SỞ KHOA HỌC VÀ CƠNG NGHỆ TP HỒ CHÍ MINH VIỆN KHOA HỌC VÀ CƠNG NGHỆ TÍNH TỐN BÁO CÁO TỔNG KẾT ỨNG DỤNG HĨA TÍNH TỐN TRONG THIẾT KẾ VẬT LIỆU HỮU CƠ BÁN DẪN Đơn vị thực hiện: PTN Hạ tầng Tính tốn Chủ nhiệm nhiệm vụ: GS.TS Trương Nguyện Thành TP HỒ CHÍ MINH, THÁNG 06/2019 SỞ KHOA HỌC VÀ CƠNG NGHỆ TP HỒ CHÍ MINH VIỆN KHOA HỌC VÀ CƠNG NGHỆ TÍNH TỐN BÁO CÁO TỔNG KẾT ỨNG DỤNG HĨA TÍNH TỐN TRONG THIẾT KẾ VẬT LIỆU HỮU CƠ BÁN DẪN Viện trưởng: Nguyễn Kỳ Phùng Đơn vị thực hiện: PTN Hạ tầng Tính tốn Chủ nhiệm nhiệm vụ: GS.TS Trương Nguyện Thành Trương Nguyện Thành TP HỒ CHÍ MINH, THÁNG 06/2019 Ứng dụng Hóa Tính toán thiết kế vật liệu hữu bán dẫn MỤC LỤC Trang MỞ ĐẦU 03 ĐƠN VỊ THỰC HIỆN 06 KẾT QUẢ NGHIÊN CỨU 07 I Báo cáo khoa học 07 II Tài liệu khoa học xuất 54 III Chương trình giáo dục đào tạo 55 IV Hội nghị, hội thảo 56 V File liệu 57 TÀI LIỆU THAM KHẢO 58 CÁC PHỤ LỤC 63 PHỤ LỤC 1: “Quantitative Structure–Property Relationships for the Electronic Properties of Polycyclic Aromatic Hydrocarbons” PHỤ LỤC 2: “Quantum Mechanical-Based Quantitative Structure–Property Relationships for Electronic Properties of Two Large Classes of Organic Semiconductor Materials: Polycyclic Aromatic Hydrocarbons and Thienoacenes” PHỤ LỤC 3: “Nature of Interlayer Carbon-Carbon Covalent Bonding in Graphene-Based Materials” Viện Khoa học Cơng nghệ Tính tốn TP Hồ Chí Minh Page Ứng dụng Hóa Tính tốn thiết kế vật liệu hữu bán dẫn MỞ ĐẦU Vật liệu bán dẫn hữu với ứng dụng đầy hứa hẹn mở kỉ nguyên phát triển công nghệ điện tử hữu cơ, đồng thời thay vị trí vốn có công nghệ silicon Được biết đến giá thành sản xuất thấp, có khả tạo thành dạng film mỏng, vật liệu hữu điện tử góp phần tạo nên thiết bị linh động nhờ vào công nghệ in đại OFETs (organic filed-effect transitors), OTFTs (organic thinfilm transitor), OLEDs (organic light-emitting diodes), OPVs (organic photovotaics) đối tượng phổ biến phân nhóm vật liệu hữu bán dẫn Mỗi đối tượng có ứng dụng vai trò sử dụng khác trình chế tạo thiết bị điện tử Ví dụ như, OLEDs dùng để chế tạo hình trình chiếu Tivi, đạt kích thước siêu mỏng màu sắc siêu thực; hay OFETs sở hữu hiệu cao tính lưu động sử dụng vai trò thiết bị khuếch đại điều khiển điện năng, sánh ngang với vật liệu silicon vơ định hình, v.v Hình 1: Ứng dụng vật liệu hữu bán dẫn Việc ứng dụng vật liệu hữu điện tử vào công nghệ sản xuất phải thỏa mãn yêu cầu khắt khe tính bền điều kiện có tác nhân oxi hóa (thường oxi), chuyển Viện Khoa học Cơng nghệ Tính tốn TP Hồ Chí Minh Page Ứng dụng Hóa Tính tốn thiết kế vật liệu hữu bán dẫn dời electron lên mức lượng diễn thuận lợi có chọn lọc, khả dẫn diện, dẫn nhiệt Các tiêu chuẩn hầu hết phải đáp ứng cách đầy đủ loại vật liệu mang lại hiệu tốt trình sử dụng Vì vậy, việc khảo sát thông số lượng ảnh hưởng đến tính yêu cầu đặt cho nhà nghiên cứu Trong đó, đối tượng quan tâm: lượng vùng cấm (band gap), ion hóa (ionization potential-IP), lực electron (electron affinitiesEA); với Band gap ứng với chuyển dời thấp lấy gần khoảng cách “orbital phân tử chứa electron có mức lượng cao nhất” (Highest Occupied Molecular Orbital-HOMO) “orbital phân tử khơng chứa electron có mức lượng thấp nhất” (Lowest Unoccupied Molecular Orbital-LUMO); IP EA có giá trị xấp xỉ độ lớn mức lượng HOMO, LUMO Giá trị thông số lượng tính tốn dựa thành tựu Hóa lượng tử, mà biết đến nhiều phương pháp phím hàm mật độ DFT (density functional theory) Tuy nhiên, với mục tiêu thiết kế, nhằm tìm loại vật liệu có giá trị sử dụng tốt với thơng số lượng ưu việt, khối lượng công việc phải thực phạm vi xây dựng phân tử tính tốn cấu trúc vô to lớn Điều này, đặt thách thức nhà nghiên cứu, đặc biệt nhà khoa học thực nghiệm thường đặt yêu cầu nhanh chóng tin cậy kết Trong nghiên cứu này, thiết kế thành cơng mơ hình Quan hệ Định lượng Cấu trúc Tính chất Phân tử (Quantitative Structure-Property Relationship) nhằm phục vụ cho việc dự đoán tính chất điện tử phân tử nhóm vật liệu Hữu bán dẫn hợp chất đa vòng thơm (Polycyclic Aromatic Hydrocarbon) vật liệu thiophene (Thienoacenes) Đồng thời, phát vấn đề trình Viện Khoa học Cơng nghệ Tính tốn TP Hồ Chí Minh Page Ứng dụng Hóa Tính tốn thiết kế vật liệu hữu bán dẫn khảo sát nghiên cứu dạng liên kết trình đánh giá tương tác lớp vật liệu Graphene Lời cảm ơn đến ICST Trong trình thực đề tài xin gửi lời cám ơn chân thành sâu sắc đến Viện Khoa học Cơng nghệ Tính tốn (ICST) hỗ trợ từ sở hạ tầng tính tốn, Sở Khoa học Cơng nghệ TpHCM cung cấp kinh phí trì tiến hành đề tài Chúng hi vọng có hội tiếp nối đề tài tới mang lại nhiều thành phát triển khoa học công nghệ TpHCM nói riêng nước Việt Nam nói chung Trân trọng cám ơn! Viện Khoa học Cơng nghệ Tính tốn TP Hồ Chí Minh Page Ứng dụng Hóa Tính tốn thiết kế vật liệu hữu bán dẫn ĐƠN VỊ THỰC HIỆN Phịng thí nghiệm: Hạ tầng Tính tốn Chủ nhiệm nhiệm vụ: GS.TS Trương Nguyện Thành Thành viên nhiệm vụ: Nguyễn Hoàng Lâm Nguyễn Thị Hoài Phan Thị Ngọc Lan Trần Thị Hải Lưu Huỳnh Văn Tuân Cơ quan phối hợp: Viện Khoa học Cơng nghệ Tính tốn TP Hồ Chí Minh Page Ứng dụng Hóa Tính tốn thiết kế vật liệu hữu bán dẫn KẾT QUẢ NGHIÊN CỨU I BÁO CÁO KHOA HỌC 1.1 Giới thiệu Vật liệu bán dẫn hữu mở kỷ nguyên cho phát triển công nghệ điện tử hữu dự đoán thay cho vật liệu silicon vô định hình.1-5 Có bốn nhóm vật liệu bán dẫn hữu cơ: diode phát quang hữu (OLEDs), transistor hiệu ứng trường hữu cơ, transistor màng mỏng hữu quang điện hữu cơ, số chúng có tính chất vật lý khác Vật liệu bán hữu dùng để chế tạo vật liệu điện tử phải bền với tác nhân oxi hóa (oxygen) có đủ độ linh động điện tích tính chất quang điện tử tốt 5,6 Để sàng lọc vật liệu thỏa mãn yêu cầu này, tính chất phân tử lượng kích thích thấp nhất, ion hóa (Ionization Potential-IP), lực electron (Electron Affinities-EA) thường sử dụng Các tính chất dự đốn thường lệ từ phép tính xác ngun lý hóa lượng tử lý thuyết hàm mật độ (Density Functional Theory-DFT) Tuy nhiên, việc tốn nhiều thời gian tài ngun tính tốn Một số lượng phương pháp hiệu chi phí dược khn khổ hóa lượng tử phát triển để dự đốn tính chất điện tử vật liệu bán dẫn hữu Ví dụ, nghiên cứu trước đây7 đề xuất orbital phân tử bán thực nghiệm sử dụng để dự đoán chiều hướng lượng vùng cấm cho phân tử lớp cho trước tính chất khác so với tính tốn trước qua xác lý thuyết hàm mật độ (DFT) việc thay đổi số Phép gần khác kết hợp mơ hình solvation với DFT để thu hiệu ứng pha ngưng tụ việc dự đốn tính chất điện tử vật rắn hữu cơ.8 Một phép tính tốn gần phổ biến việc sử dụng học lượng tử (Quantum Mechanics-QM) mơ hình Viện Khoa học Cơng nghệ Tính tốn TP Hồ Chí Minh Page Ứng dụng Hóa Tính tốn thiết kế vật liệu hữu bán dẫn học phân tử cho việc nghiên cứu đặc điểm bán dẫn hữu cơ.9 Về ứng dụng, nghiên cứu hiệu cao để định lượng khác lượng vùng cấm phân tử hydrocacbon thơm đa vịng lập tinh thể chúng.10 Hơn nữa, khả phân cực tĩnh điện khả ion hóa sử dụng mơ tả tương quan với khoảng cách orbital phân tử có chứa electron có lượng cao (Highest Occupied Molecular Orbital-HOMO) orbital không chứa electron có lượng thấp (Lowest Unoccupied Molecular Orbital - LUMO) halogenobenzenes.11 Tuy nhiên, tất phương pháp dựa tảng học lượng tử cần thời gian nỗ lực để tính tốn tính chất hợp chất Do đó, điều khơng kỳ vịng giai đoạn dự kiến ban đầu nhà thực nghiệm cần ước tính hợp lý cho lượng lớn ứng cử viên có để có danh sách ngắn từ họ xếp thứ hạng chúng tính tốn hóa lượng tử xác trước thực thí nghiệm thật Phương pháp luận phân tích liệu, “Quan hệ cấu trúc-tính chất định lượng” (Quantitative Structure-Property Relationship-QSPR),12 áp dụng rộng rãi thiết kế thuốc, dược phẩm cho việc sàng lọc hoạt động sinh học, tính chất hóa lý, phản ứng độc hại QSPR cung cấp quan hệ thực nghiệm tính chất cấu trúc hóa học đối tượng vật lý, hóa học hay sinh học, điều yêu cầu thêm tính tốn thí nghiệm Hiện có vài mơ hình QSPR sẵn có để dự đốn tính chất vật liệu bán dẫn hữu cơ, nhiệt độ thủy tinh hóa vật liệu OLED,13 cho tỷ lệ chuyển điện tích hydrocacbon thơm đa vịng (PAHs),14 cho việc dự đốn tính độc hại PAHs.15 Nó biết rộng rãi PAH thành phần nhiều vật liệu bán dẫn Viện Khoa học Cơng nghệ Tính tốn TP Hồ Chí Minh Page Ứng dụng Hóa Tính tốn thiết kế vật liệu hữu bán dẫn hữu ứng dụng thực tế Chẳng hạn, PAH thành phần cho việc tổng hợp thienoacene tetraarylethenes chế tạo vật liệu OLED.3,16-18 Với tất kiến thức chúng tơi, chưa có mơ hình QSPR có sẵn cho việc dự đốn tính chất điện tử quan trọng, là, lượng vùng cấm, khả ion hóa, lực electron cho phân tử thuộc phân lớp thienoacenes PAHs Mục đích nghiên cứu để phát triển mơ hình QSPR cho việc dự đốn tính chất điện tử lớp PAH thienoacenes Mơ hình QSPR hỗ trợ tốt việc thiết kế vật liệu bán dẫn hữu PAHs thienoacenes 1.2 Chi tiết tính tốn Cho phân tử liệu, cấu trúc chiều tối ưu hóa hồn toàn lý thuyết bán thực nghiệm MO PM7 sử dụng MOPAC2016 37 package phương pháp B3LYP/6-31+G(d) DFT sử dụng chương trình Gaussian 09 Phương pháp B3LYP/6-31+G(d) biết để dự đốn xác tính toán lượng orbital biên.38-40 Phương pháp PM7 sử dụng để kiểm chứng điều lúc trước độ lệch tương đối tính tốn khoảng cách HOMO-LUMO với phép tính tốn DFT cho phân tử lớp Khoảng cách HOMO-LUMO sử dụng để ước lượng lượng vùng cấm Dựa theo lý thuyết Koopman, khả ion hóa ước tính giá trị âm lượng orbital HOMO, tương tự vậy, lực electron ước tính giá trị âm lượng orbital LUMO.32 1.3 Mô hình Độ xen phủ orbital pi (Degree of orbital overlap-DPO) Có thực tế biết đến phổ biến hóa lý chênh lệch mức lượng HOMO-LUMO polyethylene liên hợp butadiene mơ hình hóa hạt giếng 1D với chiều dài giếng hiệu Với lý lẽ tương Viện Khoa học Công nghệ Tính tốn TP Hồ Chí Minh Page ACS Omega Article reported by Winkler and Le.21 or in combination with the artificial network model and support vector machine for predicting electroluminescence of a small set of OLED structures.22 Regarding OLED applications, the QSPR approach was used to study the glass transition temperature.23,24 QSPR models were also developed for predictions of critical electronic and thermomechanical properties of crystalline materials25,26 or energetic materials such as nitro-organic compounds.27 Also, screening metal organic framework materials for CO2 capture was studied by applying the QSPR approach with advanced machine learning algorithms.28 However, there have not been many studies regarding QSPR applications for predictions of electronic properties of organic semiconductor materials Particularly, for thienoacene, there has not been any QSPR study for its electronic properties reported till today In our recent study,29 we proposed a new model called “degree of πorbital overlap” (DPO) based on a quantum mechanical particle in two-dimensional (2D) box to develop QSPR for electronic properties of PAHs With only four topological parameters, the DPO model was able to predict electronic properties of PAHs in the particular band gap, ionization potential (IP), and electron affinity (EA) to within 0.1 eV accuracy on average compared to the explicitly calculated data In this study, we extend the DPO model to the thienoacene molecular class and further examined the accuracy of the DPO model Figure Segment of structure III and segment of IV are chosen to be the reference segments Figure DPO values of the reference segments containing only benzene rings and a thiophene ring Figure Illustration of how topological parameters d and d* are assigned fused bonds COMPUTATIONAL DETAILS 2.1 Data Sets In this study, the thienoacene class is divided into two separate subclasses: 1T-subclass and 2T-subclass Figure Illustration of how topological parameters b and b* are assigned fused bonds Figure Illustration of how topological parameters c and c* are assigned fused bonds Figure Building blocks for constructing a given thienoacene molecule of the 1T-subclass (a−d) are simplified models showing how these building blocks are related to the DPO a−d parameters Fused bonds are highlighted in bold groups 1T-subclass molecules consist of one thiophene ring with benzenes, and the 2T-subclass is those of two thiophene rings The structures having to rings of two subclasses constitute the development set of total 81 molecules for building the QSPRs, and those having 7−8 rings of the subclasses make up the test set of total 82 molecules for assessing the accuracy of the QSPRs 2.2 Computational Methods Geometries of all molecules in two data sets are fully optimized, and their electronic properties are calculated by the DFT B3LYP/6-31+G(d) level Figure Segment of structure I and segment of structure II are the reference segments Fused bonds are highlighted in bold 7517 DOI: 10.1021/acsomega.9b00513 ACS Omega 2019, 4, 7516−7523 ACS Omega Article where (nx,ny) are the quantum numbers of the HOMO orbital; h is the Planck constant, me is the mass of the electron From our previous study, we have shown that the QSRP for the IP of the PAH class has the form IP = −εHOMO = αXDPO + β (2) where α and β are fitting constants to DFT calculated values Comparing between and 2, the DPO value for a given linear acene is related to those of the 2D box by | l o nx o 2o n XDPO ∝ o + m y } o o o l2 o n ~ (3) Below, we show how XDPO is determined empirically 2.3.1 Rule for Determining DPO Value of a Thienoacene Structure In order to apply the DPO model for predicting electronic properties, namely, the band gap, IP, and EA of a given thienoacene molecule, one must first determine its DPO value according to the following procedure Step 1: Determine the reference segment by applying the following rules in the sequential order till a distinct reference segment is found a The segment with the largest number of fused rings (or fused bonds) is the reference segment b If all segments in the molecule have the same size, the segment with the largest number of parallel-fused bonds orthogonal to its direction is the reference segment Furthermore, the segment consisting of only benzenes is preferred over that having thiophene rings c If rules (a) and (b) not yield a unique segment, then the segment with the least number of overlayers is the reference segment For example, for the two thienoacenes shown in Figure 2, segment of structure I has the largest number of fused rings; therefore, it is the reference segment according to rule (a) In structure II, both segments and have the same number of fused rings; however, segment contains only benzenes and thus is preferred to be the reference segment In Figure 3, structure III has three segments with the same size According to rule (a), segments and are preferred but have the same size Using rule (b), segment of structure III is selected to be the reference segment because it has a larger number of parallel-fused bonds orthogonal to the reference direction In structure IV, in Figure 3, both rules (a) and (b) not yield a unique segment In this case, rule (c) helps to select segment to be the reference segment In the previous study, we described how to calculate the DPO value for any PAH molecule Here, we review how it is done; therefore, the instruction for assigning the DPO value for any thienoacene is easier to follow Each of the fused bonds in a PAH or thienoacene is assigned a value, a topological parameter for its contribution to the total DPO value Below is how we assign a topological value to each fused bond Step 2: Assigning a DPO topological value for each fused bond a For the reference segment that contains only benzene rings, starting from the leftmost, each fused bond has a value successively of 1, − a, − 2a, − 3a, and so on where a is the topological parameter for the PAH class If there is a thiophene ring attached on the reference segment, then the total DPO for this segment is subtracted by the parameter a*, shown in Figure Figure Examples of how to assign DPO parameters to fused bonds of theory This level of theory is known to predict frontier orbital energies accurately.3,4,30,31 The IP is estimated by the negative value of the highest occupied molecular orbital (HOMO) energy, and similarly, the EA is estimated by the negative value of the lowest unoccupied molecular orbital (LUMO) according to Koopman’s theory The HOMO−LUMO gap is used to estimate the band gap.32 2.3 Quantum Mechanical-Based DPO Model It is well known in physical chemistry that the HOMO−LUMO gap of a conjugated polyethylene such as butadiene can be modeled by a particle in a one-dimensional box model with an effective box length With a similar argument, our recent study29 suggested that the DPO model based on a simplified quantum mechanical particle in a 2D box framework for developing QSPRs for electronic properties of PAHs In the DPO model, a given PAH can be constructed by stacking the benzene ring (as building blocks) in four different ways, and thus the entire PAH molecular space can be represented by four topological parameters.29 For thienoacenes, one or more benzene rings are on the rim of a PAH that are replaced by thiophene rings For this reason, it is reasonable to suggest that the DPO model for thienoacenes can be constructed on top of that for PAHs In particular, the construct of the 1T-subclass of thienoacenes where a benzene ring is replaced by a thiophene ring is shown in Figure The cartoons on the right side of Figure illustrates how π electrons in thienoacene molecules can be modeled as the particle in a 2D box with more complicated shapes To see the direct link between the DPO model with the 2D box, let us assume benzene as a square 2D box of length d A linear acene of l benzene rings can be modeled by stacking l square boxes along the x-axis similar to Figure 1a above The HOMO orbital energy of the linear acene within the quantum mechanical 2D box model is given by | h2 ln o o x εHOMO = o + ny o m } o o ol o 8med (1) n ~ 7518 DOI: 10.1021/acsomega.9b00513 ACS Omega 2019, 4, 7516−7523 ACS Omega Article b For the other segments, there are three types: Type 1: For a segment that is paralleled to the reference one, similar assignments of the base values, that is, 1, (1 − a) and (1 − 2a) are used However, each fused bond is then adjusted by a scaling factor of dk, where k is the order of the layer above or below the segment including the first parameter assigned to fused bonds, that is, and d is also a parameter for the PAH class If a benzene ring is replaced by a thiophene ring in this segment, the scaling parameter d* is used instead Figure shows how parameter d or d* are used Type 2: For a segment with its fused bonds that form a 60° angle with the reference one, these fused bonds are assigned with the topological value b if the segment has all benzene rings For each subsequent parallel-fused bond, its value is scaled by a factor d or d* if a thiophene is at the end of the segment as shown in the top row of Figure However, when a thiophene ring is attached on the reference segment at an angle or a small benzene ring segment is fused on the other side of thiophene, these fused bonds are assigned to topological parameter b* as shown in the bottom-row structures in Figure Type 3: For segment with its fused bonds form a 120° angle with those of the reference segment, and these fused bonds are assigned by topological parameter c Similar to type 2, for each subsequent parallel-fused bond, its value is scaled by factor d or d* if a thiophene is attached at the end of the segment as shown in Figure If a thiophene ring is attached to the benzene side on the segment as shown on the last structures of Figure 7, the fused bond is assigned to the topological parameter c* instead For the PAH class, the topological parameters of a, b, c, and d determined from our previous study are 0.05, −1/4, +1/3, and +1/3, respectively With the similar procedure of using a small set of molecules that allows the independent optimization of each parameter, for the thienoacene class, the topological parameters a*, b*, c*, and d* are 0.50, 0.0, 0.0, and 0.15, respectively Consequently, we have six nonzero topological parameters in order to determine the DPO value for any PAH or thienoacene molecule Step 3: The total DPO value for a given molecule is the sum of all topological values assigned to all fused bonds Examples for assigning the DPO value for each fused bond and their total values are given below for six different thienoacene molecules The total DPO values of compounds A = 2.28, B = 2.48, C = 1.78, D = 2.42, E = 1.47, and F = 2.64 are shown in Figure Figure Plots of linear correlations between DPO values and (A) HOMO−LUMO gaps, (B) IPs, and (C) electron affinities of thienoacenes from the development set of the 1T-subclass It is interesting to note that the slopes and intercepts of all linear equations for both thienoacenes and PAHs are very similar in magnitude As shown in Figure 11, they are within the uncertainty of the linear fit This indicates that the DPO model is able to capture the correct physics of the aromatic systems and thus all aromatic systems can share the same QSPRs For this reason, we used the QSPRs of PAH for analyzing the accuracy of the DPO model for both the thienoacenes and PAH classes 3.2 Accuracy of DPO-Based QSPRs To assess the accuracy and predictability of DPO-based QSPRs for the electronic properties of these thienoacene subclasses, electronic properties of all molecules in the test set were plotted against those predicted by QSPRs, as shown in Figure 12A−C Note QSPRs of PAH are used for all assessments below Root-mean-square differences (RMSDs) between QSPRpredicted and DFT explicitly calculated properties for thienoacenes in the test set are all less than 0.1 eV This is even within the accuracy of the DFT level of theory These results are consistent with our previous results for PAH, though here we used the PAH QSPRs to further illustrate that all aromatic molecules can share same QSPRs To further illustrate this point, Figure 13 shows the QSPR-predicted and DFT explicitly calculated properties for all PAHs (34 molecules) and RESULTS AND DISCUSSIONS 3.1 DPO-Based QSPR Linear correlations between DPO values and the three electronic properties of 1-T thienoacene and 2-T thienoacene classes are shown in Figures 9A−C and 10A−C, respectively These figures show excellent linear correlations between DPOs and the electronic properties of thienoacenes with the corresponding correlation coefficients (R2) all greater than 0.9 Compared to PAHs results, almost all R2 values of the 1Tsubclass and 2T-subclass are in a similar level of correlations as those of PAHs in our previous study Linear equations for these correlations of the band gap, IP, and EA properties as functions of the DPO values are summarized in Table along with those for PAH from the previous study 7519 DOI: 10.1021/acsomega.9b00513 ACS Omega 2019, 4, 7516−7523 ACS Omega Article Figure 10 Plots of linear correlations between DPO values and (A) HOMO−LUMO gaps, (B) IPs, and (C) electron affinities of thienoacenes from the development set of the 2T-subclass Figure 11 Plots of linear QSPRs for thienoacenes: (A) HOMO− LUMO gaps, (B) IPs, and (C) electron affinities thienoacenes (82 molecules) in both test sets using the same QSPR equations from PAH Again RMSDs for all properties are less than 0.1 eV These results suggest that the DPO model is able to capture the correct physics of electronic properties of aromatic molecules, and thus their properties can be modeled by one set of QSPRs Note that the current DPO model has only six topological parameters for both PAH and thienoacenes To further examine the range of applicability of the model, Figure 14 shows QSPR predicted versus DFT explicitly calculated electronic properties for a number of thienoacenes with three and four thiophene rings using the PAH QSPRs Note these thienoacenes are not part of the QSPR development set nor the test set The results suggest that our DPO-based QSPR model can be applied to all thienoacenes that have planar structures with similar accuracy For nonplanar structures, the errors are larger due to the disruption in the resonance structure of the molecule The issue with nonplanarity in the DPO-based QSPR model has been addressed in detail in our previous study 3.3 How To Use DPO-Based QSPRs For any given PAH or thienoacene, the following procedure should be used: (a) identify all fused bonds and then select the reference segment; (b) assign a DPO topological parameter to each fused bond according to the rule described above; and (c) sum all of these values to give the total DPO value of the structure Subsequently, use the QSPRs for PAH in Table with the calculated DPO value to predict the band gap, IP, and EA of the molecule Table QSPR Equations for Band Gap, IP, and EA of PAHs and Thienoacenes (all are in eV) QSPR equation electronic property 1T-subclass 2T-subclass PAHs29 band gap IP EA y = −0.76x + 4.92 y = −0.35x + 6.14 y = +0.41x + 1.22 y = −0.63x + 4.67 y = −0.30x + 5.99 y = +0.33x + 1.31 y = −0.65x + 4.68 y = −0.30x + 6.04 y = +0.35x + 1.36 7520 DOI: 10.1021/acsomega.9b00513 ACS Omega 2019, 4, 7516−7523 ACS Omega Article Figure 12 Plots of the QSPR predicted vs DFT explicitly calculated electronic properties for thienoacenes in the test set (A) HOMO− LUMO gaps, (B) IPs, and (C) electron affinities Figure 13 Plots of QSPR-predicted vs DFT explicitly calculated electronic properties of PAHs and thienoacenes: (A) HOMO−LUMO gaps, (B) IPs, and (C) electron affinities CONCLUSIONS In this study, we applied the DPO model proposed earlier to develop QSPR for band gaps, IPs, and electron affinities of thienoacenes Electronic properties were calculated at the B3LYP/6-31+G(d) level of theory and are used to develop the QSPRs as well as to assess its accuracy for the thienoacene class We found that QSPRs for thienoacene and those for PAH found in our previous study are almost the same within the uncertainty of the calculations This indicates that the DPO model is able to capture the correct physics of electronic properties of aromatic molecules so that with only six nonzero topological parameters, the DPO model can yield a single set of linear dependence of electronic properties for both the PAH and thienoacenes classes to within the accuracy of 0.1 eV of the DFT results These results suggest the possibility for applying the DPO model to other conjugated classes of molecules in addition to other aromatic classes It will be the subject of our future studies 7521 DOI: 10.1021/acsomega.9b00513 ACS Omega 2019, 4, 7516−7523 ACS Omega Article ■ properties for seven to eight fused ring structures of 1Tsubclass thienoacene; and calculated Egap, IP, and EA (in eV) properties for seven to eight fused ring structures of 2T-subclass thienoacene (PDF) AUTHOR INFORMATION Corresponding Author *E-mail: Thanh.Truong@utah.edu ORCID Thanh N Truong: 0000-0003-1832-1526 Author Contributions All calculations are conducted and written in this manuscript All authors have read and approved the final manuscript Funding This work is supported in part by funding from The Office of Science and Technology, Ho Chi Minh City, Vietnam via the Institute of Computational Science and Technology at Ho Chi Minh City with the number of contract: 35/2017/HĐKHCNTT Notes The authors declare no competing financial interest ■ ■ ACKNOWLEDGMENTS Authors thank the University of Utah Center for HighPerformance Computing for computing resources ABBREVIATIONS QSPR, quantitative structure property relationships; PAHs, polycyclic aromatic hydrocarbons; DFT, density functional theory; DPO, degree of π-orbital overlap; OLEDs, organic lightemitting diodes; OFETs, organic field-effect transistors; OTFTs, organic thin-film transistors; OPVs, organic photovoltaics; IP, ionization potential; EA, electron affinity; HOMO, highest occupied molecular orbital; LUMO, lowest unoccupied molecular orbital; RMSD, root-mean-square difference ■ Figure 14 Plots of QSPR predicted vs DFT explicitly calculated properties of thienoacene molecules containing three to four thiophene rings: (A) HOMO−LUMO gaps, (B) IPs, and (C) EAs The black crosses are for nonplanar molecules and red dots are for planar ones The RMSD values for planar molecules are in parentheses ■ REFERENCES (1) Mori, T.; Nishimura, T.; Yamamoto, T.; Doi, I.; Miyazaki, E.; Osaka, I.; Takimiya, K Consecutive Thiophene-Annulation Approach to π-Extended Thienoacene-Based Organic Semiconductors with [1]Benzothieno[3,2-b][1]benzothiophene (BTBT) Substructure J Am Chem Soc 2013, 135, 13900−13913 (2) Usta, H.; Lu, G.; Facchetti, A.; Marks, T J Dithienosilole− and Dibenzosilole−Thiophene Copolymers as Semiconductors for Organic Thin-Film Transistors J Am Chem Soc 2006, 128, 9034−9035 (3) Brocks, G.; van den 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5804−5809 ASSOCIATED CONTENT S Supporting Information * The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsomega.9b00513 Thienoacene molecules used for determining DPO parameters; calculated Egap, IP, and EA (in eV) properties for four to six fused ring structures of 1Tsubclass thienoacene; calculated Egap, IP, and EA (in eV) 7522 DOI: 10.1021/acsomega.9b00513 ACS Omega 2019, 4, 7516−7523 ACS Omega Article and design of n-channel organic semiconductors Chem Mater 2004, 16, 4436−4451 (31) Canola, S.; Pecoraro, C.; Negri, F Modeling p-type charge transport in thienoacene analogs of pentacene Theor Chem Acc 2016, 135, 33 (32) Jezowski, S R.; Baer, R.; Monaco, S.; Mora-Perez, C A.; Schatschneider, B Unlocking the electronic genome of halogenobenzenes Phys Chem Chem Phys 2017, 19, 4093−4103 (9) Jacob, M Organic Semiconductors: Past, Present and Future Electronics 2014, 3, 594 (10) Dimitrakopoulos, C D.; Malenfant, P R L Organic thin 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Nguyen1 · Thanh N. Truong2 Received: February 2019 / Accepted: 29 April 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract This study provides a fundamental understanding of the nature of C–C interlayer covalent bonding in graphene-based materials by using the dispersion-corrected density functional theory B3LYP-D3/6-31+G(2df,p)//B3LYP-D3/6-31G(d,p) (single-point energies at the larger 6-31+G(2df,p) basis set using fully optimized geometries at the B3LYP-D3/6-31G(d,p) level) With a bilayer hydrogenated graphene model, a partial covalent bonding was found upon dehydrogenation from opposite layers between interior carbon atoms even at the distance of greater than 4.00 Å To facilitate such bonding carbon atoms must transform from its sp3 to sp2 hybridization upon dehydrogenation so that pz orbitals can extend farther for better overlap at a large distance The structure containing a single partial covalent bond was found to be less stable compared to its nonbonding triplet state However, adding normal interlayer covalent bonds at the edge helps to stabilize such partial bond In addition, forming a partial interlayer covalent bond greatly reduces band gap to 1 eV, whereas the formation of a normal covalent bond causes only a slight change in the band gap Thus, controlling the population of the two types of interlayer bonds can, therefore, open up a promising way to control the band gap for organic semiconductor materials Keywords C–C interlayer covalent bonds · Partial covalent bonding · Graphene-based materials · Band gap controlling 1 Introduction A stable single C–C sigma bond is known to form from overlapping between two sp3 hybridized carbon atoms A typical C–C sigma bond in alkanes has an average distance of 1.54 Å and can even reach to 1.71 Å under steric effects [1] However, experimental studies [2–5] have demonstrated the existence of covalent C–C interlayer bonds between adjacent layers of graphite and graphene-based materials where the layer spacing was known to be longer than typical CC single bonds The nature of such interlayer sigma bonds has not yet been well studied Fundamental understanding of interlayer bonds is crucial for broadening applications of graphene-based materials In fact, there are possibilities of controlling thermal [6, 7], mechanical [8–10] and electrical properties [11–14] * Thanh N Truong Thanh.Truong@utah.edu Institute for Computational Science and Technology, Ho Chi Minh City, Vietnam Department of Chemistry, University of Utah, 315 South 1400 East, rm 2020, Salt Lake City, UT, USA of graphene-based materials by using C–C interlayer bonds through chemical functionalization For instance, thermal conductivity can be controlled by changing density and topological configuration of these interlayer bonds, and thus it can lead to potential important thermoelectric applications [7] To the best of our knowledge, fundamental understanding of interlayer bonding has been limited It is worth to note that under the ambient temperature σ-bonds between carbons of adjacent layers were experimentally observed in graphite [2] An experimental study by Mao et al [2] showed that half of the π-bonds between graphite layers convert to interlayer σ-bonds at 17 gigapascals Rajasekaran et al [5] confirmed the existence of interlayer covalent bonding from changes in X-rays adsorption spectra of hydrogenated multi-layer graphene which is similar to those of cold-compressed graphite done by Mao et al [2] Additionally, theoretical studies [5, 15, 16] have suggested that chemical functionalization such as hydrogenation results in the formation of covalent sp3 C–C bonds between the graphene layers; however, systematic electronic structure calculations with bonding analysis for investigating fundamental nature of these covalent bonds have not been done 13 Vol.:(0123456789) 70 Page of In this study, we have carried out systematic density functional theory study on the nature of interlayer C–C covalent bond formation In particular, we examined the effects of bonding between different sites (edge or interior sites) and the effect of multiple interlayer bonding 2 Computational details A bilayer hydrogenated graphene (HG, also known as graphane) physical model was used to examine the interlayer bonding resulted from dehydrogenation of hydrogen atoms from opposite layers The model consists of two layers of six six-member ring carbon as shown in Fig. 1 The product of these processes is a bilayer dehydrogenated graphane (DHG) Two hydrogen atoms were desorbed from the same carbon centers in order to compare the bonding forming in the cases of singlet and triplet DHG These hydrogen atoms were selected on the opposite layers and are close to mirroring each other so that the corresponding interlayer CC distance is as short as possible Though, the choice among the edge and interior centers is random A similar singlelayer model was used effectively in our previous study of hydrogen migration and desorption on/from graphene [17] All stable structures were fully optimized using the density functional theory method B3LYP [18, 19] including Grimme’s D3-dispersion correction [20] with the 6-31G(d,p) basis set Energies were improved by single-point calculations at the same B3LYP-D3 level of theory but with the much larger 6-31+G(2df,p) basis set including diffuse and higher f polarization functions for carbon atoms using the fully optimized structures obtained at the 6-31G(d,p) basis set The spin-unrestricted UB3LYP method was employed in the case of triplet and quintet states It should be noted that London dispersion was found to be an important Theoretical Chemistry Accounts interaction between graphane layers [21] Natural bond orbital (NBO) analyses at the same level of theory B3LYPD3/6-31+G(2df,p) were carried out to characterize bond order and hybridization of all stable structures In addition, time-dependent density functional theory (TD-DFT) at the 6-31G(d,p) basis set was also performed to examine different electronic states of these molecular systems All calculations were performed by using Gaussian 09 package [22] 3 Results and discussion Desorption of two hydrogen atoms on HG can lead to the formation of either singlet or triplet state interior/edge DHG, where interior and edge are two terms used to indicate the position where hydrogen atoms are desorbed The singlet and triplet structures of interior bilayer DHG are shown in Fig. 2, while those of edge bilayer DHG are presented in Fig. 3 In these figures, d layers is defined as the average distance between two layers while dC–C is the distance between the two carbon atoms that form the C–C interlayer bonding Wang and co-workers [21] suggested that the interaction between HG layers consists of intermolecular dispersion, charge transfer binding, electrostatic interaction, and Pauli repulsion Comparing HG before and after dehydrogenation (see Figs. 1, 2), the interlayer spacing dlayers is decreased upon desorption of hydrogen molecule This suggests that dehydrogenation leads to more attraction between the layers either by the bond formation in the singlet state or by spin-spin coupling in the triplet state Note that the distance dC–C of the singlet DHG structure is found to be noticeably shorter than that of the triplet one This is due to the σ covalent bond formation between the two carbon atoms in the singlet structure as discussed more below Fig. 1 Optimized geometry of bilayer HG calculated at the B3LYP-D3/6-31G(d,p) level a Top view and b side view 13 (2019) 138:70 Theoretical Chemistry Accounts (2019) 138:70 Page of 8 70 Fig. 2 Optimized structures of interior bilayer DHG in the singlet state a top view and b side view and in the triplet state c top view and d side view calculated at the B3LYP-D3/6-31G(d,p) level 3.1 Interlayer sigma bond formation between two interior carbon sites Reaction energies corresponding to the desorption of H molecule from the two opposite interior sites are 473.76 kJ/mol (producing the singlet state DHG) and 358.97 kJ/mol (producing the triplet state DHG) Hence, the results show that the triplet state DHG is more stable than the singlet one by 114.79 kJ/mol (1.19 eV) (see Table 1) This result suggests that spin-spin coupling helps to stabilize the triplet bilayer DHG and its magnitude is larger than the formation of a covalent bond in the singlet state TD-DFT calculations at the singlet structure confirm that the triplet state of DHG is more stable with the vertical excitation energy of 93.59 kJ/mol (0.97 eV) This is also close to the HOMO–LUMO gap of 98.35 kJ/ mol (1.02 eV) of the singlet bilayer DHG These values are in a good agreement with data from the previous study of Muniz and co-workers [13] where the computed band gaps for hydrogenated interlayer-bonded structures range from a few meV up to approximate 1.2 eV [13] Note that the band gap of graphane is known to be about 5.4 eV [23], whereas the HOMO–LUMO gap of the bilayer HG structure in this study (Fig. 1) is 6.84 eV Our results confirm that electronic properties such as band gap can be manipulated by using these interior interlayer bonds It is interesting to point out that experimental observation [2] of interlayer covalent bond formation only under high pressure supports our results of the higher energy singlet structure where such bonding would occur It is also noted that the effects of diffuse and additional f polarization functions in the basis set as shown in Table 1 are relatively small, namely of about 5% of the singlet-triplet splitting energies NBO analyses performed on both singlet and triplet structures indicate that interior interlayer covalent bond is only formed between two carbons in the singlet bilayer DHG The bond order of this C–C interlayer bond is 0.47 even at the considerable long bond distance of 4.38 Å For this reason, we refer to this as partial covalent bond Such bonding also 13 70 Page of Theoretical Chemistry Accounts (2019) 138:70 Fig. 3 Optimized geometry of edge bilayer DHG in the singlet state a top view and b side view and in the triplet state c top view and d side view calculated at the B3LYP-D3/6-31G(d,p) level Table 1 Relative energies of bilayer DHG at different states Type of interlayer covalent bond Spin multiplicity Formation of interlayer bond Relative energies (kJ/mol) Partial interlayer covalent bond (interior sites) Singlet Triplet Singlet Triplet Yes No Yes No 114.79 (120.17) 0.00 0.00 135.89 (142.71) Normal interlayer covalent bond (edge sites) Energies are given in kJ/mol relative to that of the most stable structure Bold lines indicate ground state structures Values in parentheses are from B3LYP-D3/6-31G(d,p) level explains the shortening of the d C–C bond distance of DHG in the singlet state as compared to that of the triplet state (cf Fig. 2) 13 The spin density of triplet structure was calculated and is plotted in Fig. 4, while HOMO and LUMO molecular orbitals of the singlet structure are plotted in Fig. 5b As seen in Theoretical Chemistry Accounts (2019) 138:70 Fig. 4 Plot of spin density of interior bilayer DHG in the triplet state The blue color corresponds to regions of space where the phase of the wave function is positive and vice versa for the green in the negative regions Fig. 4, the spin density shows the locations of the two alpha spin electrons, which are on the two dehydrogenated carbon sites of the triplet DHG structure as expected In the case of singlet structure, there is a positive orbital overlap between Page of 8 70 two dehydrogenated carbon sites (HOMO orbital in Fig. 5b) characterizing a sigma covalent bond Previous studies [5, 15, 16] of graphene-based systems proposed that these interlayer bonds are from sp3 C atoms Leenaerts et al [15] argued that in order to form such interlayer covalent bond in graphite it is necessary for carbon atoms to change their hybridization from sp2 to sp3 via hydrogen adsorption In our graphane HG system, these carbon atoms are already in sp3 hybridization However, our results show that an opposite transformation is required In fact, NBO analysis shows that this partial interlayer covalent bond is a sigma bond formed by overlapping between two orbitals with 96% pz character (out of the plane) from the two sp2 (dehydrogenated) carbon atoms HOMO and LUMO orbitals of HG as well as of the singlet interior DHG are plotted in Fig. 5a, b It is a clear demonstration that HOMO and LUMO of DHG correspond to the sigma bonding and anti-bonding between the two pz orbitals In addition, the electron density of this partial covalent bond (≈ 1.7e) demonstrates that it is rather localized despite the fact that HOMO and LUMO of the corresponding HG are quite delocalized One possible explanation is that unhybridized pz orbitals extend further from the nucleus than that of sp3 orbitals and thus would facilitate greater overlap when two carbons are father apart as in this case (4.38 Å) For this reason, the two carbon atoms transform from sp3 to sp2 upon dehydrogenation to enable such interlayer bonding despite Fig. 5 Plots of HOMO and LUMO molecular orbitals of a bilayer HG, b the singlet interior bilayer DHG (a partial interlayer covalent bond), c the singlet edge bilayer DHG (a normal interlayer covalent bond) and d the singlet bilayer DHG (two interlayer bonds) 13 70 Page of the constraint from the surrounding sp3 nearest neighbor carbon atoms and doing so would further increase the C–C bond distance 3.2 Interlayer sigma bond formation between two edge carbon sites Note that carbon atoms which locate on edge sites of HG easily approach each other because of smaller steric effects Dehydrogenation from these carbon atoms is expected to form a normal interlayer covalent bond Indeed, when two hydrogen atoms are desorbed from edge carbon sites (cf Fig. 3), the edge interlayer bond is also formed at singlet state but in this case, it is a normal covalent bond with a much shorter distance of 1.63 Å Note the singlet structure shown in Fig. 3a, b is the ground state NBO results show that the bond order of such bond is 0.96 which accounts for the stability of singlet bilayer DHG In particular, the singlet structure is more stable than the triplet one by 135.89 kJ/mol (cf Table 1) This is opposite to the case of the partial interlayer covalent bond at interior sites Reaction energies corresponding to H2 desorption processes producing singlet and triplet state DHG are 221.15 and 357.04 kJ/mol, respectively NBO analysis also confirms that this sigma bond is from overlapping between two carbon sp3 orbitals The HOMO–LUMO gap of singlet DHG, in this case, is 645.30 kJ/mol (6.69 eV), which shows a slight decrease compared to the band gap of initial bilayer HG structure of 6.84 eV TD-DFT result of the vertical excitation energy of 695.66 kJ/mol (7.21 eV) is consistent with the HOMO–LUMO gap Comparing with the band gap of infinite graphane of 5.4 eV [23], this type of C–C interlayer covalent bond formation is likely to enlarge the band gap 3.3 Effects of multiple interlayer bonds Here we examine the case where two interlayer bonds can be formed, in particular, one interior and one edge interlayer bonds Note that in order to form this particular structure two desorbed hydrogen atoms on the same layer must be at least four-atom apart; otherwise, double bond formation would be preferred The product bilayer DHG structures corresponding to the three possible states, namely, singlet, triplet and quintet states are shown in Fig. 6 HOMO and LUMO orbitals of the singlet DHG are also illustrated in Fig. 5d NBO results show that the two C–C interlayer bonds consist of one partial covalent bond at distance of 4.08 Å with 13 Theoretical Chemistry Accounts (2019) 138:70 the bond order of 0.50 from the interior sites and one normal covalent bond at distance of 1.60 Å with the greater bond order of 0.98 from the edge sites In the case of multiple interlayer bonds, the singlet state is more stable compared to triplet and quintet state by more than 95 kJ/mol This analysis indicates the formation of normal interlayer covalent bond such as between edge sites would help to stabilize the formation of partial interlayer covalent bond in the interior sites Our conclusion also supports the phenomena which were observed in previous studies [8, 9] The interlayer interaction between two layers of graphene is less stable when isolated interlayer bonds are randomly distributed throughout the structure [8] On the contrary, adding of neighboring interlayer bonds (finite interlayer-bonded domains) would enhance significantly the resistance against shearing [9] 4 Conclusion By examining the nature of interlayer covalent bond formation between a bilayer hydrogenated graphene upon a dehydrogenation using density functional theory, our results extend the current fundamental understanding of chemical bonding In particular, besides the normal sigma covalent bond, it is possible to form a partial covalent bond between interior carbon sites of the opposite layers with bond order around 0.50 and at a rather large distance of order 4.00 Å Examining these individual interlayer bond formations, the normal sigma bonds are, as expected, formed by overlapping between sp3 hybridized carbon atoms at the edge resulting in stable singlet ground state product The partial interlayer bonds are, however, formed by head-to-head overlap between two unhybridized pz orbitals of the two sp2 carbon atoms in the interior sites Due to steric effect, the distance between the two carbon centers is quite large for a normal covalent bond formation; unhybridized pz orbitals, in this case, can facilitate better orbital overlap than the sp3 hybridized orbitals The singlet product is energetically less stable compared to the ground state triplet by 114.79 kJ/mol However, the singlet structure with a partial bond can be stabilized by adding an additional normal sigma covalent bond at the edge We also found that forming partial interlayer bonds can greatly reduce the band gap, whereas forming the normal interlayer covalent bonds results in a slight change in the band gap Therefore, controlling the population of these interlayer bonds can manipulate the band gap for electronic applications Theoretical Chemistry Accounts (2019) 138:70 Page of 8 70 Fig. 6 Optimized geometry of bilayer DHG (four desorbed hydrogen atoms) in a the singlet state, b the triplet state and c the quintet state calculated at B3LYP-D3/6-31G(d,p) level Acknowledgements This work is supported in part by funding from The Office of Science and Technology, Ho Chi Minh City, Vietnam via the Institute of Computational Science and Technology at Ho Chi Minh City with number of contract: 35/2017/HĐ-KHCNTT Computing resources from the University of Utah, Center for High Performance Computing are greatly acknowledged References Fokin AA, Chernish LV, Gunchenko PA, Tikhonchuk EY, Hausmann H, Serafin M, Dahl 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