Medical, Pharma, Engineering, Science, Technology and Business

^{1}Institute of Metal Research, Shenyang 110016, China

^{2}Department of Chemistry, Tangshan Normal College, Tangshan 063000, China

- *Corresponding Author:
- Ang-yang Yu

Institute of Metal Research

Shenyang 110016, China

**Tel:**13591671906

**E-mail:**[email protected]

**Received date:** June 05, 2015; **Accepted date:** June 24, 2015; **Published date:** July 14, 2015

**Citation:** Ang-yang Yu, Jing Y (2015) Computational Investigations about the Ground and Excited States’ Properties of Trans-4-N,N-Dimethylamino-4’-Nitro-Stilbene (DNS) and Trans-4-N, N-Dimethyl-Amino-4’-Cyanostilbene (DCS) Derivatives. J Theor Comput Sci 2:128. doi: 10.4172/2376-130X.1000128

**Copyright:** © 2015 Ang-yang Yu, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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The ground and lowest-lying singlet excited state geometries and dipole moments of trans-4-N,N-dimethylamino- 4’-nitro-stilbene (DNS) derivative and the trans-4-N,N-dimethyl-amino-4’-cyanostilbene (DCS) derivative are calculated at the B3LYP level of theory for the first time in this work. The vertical excitation energies and the **fluorescence** emission energies are obtained for the two **species**. The calculated results are compared with available experimental results and show good consistency. The molecular orbital analyses in these molecules have been performed. The comparison of the atomic charge distributions in the ground and excited states of both the DNS derivative and DCS derivative implies the intra molecular charge transfer (ICT) process during the **excitation** period.

Ground state; Excitation energy; Fluorescence emission; Molecular orbital; Charge transfer

During the past several years, the field of electro optical organic and nonlinear optical material has received extensive attention [1-3] because of their possible application as fluorescence probes, electro optical switches and chemical sensors. Due to the electron donating and accepting groups on opposite sides, such material, which is connected by a highly delocalized electron system, is important for the nonlinear optical properties. Stilbene and donor–acceptor (DA)- substituted stilbenes are the molecules which have been used in photo physics and photochemistry [4-7]. More or less, the interest results from the complex mechanism relevant to bond twisting in these molecules. The torsional motion of the central C=C bond in transstilbene and its analogs are responsible for the trans-cis isomerization which does not proceed through conical intersection in the excited state potential energy surface [8]. It is known that twisting of the benzonitrilo (acceptor) and dimethylamino (donor) C-N bond in N,N-dimethylaminobenzonitrile (DMABN) could lead to a twisted intramolecular charge transfer (TICT) state, which is responsible for the dual fluorescence [9,10] or displays stokes-shifted fluorescence [11] in polar solvents. TICT-based dual fluorescent systems have been used as ratio metric fluorescent chemo sensors [12]. What is more, the TICT concept has inspired the design of donor-acceptor systems which have ultra large **hyperpolarizability** [13]. Twisting motion of the NO_{2} group in nitro aromatics could result in the ultrafast **fluorescence** quenching [14] and facilitate internal conversion of the lowest singlet excited state. 4-dimethylamino-4’-cyanostilbene (DCS), is a typical stilbene which involves the process of photo induced intramolecular charge transfer (CT) in polar solvents [15-18]. Trans-4-(N,N-dimethylamino)- 4’-nitrostilbene (DNS) is a nonlinear optical dye which contains potential torsional modes in the excited states [19]. Torsional motion about a specific bond in the excited state, such as the trans-cis photo isomerization of alkenes [20,21], is an important nonradiative decay channel for many π-conjugated systems.

The trans-4-N,N-dimethylamino-4’-nitrostilbene (DNS) derivative, as well as the DCS derivative which have been shown in **Scheme 1**, are used to generate antibodies which bind donor-acceptor-substituted stilbenes to afford strong blue to green fluorescent complexes [22]. The free 1 and 2 complexes absorb with the **wavelength** maxima of 430 nm and 373 nm, respectively [23-25]. Both the derivatives’ absorption spectra display no substructure. The steady-state fluorescence spectra of them are broad and composed of no substructure. To the best of our knowledge, computational investigations of the spectroscopic properties of the ground state and the excited state of these derivatives do not exist until now. The motivation of this work is to explore the nature of the ground and the excited states, to see whether our theoretical predictions could be comparable to available experimental results, to look for the mechanism of formation of the **charge-transfer** excited state. We will focus on the neutral molecule 1 and 2 and first look at calculations in which solvent effects are not included in the present work. Some work related with investigating the solvent effects which might influence the spectroscopic properties to some extents is ongoing. The most widely used method to study excited states of such kind of molecules is time-dependent density functional Theory (TDDFT)s.

**Computational details and theory**

All predictions were made with the Gaussian 09 program package [26]. The density functional theory at the B3LYP level of theory [27-30] and the 6-311G** basis set was performed to calculate the ground-state structures and dipole moments of DNS derivative and the DCS derivative. As has been known, CIS method has been used successfully in the structure optimization of the excited state [31,32]. Since the CIS method makes use of a HF state’s orbitals in a CI procedure to deal with the higher roots and incorporated only parts of the electronic correlation effects, the excitation energies obtained by the CIS calculations are often overestimated [33]. In this work, we rectify the flaw of the CIS method by using the time-dependent DFT (TDDFT) [34-36] method to investigate the excited state properties. The TDDFT calculations are applied to the lowest-lying excited state equilibrium geometry and other excited state properties including the dipole moments, excitation energies to the lower three excited states as well as emission energies from the lowest three excited states. The emission resulted from the excited state geometries, which are the same as the ground state geometry. In this work, we have also calculated the Mulliken charges of all the atoms [37-40] in order to study the charge change between the ground and excited states. The changes of atomic charges can provide sufficient proof for the charge transfer (CT) study.

**Ground and lowest-lying singlet excited state geometries of DNS derivative and the DCS derivative**

No restrictions on symmetries were imposed on the initial structures before optimizing the stationary points of these molecules. The ground-state geometries computed at the DFT level for DNS derivative and the DCS derivative are plotted in **Figure 1** for atom labeling. The optimized structural parameters of the ground and lowestlying singlet excited states of DNS derivative and the DCS derivative calculated at B3LYP density functional method have been listed in **Table 1** of the Supporting Information which are in accordance with the atom numbering scheme shown in these figures. The optimized equilibrium geometries of the lowest-lying singlet excited states of DNS derivative and the DCS derivative are plotted in **Figure 2** and the Supporting Information has also listed the geometric parameters of these optimized structures. It should be noted that the ground-state geometries were used for geometry optimization of the first singlet excited state, namely, the lowest-lying singlet excited state. Comparing the optimized geometrical parameters of the first singlet excited state (S_{1}) with the corresponding ground state (S_{0}), the dihedral angle between dimethylamino derivative and nitrostilbene in the ground state of DNS derivative is -85.3° while the dihedral angle between dimethylamino derivative and nitrostilbene in the first excited state of DNS derivative is -91.2°. Notably, all the functional groups in the DNS derivative are in the same plane for the ground state. However, in the lowest-lying singlet excited state of DNS derivative, the dihedral angle between C=C double bond and the plane of the nitro-phenyl group is found to be -90.6° which is twisted from the ground state geometry. As for the ground state and the lowest-lying singlet excited state of the DCS derivative, the dihedral angle between C=C double bond and the plane of the aromatic ring is found to be 0°. That is to say, there are no twisted geometries for these electronic states. The dihedral angle between dimethylamino derivative and cyanostilbene in the ground state of DCS derivative is -84.9°, what is more, the dihedral angle between dimethylamino derivative and nitrostilbene in the first excited state of DCS derivative is -88.8°.

DNS derivative | DCS derivative | |
---|---|---|

Ground state | -1186.00 | -1073.71 |

Excited state | -1185.98 | -1073.62 |

**Table 1:** The energies (in Hartree) of the ground and lowest-lying singlet excited states of the DNS derivative and the DCS derivative.

Furthermore, a frequency analysis was performed on all DFT structures to confirm that all the frequencies are real for the computed stable structures. It is found that all the vibrational modes have real frequencies, which indicate that all the optimized geometries are true minima. In addition, the total energies of the ground and lowest-lying singlet excited states of the DNS derivative and the DCS derivative are given in **Table 1**. It could be found that the energies of the lowest excited state of these molecules are higher than the counterparts of the ground state.

**The vertical excitation energies and the fluorescence emission energies**

The optimized geometries of the ground state have been used to compute the vertical excitation energies (VEE) of the DNS derivative and the DCS derivative by means of TD-B3LYP calculations in the gas phase. For comparison, the results of experimental observation for the DNS derivative and the DCS derivative are also included. All the results are listed in **Table 2**. It could be seen that the vertical excitation energy of DNS derivative has the value of 2.61 eV. The excited state (S_{1}) has the highest oscillator strength (0.81) and its excitation energy of 474 nm matches very well with the experimental absorption spectra which show an absorption maximum of 430 nm. Accordingly, the vertical excitation energy of DCS derivative has the value of 3.07 eV.

DNS derivative | Vertical excitation energy | Oscillator strength | Exp[22] (absorption) | Fluorescence emission energy |
---|---|---|---|---|

S_{1} |
474 nm (2.61 ev) | 0.81 | 430 nm | 631nm (1.97 ev) |

S_{2} |
334 nm (3.71 ev) | 0.4211 | 384nm (3.23 ev) | |

S_{3} |
331 nm (3.74 ev) | 0.0000 | 315nm (3.93 ev) | |

DCS derivative |
Vertical excitation energy |
Oscillator strength |
Exp[22] (absorption) |
Fluorescence emission energy |

S_{1} |
403 nm (3.07 ev) | 1.18 | 373 nm | 427 nm (2.90 ev) |

S_{2} |
313 nm (3.96 ev) | 0.02 | 319 nm (3.89 ev) | |

S_{3} |
305 nm (4.07 ev) | 0.01 | 311 nm (3.98 ev) |

**Table 2:** The vertical excitation energies and fluorescence emission energies of the DNS derivative and the DCS derivative.

The excited state (S_{1}) has the highest oscillator strength (1.18) and its excitation energy of 403 nm matches very well with the experimental absorption spectra which show an absorption maximum of 373 nm.

By means of calculations, we will now start to characterize the emission energies. Fluorescence emission energies of the DNS derivative and the DCS derivative are also listed in **Table 2**. The states relevant for the emission are the three lowest excited states. Since the geometries of these excited states are the same as the ground state geometry according to the Frank-Condon’s rule, the ground state geometry could be used for calculating the emission energies. There is no experimental emission energy for the DNS derivative, while the experimental emission energy for the DCS derivative is 574 nm [41,42]. When compared with the available experimental information of fluorescence emission energy, our calculated results are not in good agreement with the experimental results, which might be due to the problem of choosing the appropriate functional and basis sets for the title molecules.

In addition, dipole moments of the ground state geometries of the DNS derivative and the DCS derivative are 11.26 Debye and 10.53 Debye, respectively. The corresponding excited state dipole moments for the two molecules are calculated to be 10.48 Debye and 11.34 Debye, respectively. It could be concluded that there are no substantial changes in the dipole moments of the two molecules when they are excited.

It is well-known that analysis of molecular orbitals (MOs) can provide insight into the nature of the excited states [43]. The most important molecular orbitals in molecules are the frontier molecular orbitals, called highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) [44]. The frontier orbital gap could help characterize the **microscopic** phenomenon within the molecule. The HOMO is the orbital which primarily acts as an electron donor and the LUMO is the orbital that largely acts as the electron acceptor. The 3D plots of the frontier orbitals HOMO and LUMO (in a.u.) for the ground state of DNS derivative and DCS derivative are shown in **Figure 3**. The positive phase is red and the negative one is green. It can be seen from the figure that the HOMO is distributed in nitrostilbene and N-CH_{3} moiety. The LUMO in DNS derivative is found to spread over the nitrostilbene and N-CH_{3} moiety. All the HOMO and LUMO have nodes. The nodes in each HOMO and LUMO are placed **symmetrically**. It can be seen from the figure that the HOMO is distributed in cyanostilbene and the CH_{2}-N-CH_{3} moiety. The LUMO in DCS derivative is found to spread over the cyanostilbene and the N-CH_{3} moiety. As for the excited states, it can be seen from **Figure 4** that both the HOMO and LUMO of DNS derivative are distributed in nitrostilbene and N-CH_{3} moiety. All the HOMO and LUMO have nodes. The nodes in each HOMO and LUMO are placed symmetrically. It could also be seen from the figure that the HOMO is distributed in cyanostilbene and the CH_{2}-N-CH_{3} moiety in the first excited state of DCS derivative. The LUMO in DCS derivative is found to be located at the cyanostilbene and the N-CH_{3} moiety.

The energy gap of HOMO–LUMO could explain the eventual charge transfer interaction within the molecule. The energy values of HOMO and LUMO levels for the ground state of DNS derivative are computed to be -0.1979 a.u. and -0.0914 a.u. respectively, and the energy difference is 0.1065 a.u. When the molecule excites, the HOMO and LUMO energy difference decreases to 0.0864 a.u. The high energy of HOMO means that it is easy for HOMO to donate electrons whereas the low energy of LUMO means that it is easy for LUMO to accept electrons. Since the energy gap between the LUMO and HOMO has decreased in the excited state, it is easier for the electrons of the HOMO to be excited. The energy values of HOMO and LUMO levels for the ground state of DCS derivative are computed to be -0.1952 a.u. and -0.0736 a.u., respectively, and the energy difference is 0.1216 a.u. When the molecule excites, the HOMO and LUMO energy difference decreases to 0.1112 a.u. A molecule with a small frontier orbital gap is more polarizable and is generally associated with a high chemical reactivity, low kinetic stability and is also termed as soft molecule [45,46]. The low values of frontier molecular orbital gap in the excited states indicate that both the molecules are more reactive and less stable.

**The atomic charge distributions**

The Mulliken atomic charges are displayed in **Table 3**. The charge distribution of DNS derivative shows that all the hydrogen atoms are positive, whereas nearly all the carbon atoms are negatively charged. These are the cases no matter in the ground state or the first excited state. The oxygen atoms have negative charges. The charge distribution of DCS derivative shows that all the hydrogen atoms are positive in the ground state whereas nearly all the hydrogen atoms are positive except hydrogen atom 3 and 4. What is more, all the oxygen atoms have negative charges. The atomic charges for optimized geometries of the ground state and the first excited state of DNS derivative and DCS derivative have also been analyzed in this work. The atomic charge distributions of DNS derivative and DCS derivative are shown in **Figure 5**. In order to describe the change of atomic charges obviously, we divided molecular structures into several parts and summed the atomic charge of each unit. DNS derivative was divided into four parts, nitro-benzene unit, H-C=C-H unit, methyl amino-benzene unit and derivative unit. The sum of atomic charges of nitro-benzene unit in the ground state is calculated to be -0.055778, which changes to -0.114433 in the lowest excited state. However, the sum of the derivative part displays an opposite tendency of change, which changed from 0.129097 in the ground state to 0.174263 in the lowest excited state. All of this demonstrated the charge transfer from the left part to the right part of the molecule. Therefore, it indicates strongly that the excited state of DNS derivative is an intramolecular charge transfer (ICT) state as a whole.

Atom No (1) | Atomic charge (G) | Atom No (1) | Atomic charge (E) |
---|---|---|---|

1C | -0.067 | 1C | -0.055 |

2C | -0.071 | 2C | -0.084 |

5C | -0.075 | 5C | -0.077 |

6C | -0.071 | 6C | -0.078 |

7C | -0.047 | 7C | -0.061 |

8C | -0.037 | 8C | -0.145 |

10C | -0.051 | 10C | -0.124 |

12C | 0.011 | 12C | 0.280 |

15C | -0.076 | 15C | -0.042 |

16C | -0.067 | 16C | -0.089 |

17C | -0.046 | 17C | -0.065 |

18C | 0.025 | 18C | -0.046 |

20C | -0.045 | 20C | -0.052 |

22C | 0.106 | 22C | 0.119 |

25N | 0.048 | 25N | 0.168 |

26N | -0.360 | 26N | -0.462 |

27O | -0.217 | 27O | -0.279 |

28O | -0.217 | 28O | -0.279 |

29C | -0.066 | 29C | -0.115 |

30C | -0.226 | 30C | -0.187 |

33C | -0.223 | 33C | -0.237 |

36C | -0.217 | 36C | -0.213 |

41C | 0.339 | 41C | 0.317 |

42O | -0.381 | 42O | -0.326 |

43O | -0.329 | 43O | -0.328 |

45C | -0.196 | 45C | -0.164 |

Atom No (2) |
Atomic charge (G) |
Atom No (2) |
Atomic charge (E) |

1C | -0.057 | 1C | 0.034 |

2C | -0.084 | 2C | 0.100 |

5C | -0.077 | 5C | 0.638 |

6C | -0.080 | 6C | -0.060 |

7C | -0.063 | 7C | -0.655 |

8C | -0.132 | 8C | 0.105 |

10C | -0.130 | 10C | -0.453 |

12C | 0.261 | 12C | -0.484 |

15C | -0.039 | 15C | 1.028 |

16C | -0.085 | 16C | -0.029 |

17C | -0.067 | 17C | -0.822 |

18C | -0.028 | 18C | -0.312 |

20C | -0.030 | 20C | -0.615 |

22C | -0.047 | 22C | 1.973 |

25N | -0.466 | 25N | 0.267 |

26C | -0.030 | 26C | -0.606 |

27C | -0.253 | 27C | 0.102 |

30C | -0.230 | 30C | -0.065 |

33C | -0.215 | 33C | -0.517 |

38C | 0.315 | 38C | -0.181 |

39O | -0.325 | 39O | -0.248 |

40O | -0.320 | 40O | -0.150 |

42C | 0.030 | 42C | -1.793 |

43N | -0.224 | 43N | -0.174 |

44C | -0.176 | 44C | -0.371 |

**Table 3:** The Mulliken charge distribution of the ground state (G) and the lowest
excited state (E) of DNS derivative (1) and DCS derivative (2).

Correspondingly, DCS derivative was divided into four parts, cyano-benzene unit, H-C=C-H unit, methylamino-benzene unit and derivative unit. The sum of atomic charges of methylamino-benzene unit in the ground state is calculated to be -0.137221, which changes to 0.108464 in the lowest excited state. However, the sum of similar phenomenon happened to the derivative part changes from 0.19065 in the ground state to -0.041502 in the lowest excited state. Since the methylamino-benzene unit and the derivative part display the opposite trend in the charge distribution, we could conclude that there exists the charge transfer from the derivative unit to methylamino-benzene unit. Because the derivative unit and the methylamino-benzene unit locate at the same part of the molecule, we have to assume that the excited state of DCS derivative is a locally intramolecular charge transfer (ICT) state.

We investigate the spectroscopic properties of the ground state and the excited state of trans-4-N,N-dimethylamino-4’-nitrostilbene (DNS) derivative, as well as 4-dimethylamino-4’-cyanostilbene (DCS) derivative in this work. Based on the ground state geometries, the vertical excitation energies of the two molecules are computed. The calculated results show good consistency with available experimental information. The excited state geometries of the two molecules are also calculated which form the basis of obtaining the fluorescence **emission** energies of the two molecules. Furthermore, the frontier molecular orbitals and the atomic charge distributions of DNS derivative and DCS derivative have also been analyzed. It has been found that the DNS derivative is an intramolecular charge transfer (ICT) state as a whole while DCS derivative is a locally **intramolecular** charge transfer (ICT) state.

This work is supported by the Natural Science Foundation of China (Grant No.21373025). Thanks are due to the reviewers for many constructive and valuable comments.

- Bosshard CH, Sutter K, Pretre PH, Hulliger J, Florsheimer M, et al. (2001) Advances in nonlinear optics: organic nonlinear optical materials. Gordon and Breach Publishers, Langhorne, PA.
- Kippelen B, Lackritz HS, Claus RO (1999) Organic nonlinear optical material and devices. Materials Research Society, PA.
- Lakowicz JP (1999) Principles of fluorescence spectroscopy. (2ndedn) Kluwer Academic, Hongham.
- 4. Liu F, Morokuma K (2012) Computational study on the working mechanism of a stilbene light-driven molecular rotary motor: sloped minimal energy path and unidirectional nonadiabatic photoisomerization. J Am Chem Soc 134: 4864-4876.
- . Liu F, Morokuma K (2012) Computational study on the working mechanism of a stilbene light-driven molecular rotary motor: sloped minimal energy path and unidirectional nonadiabatic photoisomerization. J Am Chem Soc 134: 4864-4876.
- Tzeli D, Theodorakopoulos G, Petsalakis ID, Ajami D, Rebek J, et al. (2012) Conformations and fluorescence of encapsulated stilbene. J Am Chem Soc 134: 4346-4354.
- Petsalakis ID, Georgiadou DG, Vasilopoulou M, Pistolis G, Dimotikali D, et al. (2010) Theoretical investigation on the effect of protonation on the absorption and emission spectra of two amine-group-bearing, red “push pull” emitters, 4-dimethylamino-4’-nitrostilbene and 4-(dicyanomethylene)-2-methyl-6-p-(dimethylamino) styryl-4h-pyran, by DFT and TDDFT calculations. J Phys ChemA 114: 5580-5587.
- Saltiel J, Sun YP (1990) Photochromism, molecules and systems (1stedn) Elsevier, Amsterdam.
- Waldeck DH (1991) Photoisomerization dynamics of stilbenes. Chem Rev 91: 415-436.
- Rettig W (1986) Charge separation in excited-states of decoupled systems–TICT compounds and implications regarding the development of new laser-dyes and the primary processes of vision and photosynthesis. Angew Chem Int Ed Engl 25: 971–988.
- Ghosh R, Palit DK (2012) ultrafast dynamics of the excited states of 1-(p-nitrophenyl)-2-(hydroxymethyl)-pyrrolidine. J Phys ChemA 116: 1993-2005.
- Grabowski ZR, Rotkiewicz K, Rettig W (2003) Structural changes accompanying intramolecular electron transfer: focus on twisted intramolecular charge-transfer states and structures. Chem Rev 103: 3899-4031.
- Yang JS, Hwang CY, Chen MY (2007) Bimodal fluorescence signaling based on control of the excited-state conformational twisting and the ground-state protonation processes. Tetra Lett 48: 3097-3102.
- Kang H, Facchetti A, Zhu P, Jiang H, Yang Y, et al. (2005) Exceptional molecular hyperpolarizabilities in twisted pi-electron system chromophores. Angew Chem Int Ed 44: 7922-7925.
- Rappoport D, Furche F (2004) Photoinduced intramolecular charge transfer in 4-(dimethyl) baminobenzonitrile–A theoretical perspective. J Am Chem Soc 126: 1277-1284.
- Amatatsu Y (2000) Ab initio configuration interaction study on electronically excited 4-dimethylamino-4’-cyanostilbene. Theor Chem Acc 103: 445-450.
- Rettig W, Majenz J (1989) Competing adiabatic photoreaction channels in stilbene derivatives. Chem Phys Lett 154: 335-341.
- Daum R, Hansson T, Norenberg R, Schwarzer D, Schroeder J, et al. (1995) Spectroscopy and dynamics of jet-cooled 4-dimethylamino-4'-cyano stilbene in the S1 state. Chem Phys Lett 246: 607-614.
- Abraham E, Oberle’ J, Jonusauskaa G, Lapouyade R, Rullie`re C, et al. (1997) Photophysics of 4-dimethylamino 4'-cyanostilbene and model compounds: Dual excited states revealed by sub-picosecond transient absorption and Kerr ellipsometry. Chem Phys 214: 409-423.
- Marder SR, Kippelen B, Jen AKY, Peyghambarian N (1997) Design and synthesis of chromophores and polymers for electro-optic and photorefractive applications. Nature 388: 845-851.
- Han WG, Lovell T, Liu T, Noodleman L (2002) Density functional studies of the ground and excited-state potential-energy curves of stilbene Cis-trans isomerization. Chemphyschem 3: 167-178.
- . Yang JS, Huang GJ, Liu YH, Peng SM (2008) Photoisomerization of the green fluorescence protein chromophore and the meta- and para-amino analogues. Chem Commun 11: 1344-1346.
- . Tian F, Debler EW, Millar DP, Deniz AA, Wilson IA et al. (2006) The effects of antibodies on stilbene excited-state energetics. Angew Chem Int Ed Engl 45: 7763-7765.
- Chong DP (1995) Recent advances in density functional methods. World Scientific, Singapore.
- Nalewajski R (1996) Topics in current chemistry: density functional theory. Springer-Verlag, Heidelberg.
- Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, et al. (2009) Gaussian 09, Revision A.02, Gaussian Inc, Wallingford, CT.
- Runge E, Gross EKU (1984) Density-functional theory for time-dependent systems. Phys Rev Lett 52: 997-1000.
- Becke AD (1993) Density functional thermochemistry. III. The role of exact exchange. J Chem Phys 98: 5648-5652.
- Stevens PJ, Devlin JF, Chabalowski CF, Frisch MJ (1994) Ab-initio calculation of vibrational absorption and circular-dichroism spectra using density-functional force-fields. J Phys Chem 98: 11623-11627.
- Yang YP, Wu X, Liu C, Huang SP (2014) Density functional theory study of neutral and singly-charged (NaBH4)n (n=1–6) nanoclusters. Chem Phys 443: 45-52.
- Lee C, Yang W, Parr RG (1988) Development of the correlation-energy formula into a functional of the electron density. Phys Rev B 37: 785-789.
- Yang BZ, Huang S, Zhong J, Huang S, Zhang HX (2015) Computational studies on the radiative and nonradiative processes of luminescent N-heteroleptic platinum(II) complexes. Org Elec 19: 7-14.
- Yu AY (2015) Theoretical calculations of the spectroscopy of CH3OH. Phys Chem: An Ind J 10(1): 07-11.
- Yang BZ, Zhang Q, Zhong J, Zhang HX (2012) Ab initio and DFT study of luminescent cyclometalated N-heterocyclic carbene organogold(III) complexes. J Mol Mod 18: 2543-2551.
- Dreuw A, Head-Gordon M (2005) Single-reference ab initio methods for the calculation of excited states of large molecules. Chem Rev 105: 4009-4037.
- Barone V, Polimeno A (2007) Integrated computational strategies for UV/Vis spectra of large molecules in solution. Chem Soc Rev 36: 1724-1731.
- Perrier A, Maurel F, Jacquemin D (2012) Single molecule multiphotochromism with diarylethenes. Acc Chem Res 45: 1173-1182.
- Mulliken RS (1955) Electronic population analysis on LCAO-MO molecular wave functions.1. J Chem Phys 23: 1833-1840.
- Mulliken RS (1955) Electronic population analysis on LCAO-MO molecular wave functions.2.overlap populations, bond orders, and covalent bond energies. J Chem Phys 23: 1841-1846.
- Mulliken RS (1955) Electronic population analysis on LCAO-MO molecular wave functions.4. Bonding and antibonding in LCAO and valence-bond theories. J Chem Phys 23: 2343-2346.
- Mulliken RS (1955) Electronic population analysis on LCAO-MO molecular wave functions. 3. Effects of hybridization on overlap and gross AO populations
- Reed AE, Curtiss LA, Weinhold F (1988) Intermolecular interactions from a natural bond orbital, donor-acceptor viewpoint. Chem Rev 88: 899-926.
- Reed AE, Weinstock RB, Weinhold F (1985) Natural-population analysis. J Chem Phys 83: 735-746.
- Powell BJ, Baruah T, Bernstein N, Brake K, McKenzie RH, et al. (2004) A first-principles density-functional calculation of the electronic and vibrational structure of the key melanin monomers. J Chem Phys 120: 8608-8615.
- Streitwieser Jr A, (1961) Molecular orbital theory for organic chemists. Wiley, NewYork.
- Rauk A (2001) Orbital interaction theory of organic chemistry. (2ndedn), Wiley–Interscience, New York.

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- Quantitative Proteomics
- Quasilinear Hyperbolic Systems
- Scientific Computing
- Semi Analytical-Solution
- Sensitivity Analysis
- Simulation Computer Science
- Smooth Complexities
- Technologies in Computer Science
- Theoretical Chemistry
- Theoretical Computer Science
- Theoretical Issues in Ergonomics Science
- Theoretical Methods
- Theoretical and Applied Science
- Three Dimensional Steady State

- European Conference on
**Computer Science**&**Engineering**

June 20-21, 2018 Oslo, Norway - International Conference on
**Big Data**, Knowledge Discovery and**Data Mining**

August 06-07, 2018 Abu Dhabi, UAE - International Conference on
**Artificial Intelligence**,**Robotics**& IoT

August 21-22, 2018 Paris, France - International Conference on
**Computational Biology**and**Bioinformatics**

Sep 05-06 2018 Tokyo, Japan - International Conference on Advancements in
**Bioinformatics**and**Drug Discovery**

November 26-27, 2018 Dublin, Ireland

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