Tian Lu

Beijing Kein Research Center for Natural Sciences

Novel nanowire technologies encompass the use of metals and crystals with a high electric transport potential and superior charge-collection properties. However, nanowires built on metals such as cadmium, gallium-arsenide and similar alloys present serious environmental and health risks. The use of carbon is a far more environmentally friendly solu...

Understanding the nature of noncovalent interactions between nonpolar small molecules is not only theoretically interesting but also important for practical purposes. The interaction mechanism of three prototype dimers (H2)2, (N2)2, and (H2)(N2) are investigated by state-of-the-art quantum chemistry calculations and energy decomposition analysis. I...

Bond order is an important concept for understanding the nature of chemical bond. In this work, we propose a novel definition of bond order, called Laplacian bond order (LBO), which is defined as a scaled integral of negative parts of Laplacian of electron density in fuzzy overlap space. Many remarkable features of LBO are exemplified by numerous s...

Multiwfn is a multifunctional program for wavefunction analysis. Its main functions are: (1) Calculating and visualizing real space function, such as electrostatic potential and electron localization function at point, in a line, in a plane or in a spatial scope. (2) Population analysis. (3) Bond order analysis. (4) Orbital composition analysis. (5...

Escherichia coli tyrosine kinase (Etk) regulates the export of pathogenic capsular polysaccharide (CPS) by intermolecularly autophosphorylating its C-terminal tyrosine cluster. The kinase Etk, however, needs to be first activated by the intramolecular phosphorylation of a tyrosine residue, Y574, next to the active site. The recently determined stru...

Energy decomposition analysis (EDA) is an important class of methods to explore the nature of interaction between fragments in a chemical system. It can decompose the interaction energy into different physical components to understand the factors that play key roles in the interaction. This work proposes an EDA strategy based on dispersion-correcte...

We have witnessed considerable research interest in the recent literature about the development and applications of quantities from the information-theoretic approach (ITA) in density functional theory. These ITA quantities are explicit density functionals, whose local distributions in real space are continuous and well-behaved. In this work, we fu...

A novel supramolecular complex (2C18@OPP) constructed from two kinds of unique nanorings, all-carboatomic cyclo[18]carbon (C18) and figure-of-eight carbon hoop (OPP), has been studied theoretically from the perspective of an extraordinary dual-motor nanorotator. The rotational barrier of C18 in OPP is extremely small at ambient temperature, implyin...

Energy decomposition analysis (EDA) is an important method to explore the nature of interaction between fragments in a chemical system. It can decompose the interaction energy into different physical components to understand the factors that play key roles in the interaction. This work proposes an energy decomposition analysis strategy based on dis...

The recently synthesized novel figure-of-eight nanohoop with two strained oligoparaphenylenes (OPPs) was theoretically designed to collect and stabilize new allotropic carbon cyclo[18]carbon (C18) through molecular assembly. The size adaptability and shape complementarity of C18 to OPP make it possible for them to combine into extraordinary ring-in...

Herein, the electronic structure and bonding character of the stable cyclo[18]carbon (C18) precursor, C18Br6, are thoroughly characterized by molecular orbital (MO), density of states (DOS), bond order (BO), and interaction region indicator (IRI) analyses. The delocalization characters of out-of-plane and in-plane π-electrons (labeled as πout- and...

The photophysical property and optical nonlinearity of an electronic push-pull mesoionic compound, 2-(4-trifluoromethophenyl)-3-methyl-4-(4-methoxyphenyl)-1,3-thiazole-5-thiolate, were theoretically investigated with a reliable computing strategy. The essence of the optical properties were then explored through a variety of wavefunction analysis me...

The stable precursor C18Br6 is of more practical significance than the refreshing but elusive cyclo[18]carbon (C18) at present, and molecular aromaticity caused by π-electron delocalization is an important issue of interest for this unusual molecule. In this paper, the electronic structure and bonding character of the C18Br6 are thoroughly characte...

This erratum corrects independent gradient model based on Hirshfeld partition of molecular density (IGMH) proposed in our previous paper (J. Comput. Chem. 2022, 43, 539–555), and a brief analysis shows why IGMH based on incorrect implementation (inversed sign) of gradient of free-state atomic densities works surprisingly better for graphically repr...

Based on the computational approach that can accurately describe their geometric structures and electronic spectra, we have theoretically studied the nonlinear optical (NLO) properties of H-capped carbon chains, H-(C≡C)n-H, for the first time. Special attention was paid to the size dependence of the molecular (hyper)polarizability of these species...

The electronic spectrum of carbon chains has not been well understood in nature and deserves further study. In the present work, (time-dependent) density functional theory [(TD-)DFT] was employed to investigate the geometric and electronic structures as well as the allowed 11Σu+ ← X1Σg+ electronic transition of the H-capped carbon chains H-(C≡C)n-H...

Cyclocarbon fully consists of sp -hybridized carbon atoms, which shows quite unusual electronic and geometric structures compared to common molecules. In this work, we systematically studied strain energy (SE) of cyclocarbons of different sizes using regression analysis method based on electronic energies evaluated at the very accurate DLPNO-CCSD(T...

Analysis of electronic wavefunction generated by quantum chemistry codes has crucial role in exploring nature of electronic structure and providing valuable information of chemical interest. A file containing wavefunction information is inevitably needed as a communicator between wavefunction analysis codes and quantum chemistry programs. There hav...

Two unique nanorings recently generated, namely cyclo[18]carbon (C18) and oligoparaphenylene (OPP), were theoretically designed to assemble an extraordinary dual-motor supramolecular rotator (2C18@OPP) with large included angle. The size adaptability and shape complementarity of guest C18 to host OPP as well as the thermodynamic analysis of 2C18@OP...

Cyclocarbon fully consists of sp-hybridized carbon atoms, which shows quite unusual electronic and geometric structures compared to common molecules. In this work, we systematically studied strain energy (SE) of cyclocarbons of different sizes using regression analysis method based on electronic energies evaluated at the very accurate DLPNO-CCSD(T)...

Multiwfn is an open‐source, freely available post‐processing software aiming for analyzing the electronic structure of molecular systems. Electronic wave function produced by most mainstream quantum chemistry programs can be processed. Performing analysis of conceptual density functional theory (CDFT) is one of the important applications of Multiwf...

The electronic spectra and (hyper)polarizability of C18-(CO)n (n = 2, 4, and 6) are studied using theoretical calculations to reveal the effect of introducing carbonyl (-CO) groups on the molecular optical properties. Successive introduction of -CO groups is observed to cause a red-shift in the absorption spectrum, but maximum absorption of all mol...

The powerful independent gradient model (IGM) method has been increasingly popular in visual analysis of intramolecular and intermolecular interactions in recent years. However, we frequently observed that there is an evident shortcoming of IGM map in graphically studying weak interactions, that is its isosurfaces are usually too bulgy; in these ca...

Concentration variation of chemical substances in complex reactions is of great chemical interest, because many valuable information about reaction, such as half-life time, dependency of reaction rate on barriers, main product of competitive reactions, the order of appearance of various substances, can be directly studied by examining time-dependen...

The photophysical property and optical nonlinearity of an electronic push-pull mesoionic compond, 2-(4-trifluoromethophenyl)-3-methyl-4-(4-methoxyphenyl)-1,3-thiazole-5-thiolate, were theoretically investigated with a reliable computing strategy. The essence of the optical properties were then explored through a variety of wavefunction analysis met...

Chemical bonds and noncovalent interactions are extraordinarily important concepts in chemistry and beyond. Using density-based quantities to describe them has a long history in the literature, yet none can satisfactorily describe the entire spectrum of interactions from strong chemical bonds to weak van der Waals forces. In this work, employing Pa...

Analysis of electronic wavefunction generated by quantum chemistry codes has crucial role in exploring nature of electronic structure and providing valuable information of chemical interest. A file containing wavefunction information is inevitably needed as a communicator between wavefunction analysis codes and quantum chemistry programs. There hav...

The bonding character, electron delocalization, and aromaticity of the cyclo[18]carbon (C 18 ) precursors, C 18 -(CO) n ( n = 6, 4, and 2), are studied by combining quantum chemical calculations and various electronic wavefunction analyses with different physical bases. It is found that C 18 -(CO) n ( n = 6, 4, and 2) molecules exhibit alternating...

The independent gradient model (IGM) originally proposed in Phys. Chem. Chem. Phys., 19, 17928 (2017) has been increasingly popular in visual analysis of intramolecular and intermolecular interactions in recent years, and it has many clear advantages over the widely employed noncovalent interaction (NCI) method, such as intrafragment and interfragm...

The independent gradient model (IGM) originally proposed in Phys. Chem. Chem. Phys., 19, 17928 (2017) has been increasingly popular in visual analysis of intramolecular and intermolecular interactions in recent years, and it has many clear advantages over the widely employed noncovalent interaction (NCI) method, such as intrafragment and interfragm...

Recently, Iyakutti and coworkers published an interesting paper studying characteristics of cyclo[12]carbon and cyclo[18]carbon as well as their interactions with graphene (Mater. Sci. and Eng. B 263 (2021) 114895). However, we found some of their calculations are obviously unreasonable and a few conclusions are misleading. Here, we make some remar...

Doping alkali metal atoms, especially lithium (Li), in nanocarbon materials has always been considered to be one of the most effective methods to improve the optical properties of the system. In this theoretical work, we doped a Li atom to the recently observed all-carboatomic molecule, cyclo[18]carbon (C18), and finally obtained two stable configu...

Considering their remarkable chemical stability, the precursors of cyclo[18]carbon (C18), C18-(CO)n (n = 2, 4, and 6), have more practical significance than the elusive C18 ring. In the present paper, the electronic spectrum and (hyper)polarizability of the C18-(CO)n (n = 2, 4, and 6) are studied by theoretical calculations and analyses for reveali...

Considering their remarkable chemical stability, the precursors of cyclo[18]carbon (C18), C18-(CO)n (n = 2, 4, and 6), have more practical significance than the elusive C18 ring. In the present paper, the electronic spectrum and (hyper)polarizability of the C18-(CO)n (n = 2, 4, and 6) are studied by theoretical calculations and analyses for reveali...

The evaluation of molecular electrostatic potential (ESP) is a performance bottleneck for many computational chemical tasks like restrained ESP charge fitting or quantum mechanics/molecular mechanics simulations. In this paper, an efficient algorithm for the evaluation of ESP is proposed. It regroups the expression in terms of primitive Gaussian ty...

Planarity is a very important structural character of molecules, which is closely related to many molecular properties. Unfortunately, there is currently no simple, universal, and robust way to measure molecular planarity. In order to fill this evident gap, we propose two metrics of molecular planarity, namely molecular planarity parameter (MPP) an...

Although the unique cyclo[18]carbon (C18) realized by recent experiments has been greatly concerned, it has so far remained elusive. In contrast, its precursors C18-(CO)n (n = 6, 4, and 2), which can be separated stably, are of more practical significance. In this paper, the bonding character, electron delocalization, and aromaticity of the C18-(CO...

Although the unique cyclo[18]carbon (C18) realized by recent experiments has been greatly concerned, it has so far remained elusive. In contrast, its precursors C18-(CO)n (n = 6, 4, and 2), which can be separated stably, are of more practical significance. In this paper, the bonding character, electron delocalization, and aromaticity of the C18-(CO...

Although the unique cyclo[18]carbon (C18) realized by recent experiments has been greatly concerned, it has so far remained elusive. In contrast, its precursors C18-(CO)n (n = 6, 4, and 2), which can be separated stably, are of more practical significance. In this paper, the bonding character, electron delocalization, and aromaticity of the C18-(CO...

Although the unique cyclo[18]carbon (C18) realized by recent experiments has been greatly concerned, it has so far remained elusive. In contrast, its precursors C18-(CO)n (n = 6, 4, and 2), which can be separated stably, are of more practical significance. In this paper, the bonding character, electron delocalization, and aromaticity of the C18-(CO...

Planarity is a very important structural character of molecules, which is closely related to many molecular properties. However, there is currently no simple, universal, and robust way to measure molecular planarity. In order to fill this evident gap, we propose two metrics of molecular planarity, namely molecular planarity parameter (MPP) and span...

The remarkable size dependence of the optical properties of cyclo[2N]carbons (N=3–15) are profoundly explored, and the relevance between aromaticity and optical properties are highlighted. The extrapolation curves fitted for energy level of frontier molecular orbitals, maximum absorption wavelength, and (hyper)polarizability of considered carbon ri...

Doping alkali metal atoms, especially lithium (Li), in nanocarbon materials has always been considered as one of the most effective methods to improve the optical properties of the system. In this theoretical work, we doped a Li atom into the recently observed all-carboatomic molecule, cyclo[18]carbon (C₁₈), and finally obtained two stab...

Graphically revealing interaction regions in a chemical system enables chemists to quickly recognize where significant interactions have formed. Reduced density gradient (RDG) has already been widely employed in literatures to visually exhibit weak interaction regions, in fact it also has the ability of revealing chemical bonding regions. Unfortuna...

Though density functional theory is widely accepted as one of the most successful developments in theoretical chemistry in the past few decades, the knowledge of how to apply this new electronic structure theory, to help us better understand chemical processes and transformations, is still an unaccomplished task. The information-theoretic approach...

In this article, we present a stand-alone, versatile and flexible code named Shermo for calculating various thermochemistry data. This code is compatible with various mainstream quantum chemistry codes, and has many unique advantages: The output information is very clear and easy to read; thermodynamic quantities can be fully decomposed to contribu...

Recently, Shuhong Xu et al. reported theoretical calculation of molecular structure, bonding, aromaticity, electron delocalization, and electronic spectrum of cyclo[18]carbon in J. Mol. Model., 26, 111 (2020). Due to inappropriate consideration of calculation strategy, misunderstanding of some analysis methods and concepts, and some errors in the d...

Graphically revealing interaction regions in a chemical system enables chemists to notice the areas at a glance where significant interactions have formed, it is very helpful in studying chemical bonds, intermolecular and intramolecular interactions. Reduced density gradient (RDG) has already been widely employed in literatures to visually exhibit...

Inspired by recent experimental observation of molecular morphology and theoretical predictions of multiple properties of cyclo[18]carbon, we systematically studied photophysical and nonlinear optical properties of cyclo[2 N ]carbons ( N = 3−15) allotropes through density functional theory. This work unveils the unusual optical properties of the sp...

p>The photophysical property and optical nonlinearity of an electronic push-pull mesoionic compond, 2-(4-trifluoromethophenyl)-3-methyl-4-(4-methoxyphenyl)-1,3-thiazole-5-thiolate were theoretically investigated with a reliable computing strategy. The essence of the optical properties were then explored through a variety of wave function analysis m...

Cyclo[18]carbon has a very unique geometry and electronic structure. We found that external electric field (EEF) has an ultrastrong regulation effect on various aspects of the cyclo[18]carbon: (1) EEF makes the shape of the cyclo[18]carbon change from a circle to an oval, the elongation is particularly striking at a large EEF magnitude (2) EEF caus...

The theoretical calculations on a direct comparison of hypervalent halogen bonds and conventional halogen bonds have been carried out at the MP2/aug-cc-pVTZ-(PP) level, in which multivalent At center acts as Lewis acid to form a collinear and non-coplanar halogen bond with H 2 O/H 2 S. This series of complexes is defined as hypervalent halogen bond...

The vibrational spectra of cyclo[18]carbon and its analogues, cyclo[2n]carbon (n=3 to 15), were carefully simulated and characterized. The in‐plane C−C stretching vibrations shows strong rigidity, while out‐of‐plane motions seem to be extremely flexible. The solvation effect can enhance signal strengths of the vibrational spectra, but does not evid...

Electrostatics and van der Waals (vdW) interactions are two major components of intermolecular weak interactions. Electrostatic potential has been a very popular function in revealing electrostatic interaction between the system under study and other species, while the role of vdW potential was less recognized and has long been ignored. In this pap...

Recently, an intriguing all-carboatomic ring, cyclo[18]carbon, was observed in the condensed phase for the first time, and it quickly attracted widespread attention. In this article, we first investigated the interaction of the cyclo[18]carbon with external environment through electrostatic potential and our recently proposed van der Waals potentia...

Cyclo[18]carbon has a very unique geometry and electronic structure. Based on quantum chemistry calculations, we found that external electric field (EEF) has ultrastrong regulation effect on various aspects of the cyclo[18]carbon. The main findings are as follows: (1) The EEF evidently affects geometric structure of the cyclo[18]carbon, and the rin...

Boron-based materials have been studied extensively due to their potential applications in hydrogen storage and sensing. Doping their surface with transition metals can improve their electronic properties and chemical reactivity. Here, we have studied the titanium-doped boron cluster containing 38 boron atoms using density functional theory, time-d...

Cooperativity effects between a regium-bonding and a pnicogen-bonding interactions in a series of MF···PH3O···MF (M = Cu, Ag, Au) ternary complexes are investigated using theoretical calculations at the MP2/aug-cc-pVTZ(-PP) level. Except for the AuF···PH3O···AuF complex, a pnicogen bond and a regium bond can coexist in each ternary complex. The cal...

Inspired by a previous experimental study on the first-order hyperpolarizabilities of 1,3-thiazolium-5-thiolates mesoionic compounds using Hyper-Rayleigh scattering technique, we theoretically investigated the UV-Vis absorption spectra and every order polarizabilities of these mesoionic molecules. Based on the fact that the photophysical and nonlin...

Calculation of molecular thermodynamic quantities is one of the most frequently involved task in daily quantum chemistry studies. In this article, we present a general, stand-alone, powerful and flexible code named Shermo for calculating various common thermochemistry data. This code is compatible with Gaussian, ORCA, GAMESS-US and NWChem and has m...

Electrostatic and van der Waals (vdW) interactions are two major components of intermolecular weak interactions. Electrostatic potential has been a very popular function in revealing electrostatic interaction between the system under study and other species, while the role of vdW potential is less recognized and has long been ignored. In this paper...

Electrostatic and van der Waals (vdW) interactions are two major components of intermolecular weak interactions. Electrostatic potential has been a very popular function in revealing electrostatic interaction between the system under study and other species, while the role of vdW potential is less recognized and has long been ignored. In this paper...

cyclo[18]carbon is an all-carboatomic ring observed recently in experiment. Inspired by the distinctive feature in structure and bonding nature, we explored comprehensively its bonding character, electron delocalization, and aromaticity by quantum chemistry calculation and wavefunction analysis. Bond order analysis reveals that this sp-hybridized a...

The electronic spectrum and optical nonlinearity of the sp-hybridized cyclo[18]carbon with novel topology are studied by means of (time-dependent) density functional theory calculations. Molecular orbital analysis shows that the energy levels of σ molecular orbitals of the cyclo[18]carbon are very low, and the energies of two sets of high-lying π m...

Inspired by a previous experimental study on the first-order hyperpolarizabilities of 1,3-thiazolium-5-thiolates mesoionic compounds using Hyper-Rayleigh scattering technique, we theoretically investigated the UV-Vis absorption spectra and every order polarizabilities of these mesoionic molecules. Based on the fact that the photophysical and nonlin...

The unique properties of chemical materials are usually related to the topology and size of their constituent unit. Inspired by a previous report on the synthesis of a separable catenane composed of two Möbius-conjugated nanohoops, we theoretically predicted the optical properties of the Möbius monomer, its Hückel analogue, and some structures deri...

Analysis of electronic wavefunction generated by quantum chemistry codes has crucial role in exploring nature of electronic structure and providing valuable information of chemical interest. A file containing wavefunction information is inevitably needed as a communicator between wavefunction analysis codes and quantum chemistry programs. There hav...

Analysis of electronic wavefunction generated by quantum chemistry codes has crucial role in exploring nature of electronic structure and providing valuable information of chemical interest. A file containing wavefunction information is inevitably needed as a communicator between wavefunction analysis codes and quantum chemistry programs. There hav...

Benziporphyrins are versatile macrocycles exhibiting aromaticity switching behaviors. The existence of both Hückel and Möbius (anti)aromaticity has been reported in these systems, whose validity is respectively governed by the [4n+2] and [4n] π-electron rule on the macrocyclic pathway. Despite the experimental evidence on the floppiness of benzipor...

The characteristic of π electrons has a crucial role in determining various properties of chemical systems, such as reactivity, aromaticity and spectroscopy. There are a large number of methods could be used for investigating π electronic structure, for example, the well-known electron localization function and multicenter bond order. For completel...

Although cyclo[18]carbon has been theoretically and experimentally investigated since long time ago, only very recently it was prepared and directly observed by means of STM/AFM in condensed phase (Kaiser et al., Science , 365 , 1299 (2019)). The unique ring structure and dual 18-center π delocalization feature bring a variety of unusual characteri...

The conversions of photophysical and nonlinear optical (NLO) properties in [32]octaphyrins(1.0.1.0.1.0.1.0) following macrocyclic isomerization between Hückel and Möbius topologies have been studied in detail by means of quantum chemistry calculations. Compared to their quasi-planar analogues, the twisted Möbius and the figure-eight Hückel conforme...

This work studies the underlying nature of H-bonds (HBs) of different types and strengths, and tries to predict binding energies (BEs) based on the properties derived from wavefunction analysis. A total of 42 HB complexes constructed from 28 neutral and 14 charged monomers were considered. This set was designed to sample a wide range of HB strength...

In this work, we report a systematic study on the global and local aromaticity of acenes using a series of model structures from 2-acene to 11-acene. A recently developed ansatz, an information-theoretic approach coached into density functional reactivity theory has been employed, which essentially provides different density functionals characteriz...

A comprehensive investigation of the aromaticity control process of expanded porphyrins was carried out using a variety of visual criteria for the first time. The results show that the indicators based on magnetic property can be used to inspect the global aromaticity of [32]octaphyrins(1.0.1.0.1.0.1.0), while the methods according to electronic (d...

Theoretical researches on the dimers formed by CO with halides of the multivalent astatine as a Lewis-acid center are conducted to examine the typical characteristics of supervalent halogen bond. Calculation on MP2/aug-cc-pVTZ level reveals that the multiple nucleophilic sites of multivalent halide monomers can promote the formation of various type...

It is well-known that the kinetic energy density (KED) functional is the most difficult to approximate in density functional theory (DFT), yet to take full advantage of DFT with its density-based descriptive capability of molecular properties, an accurate account of KED is a must. To have a better idea of how an approximate KED formula behaves and...

Regium bonds interaction between phosphine oxide (H3PO), the trans phosphinuous acid (T-PH2OH), the cis phosphinuous acid (C-PH2OH) and MX (M═Cu, Ag, Au; X═F, Cl, Br) complexes were investigated by means of ab initio MP2/aug-cc-pVTZ method. For phosphinuous acid and MX complexes, two types of regium bonded interaction (trans and cis complexes) are...

Originated from the cyclic delocalization of electrons resulting in extra stability and instability, aromaticity and antiaromaticity are important chemical concepts whose appreciation and quantification are still much of recent interest in the literature. Employing information-theoretic quantities can provide us with more insights and better unders...

The bonding mechanisms between DEHP, PFOS, butylparaben and benzo[a]pyrene with the DNA were recently published [1] and showed intriguing mechanisms of complex formation between these priority pollutants and the gene core fragment of the p53 suppressor which were analyzed at the electronic level. The study supplied also important bonding data, incl...

Very recently [J. Phys. Chem. A 2018, 122 (11), 3087–3095], we proposed to employ the Pauli energy to identify and determine strong covalent interactions (SCI), whose bond order are equal to or larger than two. This is done through the signature isosurface shape between the two bonding atoms. We discovered that the signature shape for a double, tri...

Intermolecular interaction of XH2P···MY (X = H, CH3, F, CN, NO2; M = Cu, Ag, Au; Y = F, Cl, Br, I) complexes was investigated by means of an ab initio method. The molecular interaction energies are in the order Ag < Cu < Au and increased with the decrease of RP···M. Interaction energies are strengthened when electron-donating substituents X connect...