The time-dependent coupled perturbed Hartree–Fock/density-functional-theory (TDHF/TDDFT) approach has been reformulated based on nonorthogonal localized molecular orbitals (NOLMOs). Based on the NOLMO Fock equation, we have derived the corresponding NOLMO-TDHF/TDDFT equations up to the third order, and the formula for the frequency-dependent (hyper)polarizabilities has been given. Our approach has been applied to calculate both static and dynamic (hyper)polarizabilities of molecules varying from small molecules to large molecules. The NOLMO-TDHF/TDDFT approach can reproduce the reference canonical molecular orbital (CMO) results for all of our testing calculations. With the help of ongoing development of optimized local virtual molecular orbitals, the NOLMO-TDHF/TDDFT approach would be a very efficient method for large system calculations and tp achieve linear scaling.

Focusing on the interesting new concept of all-metal electride, centrosymmetric molecules e–+M2+(Ni@Pb12)2–M2++e– (M = Be, Mg, and Ca) with two anionic excess electrons located at the opposite ends of the molecule are obtained theoretically. These novel molecular all-metal electrides can act as infrared (IR) nonlinear optical (NLO) switches. Whereas the external electric field (F) hardly changes the molecular structure of the all-metal electrides, it seriously deforms their excess electron orbitals and average static first hyperpolarizabilities (β0e(F)). For e–+Ca2+(Ni@Pb12)2–Ca2++e–, a small external electric field F = 8 × 10–4 au (0.04 V/Å) drives a long-range excess electron transfer from one end of the molecule through the middle all-metal anion cage (Ni@Pb12)2– to the other end. This long-range electron transfer is shown by a prominent change of excess electron orbital from double lobes to single lobe, which forms an excess electron lone pair and electronic structure Ca2+(Ni@Pb12)2–Ca2++2e–. Therefore, the small external electric field induces a dramatic β0e(F) contrast from 0 (off form) to 2.2 × 106 au (on form) in all-metal electride molecule Ca(Ni@Pb12)Ca. Obviously, such switching is high sensitive. Interestingly, in the switching process, such long-range excess electron transfer does not alter the valence and chemical bond nature. Then, this switching mechanism is a distinct nonbonding evolution named electronic structure isomerization, which means that such switching has the advantages of being fast and reversible. Besides, these all-metal electride molecules also have a rare IR transparent characteristic (1.5–10 μm) in NLO electride molecules, and hence are commendable molecular IR NLO switches. Therefore, this work opens a new research field of electric field manipulated IR NLO switches of molecular all-metal electrides.

Quantum chemistry calculations at the level of (TD)-DFT plus PCM solvent models are employed for analyzing potential energy surfaces and as a result two local minima with D2, two local minima with C2H, and one second-order transition state with D2H group symmetry are found in both ground S0 and excited-state S1 potential energy surfaces. Simulated vibronic coupling distributions indicate that only second-order transition states with D2H group symmetry are responsible for observed absorption and fluorescence spectra of rubrene and vibrational normal-motions related with atoms on the aromatic backbone are active for vibronic spectra. The Stokes shift 1120 cm−1 (820 cm−1) and vibronic-band peak positions in both absorption and fluorescence spectra in non-polar benzene (polar cyclohexane) solvent are well reproduced within the conventional Franck–Condon simulation. By adding damped oscillator correction to Franck–Condon simulation, solvent enhanced vibronic-band intensities and shapes are well reproduced. Four (three) normal modes with vibration frequency around 1550 cm−1 (1350 cm−1) related to ring wagging plus CC stretching and CH bend motions on the backbone are actually interpreted for solvent enhanced absorption (fluorescence) spectra of rubrene in benzene and cyclohexane solutions.

Density functional theory calculations are employed to study the mechanism of photoselective catalytic reduction of 4-bromobenzaldehyde (4-BBA) in acetonitrile and in ethanol solvents. A totally relaxed Ti3O9H6 cluster model is proposed to represent titanium dioxide (TiO2) surfaces. The reduction selectivity of an adsorbed 4-BBA molecule on Ti3O9H6 has been investigated. Owing to the difference in the proton and H atom donating capabilities between explicit CH3CN and C2H5OH solvent molecules, the photocatalytic reduction of 4-BBA is the debromination process in acetonitrile, whereas in ethanol it is the carbonyl reduction process. Therefore 4-BBA can be selectively reduced to benzaldehyde in acetonitrile and 4-bromobenzyl alcohol in ethanol, respectively. Our computational results have verified the reaction mechanism proposed by experiments and show that the debromination of 4-BBA would be efficient if both 4-BBA and Ti3O9H6 have an extra photoelectron. The Ti3O9H6 cluster, playing a role as a hydrogen source and a bridge to transfer photoelectrons from bulk TiO2, would have potential to be an ideal molecular model for understanding photocatalytic reactions on the TiO2 surface.

Theoretically designed alkali-doped aziridine M–(C2NH5)n (M = Li, Na and K; n = 1, 2, 3, and 4) are investigated by density functional theory (DFT) and time-dependent TD-DFT. The interaction energies at optimized electronic structures indicate that alkali-doped aziridine are quite stable. The natural population analysis of charges on alkali atoms show that all positive and electronic transitions to LUMO orbitals are large, so that the designed compounds not only have electride features, but also have large flexible ligands. This leads to a high-performance nonlinear optical response (NLO) and this remarkable NLO response mainly comes from alkali atoms. By calculating the first hyperpolarizabilities for M–(C2NH5)4 with M@Calix[4]pyrrole for comparison, we demonstrate that enhancements of the NLO response of M–(C2NH5)4 are 10 to 100 times larger than those of M@Calix[4]pyrrole, and in particular, the largest first hyperpolarizability values of Na–(C2NH5)4 is up to 3.4 × 106 (a.u.).

We exhibit theoretically a series of 12-valence-electron pentaatomic species CLi3E (E = N, P, As, Sb, Bi) and CLi3E+ (E = O, S, Se, Te, Po). The analyses of potential energy surfaces indicate that the C2v structures with a planar tetracoordinate carbon are the global minimum in these species except for E = N, P. A localized CE double bond is found in the planar tetracoordinate carbon species. The molecular orbitals and the valence populations reveal that the CE double bonds in CLi3E are different from those in CLi3E+. The thermodynamic and kinetic calculations show that some of the planar tetracoordinate carbon species are stable and are likely to exist in the gas phase.

Coupled-perturbed self-consistent-field (CPSCF) approach has been broadly used for polarizabilities and hyperpolarizabilities computation. To extend this application to large systems, we have reformulated the CPSCF equations with nonorthogonal localized molecular orbitals (NOLMOs). NOLMOs are the most localized representation of electronic degrees of freedom. Methods based on NOLMOs are potentially ideal for investigating large systems. In atomic orbital representation, with a static external electric field added, the wave function and SCF operator of unperturbed NOLMO-SCF wave function/orbitals are expanded to different orders of perturbations. We have derived the corresponding equations up to the third order, which are significantly different from those of a conventional CPSCF method because of the release of the orthogonal restrictions on MOs. The solution to these equations has been implemented. Several chemical systems are used to verify our method. This work represents the first step toward efficient calculations of molecular response and excitation properties with NOLMOs.

The density functional theory (M06-2X) method has been employed to investigate the selective photoreduction mechanism in ethanol and acetonitrile solvents for 4-bromobenzaldehyde (4-BBA) reduced by photoelectrons, which are produced by illumination of TiO2. The solvent effects of ethanol and acetonitrile are considered by the SMD solvent model. The computational results show that the reaction is selective in different solvents. In ethanol solvent, the carbonyl reduction process is favored both in thermodynamics and kinetics, and 4-BBA could be reduced to the product, 4-bromobenzyl alcohol. However, owing to it not being a good proton donor solvent, the debromination reduction process in acetonitrile is favored. These results are consistent with the experimental observations.

A series of singlet and triplet wheel-type clusters obtained through an electronic method, i.e., adding two and four electrons into X©BnHnm [(X, m) = (B, +1), (C, +2) for n = 5; (X, m) = (Be, 0), (B, +1) for n = 6], have been studied theoretically. With the increase of the number of electrons, the sizes of peripheral boron rings tend to decrease due to the increase of negative charges on the boron rings. The results of the kinetic stability and the electronic stability suggest that the triplet C©B5H5 and singlet Be©B6H6 are stable and may be detected experimentally. Nucleus-independent chemical shift and molecular orbital analysis reveal that some wheel-type clusters with the planar ring possess aromaticity properties that are attributed to the delocalized π electrons conforming to the Huckel rule, i.e. 4n + 2 for singlets or 4n for triplets. These findings from this work are significant for designing novel wheel-type clusters.

Modulation of intermolecular interactions in response to external electric fields could be fundamental to the formation of unusual forms of water, such as water whiskers. However, a detailed understanding of the nature of intermolecular interactions in such systems is lacking. In this paper, we present novel theoretical results based on electron correlation calculations regarding the nature of H-bonds in water whiskers, which is revealed by studying their evolution under external electric fields with various field strengths. We find that the water whiskers consisting of 2–7 water molecules all have a chain-length dependent critical electric field. Under the critical electric field, the most compact chain structures are obtained, featuring very strong H-bonds, herein referred to as covalent H-bonds. In the case of a water dimer whisker, the bond length of the novel covalent H-bond shortens by 25%, the covalent bond order increases by 9 times, and accordingly the H-bond energy is strengthened by 5 times compared to the normal H-bond in a (H2O)2 cluster. Below the critical electric field, it is observed that, with increasing field strength, H-bonding orbitals display gradual evolutions in the orbital energy, orbital ordering, and orbital nature (i.e., from typical π-style orbital to unusual σ-style double H-bonding orbital). We also show that, beyond the critical electric field, a single water whisker may disintegrate to form a loosely bound zwitterionic chain due to a relay-style proton transfer, whereas two water whiskers may undergo intermolecular cross-linking to form a quasi-two-dimensional water network. Overall, these results help shed new insight on the effects of electric fields on water whisker formation.

The non-orthogonal localized molecular orbital (NOLMO) is the most localized representation of electronic degrees of freedom. As such, NOLMOs are thus potentially the most efficient for linear-scaling calculations of electronic structures for large systems. However, direct ab initio calculations with NOLMO have not been fully implemented and widely used, partly because of the slow convergence issue in the optimization of NOLMO. Towards realizing the potential of NOLMO for large systems, we applied an energy minimum variational principle for carrying out ab initio self-consistent-field (SCF) calculations with NOLMOs. We developed an effective preconditioning approach using the diagonal part of the second order derivatives and show that the convergence of the energy optimization is significantly improved. The speed of convergence of the energy and density are comparable with that of the conventional SCF approach, thus paving the way for the optimization of NOLMO in linear scaling calculations for large systems.

Oxazolidinones can be synthesized through an organocatalytic cascade reaction of stable sulfur ylides and nitro-olefins. This process, sequentially catalyzed by thiourea and N,N-dimethylaminopyridine (DMAP), is theoretically studied using density functional theory by the continuum solvation model. It is shown that the rate- and stereoselectivity-determining step is the addition reaction of sulfur ylide to the nitro-olefin with two competing reaction channels. One channel is where the nitro-cyclopropane is generated first and then converted into isoxazoline N-oxide through a DMAP-catalyzed rearrangement. The other channel is the direct generation of the isoxazoline N-oxide intermediate. DMAP plays an important role in the reaction as a nucleophilic catalyst. The mechanism for the important rearrangement reaction proposed by Xiao et al. (J. Am. Chem. Soc. 2008, 130, 6946–6948) is not appropriate as the reaction energy barrier is too high; a 10-step mechanism determined by our theoretical calculations is more feasible as the energy barrier is becoming much less than that by Xiao. It is the first time that the Hofmann rearrangement involved in the cascade organocatalysis is confirmed by theoretical calculations. Our result of the stereoselectivity for the synthesis of oxazolidinones is in good agreement with the experiment.

The elongation method, proposed in the early 1990s, originally for theoretical synthesis of aperiodic polymers, has been reviewed. The details of derivation of the localization scheme adopted by the elongation method are described along with the elongation processes. The reliability and efficiency of the elongation method have been proven by applying it to various models of bio-systems, such as gramicidin A, collagen, DNA, etc. By means of orbital shift, the elongation method has been successfully applied to delocalized π-conjugated systems. The so-called orbital shift works in such a way that during the elongation process, some strongly delocalized frozen orbitals are assigned as active orbitals and joined with the interaction of the attacking monomer. By this treatment, it has been demonstrated that the total energies and non-linear optical properties determined by the elongation method are more accurate even for bio-systems and delocalized systems like fused porphyrin wires. The elongation method has been further developed for treating any three-dimensional (3D) systems and its applicability is confirmed by applying it to entangled insulin models whose terminal is capped by both neutral and zwitterionic sequences.

The detailed potential energy surfaces (PESs) of poorly understood ion–molecule reactions of CH3O– with O2(X3Σg–) and O2(a1Δg) are accounted for by the density functional theory and ab initio of QCISD and CCSD(T) (single-point) theoretical levels with 6-311++G(d,p) and 6-311++G(3df,2pd) basis sets for the first time. For the reaction of CH3O– with O2(X3Σg–) (3R), it is shown that a hydrogen-bonded complex 31 is initially formed on the triplet PES, which is 1.8 kcal/mol above reactants 3R at the CCSD(T)//QCISD level, from which all the products P1–P8 can be generated. As to the reaction of CH3O– with O2(a1Δg) (1R), it is found that the two energetically low-lying complexes of 11(−31.5 kcal/mol) and 12(−24.1 kcal/mol) are initiated on the singlet PES. Starting from them, a total of seven products may be possible, that is, besides P1, P2, P3, P4, and P8, which are the same as on the triplet PES, there exist also another two products, P9 and P10. For both reactions, taking the thermodynamics and kinetics into consideration, the hydride-transfer species P1(CH2O + HO2–) should be the most favorable product followed by P8(e + CH2O + HO2), which is a secondary product of electron-detachment from P1, and the generation of endothermic P7(17.7 kcal/mol) for the reaction of CH3O– with O2(X3Σg–) is also possible at high temperature, whereas the remaining products are negligible. The measured branching ratio of products for CH3O– with O2(X3Σg–) by Midey et al. is 0.85:0.15 for P1 and P8, and that of CH3O– with O2(a1Δg) is 0.52:0.48 with more P8, which can be rationalized by our theoretical results that P8 on the triplet PES is 4.9 kcal/mol above 3R, whereas both P1 and P8 on the singlet PES are very low-lying at 45.6 and 25.2 kcal/mol below 1R energetically. The measured total reaction rate constant of CH3O– with O2(a1Δg) is k = 6.9 × 10–10 cm3 s–1 at 300 K, which is larger than that of k = 1.1 × 10–12 cm3 s–1 for the reaction of CH3O– with O2(X3Σg–). This is understandable because both P1 and P8 on the singlet PES can be generated barrierlessly, whereas to give all the products on the triplet PES has to pass the barrier of 31(1.8 kcal/mol) at the CCSD(T)//QCISD level. It is expected that the present theoretical study may be helpful for understanding the reaction mechanisms related to CH3O– and even CH3S–.

The elongation method, developed in our groups, is an ab initio method approaching order O(N) type scalability with high efficiency and high accuracy (error <10−8 au/atom in total energy compared to the conventional calculation) that can be applied to any one-dimensional (polymer), two-dimensional (surface) or three-dimensional (solid material) systems. For strongly delocalized systems, however, the accuracy of the original elongation method for the targeted entire systems declines by approximately two orders of magnitude in the total energy as compared to the value obtained by the earlier implemented version of the elongation method for nondelocalized systems. The relatively small differences (10−6–10−8 au) between the elongation method and conventional method total energies have caused more serious errors in the second hyperpolarizability, γ, especially in nano-scale systems which have accompanying strong delocalization. In order to solve this problem, we have incorporated a simple correction technique based on an additional “orbital basis” to the “region basis” in our original elongation method procedures. Some not so-well-localized orbitals are incorporated into the interaction with the attacking molecule. This treatment has been applied to some model nano- and bio-systems that previously have shown strong delocalization, and the high accuracy in the energy obtained for nonstrongly delocalized systems was retained even for the strongly delocalized systems, both for the energies and for the second hyperpolarizabilities. This is a major breakthrough and now expands the systems for which the elongation method can be used to calculate and predict second-order nonlinear optical properties for delocalized systems.

An ab initio study of the effect on nonlinear optical (NLO) properties of medium-size polymethineimine (PMI) chains caused by doping with an alkali metal atom along the backbone is presented. Both the electronic and (preliminary) vibrational static first hyperpolarizabilities are investigated. Doping leads to the injection of an excess electron into the PMI chain, which is accompanied by major enhancement of its NLO response. Along with the hyperpolarizability, other electronic and structural properties depend strongly upon the position of doping along the chain. The vibrational contribution is larger than the corresponding electronic one for most of the cases studied.

Möbius container molecules C64H8, C60N4H4, and C58N6H2 with topological one-sided characteristics were constructed at the first time by imitating natural trumpet shells. The structure is an open cage with an inner hexagonal bridge. The bridge joints the outer and inner surfaces of the cage to form a new one-sided Möbius structure. The optimized structures of the three molecules in the singlet (the ground state), triplet and quintet states are obtained using the density functional theory (B3LYP). For the ground state structures of the three Möbius molecules, their oxidizabilities are weaker than that of the C60 and reducibilities are close to that of the stable C80 cage and slightly stronger than that of the C60. These may show that the unusual Möbius structures have some stability. Their potential properties were predicted, for example, the special aromaticity of the bridge ring due to the unique interaction between the bridge and the cage wall. These findings enlarge the knowledge of Möbius molecules. The idea of bionic and topological imitating in chemistry may promote the design of new complex-shaped nano-molecules and molecular devices.

To realize the chemistry of a multicage organic molecule with excess electron, as a model, by confining an excess electron inside a double-cage single molecule, the structures of e−@C24F22(NH)2C20F18 (e−@AB) and e−@C20F18(NH)2C20F18 (e−@BB′) are obtained at the B3LYP/6-31G(d) + 4s4p theory level. It is confirmed that the excess electron is mainly confined inside one cage with larger interior electronic attractive potential (A for e−@AB and B for e−@BB′) in the ground state, while the electron is localized in the other one in the first excited state. Owing to such excess electron localizations, an interesting intercage excess electron transfer transition takes places. This intercage excess electron transfer transition exhibits five characteristics: (1) the excess electron transfer from one cage to another (A → B for e−@AB and B → B′ for e−@BB′); (2) the transition is between the ground and first excited state; (3) the wavelength and strength are the largest; (4) the transition accompanies a significant charge transfer (Δq > 0.8) and molecular dipole moment change (Δμ > 20 D); (5) the transition corresponds to SOMO → LUMO. For the transition, the oscillator strength is larger and the wavelength is shorter for the asymmetric structure (e−@AB) than for the symmetric one (e−@BB′), which indicates that the intercage excess electron transfer transition may be regulated by changing the size of cage. This work is useful for the designs of organic electronic sponges (porous organic electrides), organic conductor with excess electrons, and photoelectric and nanoelectronic devices.

The density functional theory (M06-2X) method has been employed to investigate the selective photoreduction mechanism in ethanol and acetonitrile solvents for 4-bromobenzaldehyde (4-BBA) reduced by photoelectrons, which are produced by illumination of TiO2. The solvent effects of ethanol and acetonitrile are considered by the SMD solvent model. The computational results show that the reaction is selective in different solvents. In ethanol solvent, the carbonyl reduction process is favored both in thermodynamics and kinetics, and 4-BBA could be reduced to the product, 4-bromobenzyl alcohol. However, owing to it not being a good proton donor solvent, the debromination reduction process in acetonitrile is favored. These results are consistent with the experimental observations.

We exhibit theoretically a series of 12-valence-electron pentaatomic species CLi3E (E = N, P, As, Sb, Bi) and CLi3E+ (E = O, S, Se, Te, Po). The analyses of potential energy surfaces indicate that the C2v structures with a planar tetracoordinate carbon are the global minimum in these species except for E = N, P. A localized CE double bond is found in the planar tetracoordinate carbon species. The molecular orbitals and the valence populations reveal that the CE double bonds in CLi3E are different from those in CLi3E+. The thermodynamic and kinetic calculations show that some of the planar tetracoordinate carbon species are stable and are likely to exist in the gas phase.

The non-orthogonal localized molecular orbital (NOLMO) is the most localized representation of electronic degrees of freedom. As such, NOLMOs are thus potentially the most efficient for linear-scaling calculations of electronic structures for large systems. However, direct ab initio calculations with NOLMO have not been fully implemented and widely used, partly because of the slow convergence issue in the optimization of NOLMO. Towards realizing the potential of NOLMO for large systems, we applied an energy minimum variational principle for carrying out ab initio self-consistent-field (SCF) calculations with NOLMOs. We developed an effective preconditioning approach using the diagonal part of the second order derivatives and show that the convergence of the energy optimization is significantly improved. The speed of convergence of the energy and density are comparable with that of the conventional SCF approach, thus paving the way for the optimization of NOLMO in linear scaling calculations for large systems.

The elongation method, proposed in the early 1990s, originally for theoretical synthesis of aperiodic polymers, has been reviewed. The details of derivation of the localization scheme adopted by the elongation method are described along with the elongation processes. The reliability and efficiency of the elongation method have been proven by applying it to various models of bio-systems, such as gramicidin A, collagen, DNA, etc. By means of orbital shift, the elongation method has been successfully applied to delocalized π-conjugated systems. The so-called orbital shift works in such a way that during the elongation process, some strongly delocalized frozen orbitals are assigned as active orbitals and joined with the interaction of the attacking monomer. By this treatment, it has been demonstrated that the total energies and non-linear optical properties determined by the elongation method are more accurate even for bio-systems and delocalized systems like fused porphyrin wires. The elongation method has been further developed for treating any three-dimensional (3D) systems and its applicability is confirmed by applying it to entangled insulin models whose terminal is capped by both neutral and zwitterionic sequences.