer for the improvement of photovoltaic performance. Using density functional theory and time-dependent density functional theory, we investigated the electronic, optical and charge transfer properties of a series of new designed copolymers based on the reported copolymer Pa0 which is composed of a donor fluorene unit and an acceptor 4,7-dithien-2-yl-2,1,3-benzothiadiazole. We first obtained two copolymers Pb0 and Pc0 by replacing the benzothiadiazole (BTZ) with two different strong acceptors units to decrease the LUMO level of conjugated polymers. Then, we designed Pa1, Pb1 and Pc1 copolymers by adding a substituent methyl group to the thiophene spacer unit (T). Bulk-heterojunction photovoltaic cells were designed with the copolymers as the donors and PCBM as the acceptor. Our results show that the cells based on Pb1 and Pc1 have a suitable electronic structure with energy conversion efficiency exceeding 10%. Moreover, we used Marcus theory to evaluate the intermolecular charge transfer (inter-CT) and recombination (inter-CR) rates of these cells (copolymer/PCBM). The ratio Kinter-CT/Kinter-CR of Pc1/PCBM heterojunction is about 106 times higher than that of Pb1/PCBM which clearly reveals that the designed donor molecule Pc1 will be a promising candidate for high performance organic photovoltaic devices. Our strategy to design novel donor copolymers provides a theoretical guideline for further improving in electrical, optical properties and the efficiency of the photovoltaic device.

Tully-type mixed time-dependent long-range corrected density-functional tight-binding/classical surface-hopping photodynamics is used to investigate the nature of and time scales for energy and charge transfer in the simplest model of an organic photovoltaic heterojunction, namely a single molecule of buckminsterfullerene (C60) together with a single molecule of pentacene. The distinction between energy and charge transfer is more difficult to make in practical calculations than might at first seem to be the case, but several criteria are used to make a clear distinction between these two phenomena. It is found that the excitation fluctuates from one molecule to the other, with the first change within about 20 fs. However it is only after 188(+/-28) fs that real charge transfer occurs. This is commensurate with what is known from experiment and very different from the severe underestimate obtained when the same calculation is repeated without a long-range correction. The long-range charge separation is not feasible to simulate in this model due to lack off appropriate charge collection sinks. We believe that these encouraging results obtained with time-dependent long-range corrected density-functional tight-binding/classical surface-hopping photodynamics opens the way, because of their intrinsic computational efficiency compared with time-dependent long-range corrected density-functional theory/classical surface-hopping photodynamics, to investigating a larger variety of increasingly realistic model organic photovoltaic heterojunctions.

Exciton formation leads to J-bands in solid pentacene. Describing these exciton bands represents a challenge for both time-dependent (TD) density-functional theory (DFT) and for its semi-empirical analog, namely, for TD density-functional tight binding (DFTB) for three reasons: (i) solid pentacene and pentacene aggregates are bound only by van der Waals forces which are notoriously difficult to describe with DFT and DFTB, (ii) the proper description of the long-range coupling between molecules, needed to describe Davydov splitting, is not easy to include in TD-DFT with traditional functionals and in TD-DFTB, and (iii) mixing may occur between local and charge transfer excitons, which may, in turn, require special functionals. We assess how far TD-DFTB has progressed toward a correct description of this type of exciton by including both a dispersion correction for the ground state and a range-separated hybrid functional for the excited state and comparing the results against corresponding TD-CAM-B3LYP/CAM-B3LYP+D3 results. Analytic results for parallel-stacked ethylene are derived which go beyond Kasha's exciton model [M. Kasha, H. R. Rawls, and A. El-Bayoumi, Pure Appl. Chem. 11, 371 (1965)] in that we are able to make a clear distinction between charge transfer and energy transfer excitons. This is further confirmed when it is shown that range-separated hybrids have a markedly greater effect on charge-transfer excitons than on energy-transfer excitons in the case of parallel-stacked pentacenes. TD-DFT calculations with the CAM-B3LYP functional and TD-lc-DFT calculations lead to negligible excitonic corrections for the herringbone crystal structure, possibly because of an overcorrection of charge-transfer effects (CAM refers to Coulomb attenuated method). In this case, TD-DFT calculations with the B3LYP functional or TD-DFTB calculations parameterized to B3LYP give the best results for excitonic corrections for the herringbone crystal structure as judged from comparison with experimental spectra and with Bethe-Salpeter equation calculations from the literature.

In search of novel high-performance materials for use in organic solar cells, we used density-functional theory and time-dependent density functional theory to design a series of organic small molecules derived from the recently synthesized BT(-2T-DCV-Hex)2 donor molecule. In this work, we replaced the BT unit by different acceptors in order to improve their electronic properties, optical absorption and performance in organic solar cell applications. We found that the hybrid functional B3PW91 with the 6-31G(d) basis set gave highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy levels of the BT(-2T-DCV-Hex)2 in better agreement with the experimental oxidation and reduction potentials. However, the range-separated hybrid functional WB97XD was the most appropriate functional for describing the maximum absorption wavelength. Our calculation indicate that the designed small molecules donor proposed here are expected to offer better performances compared to the BT(-2T-DCV-Hex)2, such as a lower HOMO energy, a narrower HOMO-LUMO energy gap, a larger absorption range and may lead to power conversion efficiencies reaching the (7–9)% range.

Experimental measurement on oligomeric 4-(methoxyphenyl)acetonitrile (OMPA) synthesized via an electrochemical method indicated that the average chain length for OMPA was around 5 units (5-MPA) [J Mol Struct 1031:186 (2013)], but did not provide enough information to completely characterize the chemical structure of the molecule. Nevertheless a possible structure was proposed on the basis of 13C NMR and the spin density hypothesis for radical polymerization. A more complete validation of the resultant structure is needed to show the extent to which the structure is consistent with a variety of measured properties. This is done here for the infrared (IR), ultraviolet–visible (UV–vis), and photoluminescence (PL) spectra of 5-MPA which are found to agree reasonably well with the experimentally measured spectra of OMPA. Electronic structure information regarding the highest-occupied molecular orbital (HOMO) and the lowest-unoccupied molecular orbital (LUMO) energies, ionization potentials and electron affinities, as well as optical properties (UV–vis, PL) is also provided.

Novel low-band-gap copolymer oligomers are proposed on the basis of density functional theory (DFT) quantum chemical calculations of photophysical properties. These molecules have an electron donor-accepter (D-A) architecture involving poly(3-hexylthiophene-2,5-diyl) (P3HT) as D units and furan, aniline, or hydroquinone as A units. Structural parameters, electronic properties, highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gaps and molecular orbital densities are predicted. The charge transfer process between the D unit and the A unit one is supported by analyzing the optical absorption spectra of the compounds and the localization of the HOMO and LUMO.

Excited states are often treated within the context of time-dependent (TD) density-functional theory (DFT), making it important to be able to assign the excited spin-state symmetry. While there is universal agreement on how Δ〈Sˆ2〉, the difference between 〈Sˆ2〉 for ground and excited states, should be calculated in a wave-function-like formalism such as the Tamm–Dancoff approximation (TDA), confusion persists as to how to determine the spin-state symmetry of excited states in TD-DFT. We try to clarify the origins of this confusion by examining various possibilities for the parameters (σ1,σ2) in the formula Δ〈Sˆ2〉=[Δ〈SˆTDA2〉(X→)+Δ〈SˆTDA2〉(Y→∗)+σ1Δ〈Sˆmixed2〉(X→,Y→∗)]/(X→†X→+σ2Y→†Y→), where X→ is the particle–hole part and Y→ is the hole–particle part of the response theory vector. A first principles derivation leads directly to (σ1,σ2)=(+1,−1) which we argue is the best simple formula linking spin with energy, albeit approximately. On the other hand, if the desire is to recover wave-function-like values of Δ〈Sˆ2〉, then we argue that the choice (σ1,σ2)=(+1,+1) should be made. Additional examples are offered to justify that the choice of σ1=0 should also be made when seeking wave-function-like values of Δ〈Sˆ2〉.