Feng Long Gu

A new localization scheme for the elongation method

A different localization scheme for the elongation method is developed based on regional molecular orbitals. This scheme is more efficient and more accurate than the previous one especially for covalently bonded systems with strongly delocalized pi electrons. Ab initio test calculations have been performed on three model systems: water chains, polyglycine, and cationic cyanine chains. The dependence on the size of the starting clusters and the effect of the basis set are investigated. Our results are compared with conventional ab initio calculations and it is found in all cases that the error per added unit levels off to a satisfactorily small value as long as the starting cluster is sufficiently large.

Coupled-perturbed Hartree–Fock theory for infinite periodic systems: Calculation of static electric properties of (LiH)n, (FH)n, (H2O)n, (–CNH–)n, and (–CH=CH–)n

Previously we have shown how to obtain the electric properties of a polymer or other periodic system at the coupled Hartree–Fock level by direct, analytical calculation rather than by extrapolation of oligomer results. Here we add computationally simpler noniterative formulas and test the methodology for the longitudinal dipole moment (μ), polarizability (α), first hyperpolarizability (β), and second hyperpolarizability (γ) of five quasilinear polymers: (LiH)n, (FH)n, (H2O)n, trans-polymethineimine (–CNH–)n, and trans-polyacetylene (–CH=CH–)n. The polymer values are in good agreement with large-oligomer calculations. In this connection the role of phase factors, particularly in determining the dipole moment, is elucidated. We are now in a good position to include electron correlation using methods analogous to those employed for molecular systems.

Lithium Salt Electride with an Excess Electron Pair—A Class of Nonlinear Optical Molecules for Extraordinary First Hyperpolarizability

A new lithium salt electride with an excess electron pair is designed, for the first time, by means of doping two sodium atoms into the lithium salt of pyridazine. For this series of electride molecules, the structures with all real frequencies and the static first hyperpolarizability (beta 0) are obtained at the second-order Møller-Plesset theory (MP2). Pyridazine H 4C 4N 2 becomes the lithium salt of pyridazine Li-H 3C 4N 2 as one H atom is substituted by Li. The lithium salt effect on hyperpolarizability is observed as the beta 0 value is increased by about 170 times from 5 to 859 au. For the electride effect, an electride H 4C 4N 2...Na 2 formed by doping two Na atoms into pyridazine, the beta 0 value is increased by about 3000 times from 5 to 1.5 x 10 (4) au. Furthermore, combining these two effects, that is, lithium salt effect and electride effect, more significant increase in beta 0 is expected. A new lithium salt electride Li-H 3C 4N 2...Na 2 is thus designed by doping two Na atoms into Li-H 3C 4N 2. It is found that the new lithium salt electride, Li-H 3C 4N 2...Na 2, has a very large beta 0 value (1.412 x 10 (6) au). The beta 0 value is 2.8 x 10 (5) times larger than that of H 4C 4N 2, 1644 times larger than that of Li-H 3C 4N 2, and still 93 times larger than that of the electride H 4C 4N 2...Na 2. This extraordinary beta 0 value is a new record and comes from its small transition energy and large difference in the dipole moments between the ground state and the excited state. The frequency-dependent beta is also obtained, and it shows almost the same trends as H 4C 4N 2 << Li-H 3C 4N 2 << H 4C 4N 2...Na 2 << Li-H 3C 4N 2...Na 2. This work proposes a new idea to design potential candidate molecules with high-performance NLO properties.

An elongation method for large systems toward bio-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.

The nitrogen edge‐doped effect on the static first hyperpolarizability of the supershort single‐walled carbon nanotube

The nitrogen edge‐doped effect on the structure, dipole moment, and first hyperpolarizability of the supershort single‐walled carbon nanotube (5, 0) has been studied systematically. For the nitrogen edge‐doped effect on the structure, the mean diameter on the nitrogen‐doped side (Du) decreases as the number of doped‐nitrogen (n) increases (4.044 (1) > 3.991 (2) > 3.941 (3) > 3.891 (4) > 3.844 Å (5)). Significantly, the nitrogen edge‐doped effects on the dipole moment and first hyperpolarizability are revealed for the first time and these new effects are dramatic for the supershort single‐walled carbon nanotube (5, 0). Among the β0 values of these seven nitrogen‐doped structures, the largest β0 (3155 au) is larger by almost 450 times than the very small β0 (7 au) of undoped structure (D5h). For nitrogen‐doped structures, the order of the β0 values is 3155 (1) > 2677 (2A) ≈ 2817 (2B) > 1465 (3A) ≈ 1458 (3B) > 670 (4) > 254 au (5), which shows two interesting relationships between the β0 value and nitrogen‐doped number: (1) the smaller the nitrogen‐doped number, the larger the β0 value. (2) The structures with the same number of doped‐nitrogen have almost the same β0 values (1465 for 3A and 1458 au for 3B). As for the frequency‐dependent β (−ω; ω, 0) and β (−2ω; ω, ω), the dependence on the nitrogen‐doped number (n) is similar to the case of static β0. For β (−2ω; ω, ω) values at ω = 0.005 au are 3220 (1) > 2720 (2A) ≈ 2862 (2B) > 1480 (3A) ≈ 1477 (3B) > 676 (4) > 256 au (5). In addition, the important monotonic dependences of the β value on the Du and electronic spatial extent 〈R2〉 are also observed. The new knowledge of influence the β value will be beneficial to design high‐performance nonlinear optical (NLO) materials.

Efficiency and accuracy of the elongation method as applied to the electronic structures of large systems.

Current state of development of the elongation method originally proposed by Imamura is presented. Recent progress in methodology, including geometry optimization and employment of the fast multiple method, is highlighted. The accuracy and efficiency of the elongation method as compared to exact canonical Hartree–Fock and Kohn–Sham approaches are discussed. Potential applications are illustrated by wide range of calculations for model systems. The elongation calculations are demonstrated to be much more efficient compared to the conventional ones with high accuracy maintained. The elongation CPU time is shown by the model calculations as linear or sub‐linear scaling for quasi‐one‐dimensional systems. Future work of development into post‐Hartree–Fock methodologies are pointed out.

Nonlinear optical properties of polydiacetylene with donor-acceptor substitution block

The elongation finite-field (elongation-FF) method is applied to donor/acceptor substituted polydiacetylenes (PDAs) for the estimation of substituent effects on nonlinear optical (NLO) properties. The first hyperpolarizability (beta) and the second hyperpolarizability (gamma) of PDA with separated donor and acceptor substitution blocks have much larger values than those of the other substituted PDAs. For the PDAs with donor and acceptor substitution blocks, the relationship between the NLO properties and the block period is examined. It is shown, from the local density of states, that gamma of a system with a quantum well structure has a maximum value at a certain block size. This indicates that by tuning the size of proper block it is possible to achieve the largest gamma value in block polymers. Furthermore, the through-space/bond interaction analysis is performed to examine the pi-conjugation effects on the NLO properties for particular substituted PDA. It is demonstrated by our quantitative analysis that beta is affected by electron transfers in the molecule, and the quantum well structure is critical for gamma improvement.

Excess electron is trapped in a large single molecular cage C60F60

A new kind of solvated electron systems, sphere‐shaped e−@C60F60 (Ih) and capsule‐shaped e−@C60F60 (D6h), in contrast to the endohedral complex M@C60, is represented at the B3LYP/6‐31G(d) + dBF (diffusive basis functions) density functional theory. It is proven, by examining the singly occupied molecular orbital (SOMO) and the spin density map of e−@C60F60, that the excess electron is indeed encapsulated inside the C60F60 cage. The shape of the electron cloud in SOMO matches with the shape of C60F60 cage. These cage‐like single molecular solvated electrons have considerably large vertical electron detachment energies VDE of 4.95 (Ih) and 4.67 eV (D6h) at B3LYP/6‐31+G(3df) + dBF level compared to the VDE of 3.2 eV for an electron in bulk water (Coe et al., Int Rev Phys Chem 2001, 20, 33) and that of 3.66 eV for e−@C20F20 (Irikura, J Phys Chem A 2008, 112, 983), which shows their higher stability. The VDE of the sphere‐shaped e−@C60F60 (Ih) is greater than that of the capsule‐shaped e−@C60F60 (D6h), indicating that the excess electron prefers to reside in the cage with the higher symmetry to form the more stable solvated electron. It is also noticed that the cage size [7.994 (Ih), 5.714 and 9.978 Å (D6h) in diameter] is much larger than that (2.826 Å) of (H2O)20− dodecahedral cluster (Khan, Chem Phys Lett 2005, 401, 85).

Application of the elongation method to nonlinear optical properties: finite field approach for calculating static electric (hyper)polarizabilities

A novel finite-field approach for calculating electric (hyper)polarizabilities based on the elongation method is developed. The method was tested at the semi-empirical PM3 level by using three model systems: the hydrogen chain, the water chain and polyacetylene. The results satisfactorily reproduce the ‘exact’ MOPAC values. The most important advantage of this approach is the large saving of computer time since the dimension of the SCF equation remains the same regardless of the number of atoms in the system. Thus, it is a very useful tool to treat large systems. The method can also be applied to building up a chain containing an arbitrary sequence of monomers.

Describing electron correlation effects in the framework of the elongation method—Elongation-MP2: Formalism, implementation and efficiency

The extension of the elongation method into description of electron correlation effects at ab intio level is presented. The formalism and implementation of the elongation‐MP2 methodology is discussed. The results of calculations for model systems are presented to illustrate efficiency and accuracy of the method. Directions of the further development are highlighted.