**1. Introduction**

Graphene-enhanced Raman scattering (GERS) and graphene- mediated SERS (G-SERS) have been known for molecular trace detection in the nanomaterial substrate surface [1, 2].

In SERS, the Raman scattering intensity is related to laser intensity IL and polarizability tensor α by the expression [3]:

$$\mathcal{I} = \frac{8\pi (a \pm a\_{I\prime})^4 I\_L \sum a\_{\sigma\rho}^2}{\Re C^4}$$

Where ω is the frequency of incident laser and ωI'<sup>I</sup> is the molecular transition frequency between states I and I<sup>0</sup> .

Electromagnetic effect leads to amplification of laser and scattering intensity. Chemical effects, including static chemical enhancement, molecular resonance, and charge-transfer effect, contribute to the change in polarizability derivatives with respect to internal coordinates.

Graphene is used as part of SERS substrates to prepare additional chemical enhancement also as an assistant for "hot spots, which effectively amend the spectral enhancement result. The Raman spectra amplification of the molecules that were attracted to the graphene substrate occurred due to charge transfer [4, 5].

So far, few studies based on quantum chemical calculations for GERS and G-SERS process have been presented, due to the great challenges in modeling the graphenemolecule structure (including cluster model and periodic model) and the related charge transfer effect during the SERS process [6].

For gold component, SERS mechanisms involve off-resonance chemical effect (static chemical enhancement), on-resonance chemical effect) molecular resonance and charge-transfer resonance (and electromagnetic effect (surface plasmon resonance). DFT calculations take into account the effect of molecule-metal interaction and changes in electronic structure for both off- and on-resonance chemical enhancement. Molecular resonance is not considered due to absence of excitation in visible region.

Titanium dioxides (TiO2) due to its interesting general properties including photocatalysis, catalysis, antibacterial effects, and in civic as self-cleaning that affect the quality of life are taken into consideration [7, 8]. The attractive physical and chemical features of TiO2 depend on the crystal phase, size, and form of particles. For example, varying phases of crystalline TiO2 have different band gaps of the rutile phase of 3.0 eV and anatase phase of 3.2 eV; defining the photocatalytic efficiency of TiO2 [9].

Titanium dioxide nanoparticles with a high refractive index (n = 2.4) are appropriate for toothpaste, pharmaceuticals, coatings, papers, inks, plastics, food products, cosmetics, and the textile industry [10].

One of the best materials used in the above cases is TiO2 doped with noble metals such as gold [11]. TiO2 between B/N-doped graphene and Au clusters as electrodes, enhanced charge transport properties shows.

In this work, we concentrated on the interaction between TiO2, Au, and graphene, in which graphene is presented as a substrate component in SERS.

For investigation of the chemical enhancement mechanism related to graphene based SERS, we used density functional theory (DFT) on the TiO2 /gold complexes with pure graphene, and B/N doped graphene.

## **2. Results and discussion**

Gaussian 09 packages were applied for Theoretical calculations and Hyperchem software for drawn molecules. By B3LYP functional, Molecules and compounds were optimized and calculated. The basis sets for graphene, B/N doped graphene were described using basis sets of 3–21 + G (d, p) and the basis sets for Au atoms were used LANL2DZ.

Excitation spectra were calculated using DFT-optimized configurations with the CAM-B3LYP (long-range corrected effect) functional and the same basis sets [12, 13].

As shown in **Figure 1**, geometric optimization was applied on different compounds including TiO2/Au-graphene, and TiO2/Au-graphene-Au with complete graphene cluster, TiO2/graphene (internal), TiO2/Au-GN (N-doped graphene), and TiO2/Au-GB (B-doped graphene).

Calculated Raman spectra of TiO2/gold/graphene compounds were shown in **Figures 2** and **3**. The (a) in **Figure 2** corresponds to the Raman spectrum of TiO2

*A DFT Investigation on Different Graphene Based Substrates on SERS: A Case Study of… DOI: http://dx.doi.org/10.5772/intechopen.109033*

**Figure 1.**

*Geometric optimization of TiO2/gold/graphene compounds: (a) pure graphene (b) B-doped graphene (c) N-doped graphene (d) TiO2/ graphene (internal) (e) TiO2/graphene (external) (f) TiO2/Au-graphene (g) TiO2/3Augraphene (h) TiO2/Au-GB (B-doped graphene) (i) TiO2/Au-GN (N-doped graphene).*

molecule, the (b) in **Figure 2** is the calculated Raman spectrum of the TiO2/Au-G complex, and the (c) in **Figure 2** is the calculated Raman spectrum of the TiO2/Au-G-Au complex based on pure graphene cluster.

The major characteristic Raman peaks of TiO2 molecule are located at 420 cm<sup>1</sup> , 490 cm<sup>1</sup> , 650 cm<sup>1</sup> , and 760 cm<sup>1</sup> . In the Raman spectrum of the TiO2/Au- graphene composite, the major characteristic Raman peaks at 490 cm<sup>1</sup> and 760 cm<sup>1</sup> redshifted to 470 cm<sup>1</sup> and 755 cm<sup>1</sup> , respectively. In the Raman spectrum of the TiO2/ Au- graphene -Au composite, the major characteristic Raman peaks at 470 cm<sup>1</sup> and 755 cm<sup>1</sup> red-shifted to 440 cm<sup>1</sup> and 750 cm<sup>1</sup> , respectively. The red-shift of Raman peaks is related to changes in the linked bond distances. For instance, longer Ti-O bond distance caused by Ti-Au binding leads to smaller wavenumber (lower force constants) of Ti-O stretching vibration mode.

We have compared the Raman intensities of TiO2/gold/graphene compounds. As shown in **Figure 2**, we can see that the Raman intensity of TiO2/Au- graphene -Au is larger than that of TiO2 molecule. For Raman peaks position at 490 cm<sup>1</sup> and 760 cm<sup>1</sup>

#### **Figure 2.**

*Raman spectra of TiO2/gold/graphene compounds, (a) TiO2 molecule (b) TiO2/Au-graphene (c) TiO2/Augraphene-Au.*

(TiO2), the Raman intensities are about 60 (a.u.) and 50 (a.u.), respectively and for TiO2/Au- graphene -Au are about 200 (a.u.) and 220 (a.u.), respectively. The reason can be considered due to the intensity enhancement by Au atoms.

*A DFT Investigation on Different Graphene Based Substrates on SERS: A Case Study of… DOI: http://dx.doi.org/10.5772/intechopen.109033*

**Figure 3.** *Raman spectra of (a) TiO2/graphene (b) TiO2/GB (c) TiO2/GB-Au.*

The SERS enhancement factor (EF) has been defined: EF <sup>¼</sup> ISERS INormal where ISERS and INormal are the peak intensity on TiO2/Au- graphene -Au and TiO2, respectively. For peaks position at 490 cm�<sup>1</sup> and 760 cm�<sup>1</sup> , the EF is: [14]

$$(EF)\_{490} = \frac{I\_{SERS}}{I\_{Normal}} = \frac{200}{60} = 3.3$$

$$(EF)\_{760} = \frac{I\_{SERS}}{I\_{Normal}} = \frac{220}{50} = 4.4$$

The intensity of the SERS signals is enhanced by up to 3 fold. The Raman spectra amplification of the molecules can be related to the due to charge transfer between TiO2 molecule and Au atoms.

The (a) in **Figure 3** corresponds to the Raman spectrum of TiO2/G complex, the (b) in **Figure 3** is the calculated Raman spectrum of the TiO2/ GB (boron doped) complex, and the (c) in **Figure 3** is the calculated Raman spectrum of the TiO2/GB-Au complex.

In the Raman spectrum of (a) the TiO2/graphene composite, the major characteristic Raman peaks of TiO2 at 470 cm�<sup>1</sup> and 730 cm�<sup>1</sup> and the Raman peaks of graphene at 1330 cm�<sup>1</sup> , 1410 cm�<sup>1</sup> and 1546 cm�<sup>1</sup> . In the Raman spectrum of (b) the TiO2/ GB composite, the major characteristic Raman peaks red-shifted 470 cm�<sup>1</sup> , 670 cm�<sup>1</sup> , 1270 cm�<sup>1</sup> , 1360 cm�<sup>1</sup> and 1546 cm�<sup>1</sup> , respectively. In the Raman spectrum of (c) the TiO2/GB-Au composite, the major characteristic Raman peaks red-shifted 458 cm�<sup>1</sup> , 580 cm�<sup>1</sup> , 1265 cm�<sup>1</sup> , 1370 cm�<sup>1</sup> and 1525 cm�<sup>1</sup> , respectively. The red-shift of Raman peaks is related to changes in the linked bond distances.

The intensities of all particular Raman peaks were significantly improved under the Presence of gold atoms (**Figure 3c**). Whereas, with the presence of boron atom, the intensity of the Raman peaks decreases and the perturbations increases (**Figure 3b**), which show the presence of impurities in the graphene.

As shown in **Figure 4**, we have compared the Raman intensities of TiO2/ GB and TiO2/ GN compounds. We can see that the Raman intensity of TiO2/ GN (**Figure 4b**) is lower than of TiO2/ GB (**Figure 4a**) composite and the Raman peaks were shifted to smaller wavenumber (lower force constants). This could be due to the weaker bands of TiO2/ GN composite than the TiO2/GB composite.

We have compared the HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) of TiO2/gold/graphene compounds. The energy difference between the HOMO and LUMO is named the HOMO–LUMO gap [15]. The difference in energy between these two frontier orbitals can be used to estimate the strength and stability of complexes [16]. The higher of the gap's energy, the molecule will be more stable and the harder to excite.

As shown in **Figure 5**, we have compared the HOMO and LUMO of TiO2/ GB, TiO2/ GN TiO2/ GB-Au and TiO2/GN-Au composites.

$$(\Delta E)\_{TiO\_2/G\_8} = -0.03858 - (-0.17867) = 0.14009 \text{ Hartree}$$

$$(\Delta E)\_{TiO\_2/G\_N} = 0.01502 - (-0.11311) = 0.12813 \text{ Hartree}$$

$$(\Delta E)\_{TiO\_2/G\_8-Au} = -0.08651 - (-0.24520) = 0.15869 \text{ Hartree}$$

$$(\Delta E)\_{TiO\_2/G\_N-Au} = -0.08106 - (-0.22632) = 0.14526 \text{ Hartree}$$

The HOMO and LUMO energy of the compounds is calculated above. The largest energy difference is related to the composite of TiO2/GB-Au with the value of 0.15869 Hartree.

*A DFT Investigation on Different Graphene Based Substrates on SERS: A Case Study of… DOI: http://dx.doi.org/10.5772/intechopen.109033*

**Figure 4.** *Raman spectra of (a) TiO2/ GB (b) TiO2/GN.*

*The HOMO and LUMO of (a) TiO2/ GB (b) TiO2/ GN (c) TiO2/ GB-Au (d) TiO2/GN-Au composites.*
