Sunday, October 27, 2019
Dennis Rader: The BTK Killer
Dennis Rader: The BTK Killer When you hear the words SERIAL KILLER, you instantly think about people like Jeffrey Dahmer, Ed Gein, Ted Bundy, or Charles Manson. You dont think about a family man with a wife and two children, county board member, President of the church congregation council, or a Cub Scout leader. Dennis Rader possessed all of these shining attributes. He also possessed a dark secret. This secret had festered in him from an early age and grew as he got older. Dennis Rader had fantasies about bondage, control, and torture which eventually led to murder. Raders reign of terror began in 1977 and ended with his capture in 2005; almost 30 years later. He labeled his victims as projects.3 He hunted his prey in stages he described as the trolling stage and stalking stage.3 He even called the tools used for his trade his hit kit.3 Dennis Rader was a stone cold killer who had no plans of stopping. The letters BTK stands for Bind, Torture and Kill, which was Raders mode of operation and a name he gave to himself. Throughout the years and in numerous communications with the police, he talked about his need for acknowledgment. In the 1990s BTK had disappeared from sight when, without explanation, he re-emerged in 2004. This re-emergence was more than likely due to his need for acknowledgment or public attention. In 2004, Rader started sending multiple letters, clues, and photos to the authorities that led to his capture and arrest in 2005. In the Beginning Dennis Rader was born on March 9, 1945. His parents were William and Dorothea Rader. His family moved to Wichita Kansas when Dennis was little. While growing up, Rader appeared to be a normal child. He was a member of the Boy Scouts and a church youth group member. He attended Riverview Elementary School1 and was described as a student with withdrawn tendencies.1 Rader later admitted that he developed fantasies about bondage, control and torture from an early age, while still in grade school.1 As he got older, he had fantasies about tying girls up and having his way with them.1 He also admitted to killing cats and dogs as a youth by hanging them.1 He began to perfect the art of hiding his dark secret from everyone at an early age. 1974-The Killing Begins It all started when a family of four, the Otero Family, was brutally and maliciously murdered in their home on January 15th, 1974. These four murders, along with six others, would leave the authorities, media, people of Wichita Kansas, and people around the world baffled and in fear for the next 30 years. A killer was on the loose and Bind, Torture, Kill was his mode of operation. Joseph Sr., Julie, Joseph II, and Josephine Otero were the BTK Killers first victims. Their family consisted of the husband, wife, and 5 children. Only two of the children were murdered and they were the children that were home on the day of the murders. These murders occurred in the early morning hours. Dennis Rader invaded their home at gunpoint and ordered everyone into a bedroom where he tied them up. He tried to kill Joseph Sr. first by putting a bag over his head and pulling tight, but somehow a hole was torn in the bag. He later went back and put another bag over Joseph Sr. head and strangling him with a cord. Julie Otero was the second victim to be killed by Rader. He tried to kill Julie with his hands at first but when that didnt work, he strangled her with a cord. Nine year old Joseph II was the third victim. Joseph was moved to another bedroom and suffocated with two bags placed on his head. The fourth and final victim, on this day, was Josephine Otero. She was eleven year s old. Rader took Josephine to the basement of their house and hung her from the drainage pipe. Rader admitted to having sexual fantasies after she was hung.3 He masturbated on her legs and a pipe near where she was hung. His DNA left at the scene was later matched to other killings. BTKs fifth victim was Katherine Bright. She was killed by Rader in April 1974; just four short months after the Oteros were murdered. She was 21 years old. Radar broke into her house and waited for her to come home but he didnt expect for her brother (Kevin Bright) to be with her. He made her brother tie her up first, and then he tied her brother up in another room in the house. Kathryn put up a fight for her life and was eventually stabbed several times by Rader. She later died in the hospital. Her brother escaped during Raders fight with Kathryn but was shot in the head while he fled. Kevin may be the only person to see the serial killer and live (although his description still didnt help the police capture BTK in the 70s). 1977-The Killing Continues It had been 3 years since the Otero family and Kathryn Bright was brutally murdered by the BTK Killer. His sixth victim was Shirley Vian Relford, 24. Rader admitted in court that Relfords murder was completely random.3 He actually planned on killing a particular person but when he went to knock on the door, no one answered. After continuing to troll the neighborhood, he knocked on one other door and got no response. He approached a little boy, watched what house the little boy went into and followed him. When he got inside the house, he put Shirleys three young children in the bathroom and then tied Shirley up and strangled her. He left his semen on some panties that were found next to her body. December 1977, BTK struck again. This time his victim was Nancy Fox, 25. She was victim number 7 and Rader labeled her as Project Fox Hunt5. He had apparently been watching Fox for a long time, stalking her. He would go by her house several times, rummage through her mailbox to find out what her name was, and stalked her at her job.3 On this night in December, he went by her house and knocked on her door but when no one answered, he broke in. He waited in her house in the kitchen and when she got home, he told her he was going to rape her and tied her to the bed. Afterwards, he strangled her. He left semen on a nightgown that was found next to her body. Rader later described Foxs murder as the perfect hit6(pp. 53) because he said that there was no interference in the killing. 1985-Eight Years Later Eight years after Nancy Fox was murdered, BTK was back on the scene and ready for his next victim. That victim was Marine Hedge, 53. Rader labeled her as Project Cookie.6(pp. 92) The sad part about this murder is that Hedge lived on the same street as Rader; only six doors down to be exact. He broke into her house and waited for her. When she came home, she was not alone. She had a male friend with her so Rader hid out in the house and waited for her male friend to leave. Once her male friend left, Rader strangled her in her bed with his bare hands. Hedge was the first victim where Rader moved the body from the house after killing them. He took her body to his churchs basement and posed it for photographs. Her body was later found in a ditch on the roadside. 1986-Victim #9 On September 16, 1986, Vicki Wegerle became BTKs ninth victim. She was 28 years old. Rader used trickery to get in to Wegerles house. He posed as a telephone repair man3 with a uniform and a hard hat. He called his outfit for this murder his hit clothes.3 When he got into her house, he pulled a gun on her and attacked her. She put up a fight for her life but he eventually overpowered her and strangled her with a nylon sock. He also posed her body for photographs as he had previously done to Hedge. It was later found out that Vicki was not dead when Rader left her house; he only thought she was dead. She later died when the paramedics couldnt revive her. 1991-Final Victim-5 years later BTKs last and final victim was Delores Davis, who was murdered on January 19, 1991. She was 62 years old. By this time, a decade had passed since BTK began his killing spree. Rader had previously cased the place before3 and this time she was in the house. It appears as though Rader had gotten lazy by the 10th murder because he threw a concrete cinder block through Daviss patio glass door and bombarded his way into her house. He made no attempt to conceal the noise that the shattering glass made. He pretended to be a wanted criminal and eventually strangled Davis. She was the second victim that Rader had moved from the location of the murder. Her body was dumped under a bridge. She too was posed and photographed after being killed. Raders mask was left by her face. The Investigation The BTK investigation began in the mid 1970s, spanned the length of 30 years, and concluded with the arrest and conviction of Dennis Rader in 2005. In the early 1980s, the Wichita Police Chief created a secret task force6(pp.86) of special investigators to work on the BTK case. They were the team that hunted BTK. This team was called the Ghostbusters.6(pp. 85) There were tons of calls and tips throughout the BTK investigation. Investigators came up with lists to eliminate and compare suspects. They put together a list with tens of thousands of names 6 (pp.88) This list included men who went to the local college, men who worked with any of the victims, men who were between 21 and 35 years of age in 1974 and lived in the county6(pp. 88), and mostly men with any kind of sex/torture/perverse/stalking behavior on their criminal record. Several of the detectives went door-to-door to most of these suspects houses and asked outright if they would submit to DNA testing. Suspects who were unwi llingly to be tested were placed under surveillance. In the Otero murders, police interviewed more than 1500 people6(pp. 31) to no avail. Police originally thought that organized crime families or drugs may have been involved in the family murders. Some police didnt want to accept the fact that a serial killer may have been on the loose or that there were similarities in the Otero and Bright killings. It wasnt until BTK starting sending the police clues about the murders that they put it all together and realized that a serial killer was on the loose. Three of the victims worked at the same location; Colemans. Even when Kathryns brother Kevin (who survived the attack) gave the police a description of his attacker, they never caught him. Even with all of the man hours and leg work put into the investigation, BTK was not caught back then. From 1991 until 2004, when BTK resumed communication with the police, the trail for the serial killer had gone completely cold. Search and Arrest Warrants and Subpoenas There were several search and arrest warrants issued in the BTK case in the later years. In the beginning, there was mostly list compiling and DNA tests done to eliminate suspects but no definite leads as to who BTK was. There were too many suspects and police kept hitting dead ends. In December 2004, the television station KSN reported that Roger Valadez had been arrested in connection with the BTK killings. The report was based on an anonymous tip that was inaccurate. Mr. Valadez was arrested early that morning on charges of criminal trespassing and housing code violations12 but it was somehow leaked that he was a suspect in the BTK murders. A search warrant was executed on his home. He was cleared by DNA tests of any criminal activity related to the BTK killer.6(pp. 227) Valadez later sued the television station and won. In 2005, police obtained a warrant for the medical records of Raders daughter (Kerri Rader) which was a familial match with semen collected at an earlier crime sc ene.13 His daughters DNA match and other evidence that police had accumulated while surveilling Rader gave them probable cause for a search warrant. Raders home, vehicle, church and office were also searched for evidence after the warrant was executed. Also, a search warrant for Raders DNA was executed after he was arrested. He was cheek swabbed while in police custody. Four swabs were taken; two were immediately sent to the county forensic lab and the other two went to the forensic lab in Topeka, Kansas. 6(pp. 269) Interviews Rader was interviewed by the police in 2005. He talked in the third person as though Dennis Rader was someone else. He ducked questions for many hours. Rader gave away nothing during his interview. He spoke to the detectives as equals, noting that he too was in law enforcement.6 Interrogations In September 1986, Bill Wegerle was interrogated by the police and suspected of killing his wife Vicki Wegerle. He was given two lie detector tests and he failed both.6(pp. 102) He was interrogated for hours and asked a lot of probing questions about his and his wifes relationship. Wegerle told the police that on his way home from work, he saw his own car ride right by him and he saw someone else driving it but he didnt think anything of it at the time.16 They mainly wondered how he sat in the house for forty-five minutes before he found her body.6(pp. 101) The police did not believe Bill initially but later contributed him failing both lie detector tests to the stress of a grieving husband. Dennis Rader was interrogated by FBI profiler Bob Morton and Wichita Police Lt. Ken Landwehr shortly after his arrest in 2005. He was arrested on February 25, 2005 as a suspect in the BTK killings. He was formally charged with the murders on February 28, 2005.9 It was during this interrogation that Dennis Rader confessed to being the BTK killer. His 16 hour confession was given in full and of his own free will and recorded on over 20 DVDs.9 Rader knew that he was going to kill again and he told the officers who interrogated him this. He was already in the process of stalking his next victim when he was arrested. Seizure and Analysis of Forensic Evidence There was a ton of evidence and more than enough to get a conviction once BTK was captured. Due to his sexual perversion, he left semen at most of the locations of his killings. Although BTK wasnt caught until 3 decades later, the case was never closed and police had evidence stored from all of the crime scenes. Rader stayed in contact with police through the years taunting them and sending them clues that would later be used to catch and convict him. For example, Rader was so pleased with himself after he killed Nancy Fox that he called the police the next morning to gloat about it. He spoke 15 words during a three-second span of a seven second recording. The audio quality of the call, taped at a slow speed, so was poor it was not released to the public until August 1979. The tape was sent to the Washington DC, FBI laboratory but it was too brief and distorted by background noise to make a comparison voiceprint.5 This tape was kept as evidence and more than likely presented during R aders trial. Semen was found on or near the bodies of his victims Josephine Otero, Shirley Vian and Nancy Fox; all of the semen was matched to Rader. Also, DNA obtained from fingernail scrapings of Vicki Wegerles left hand matched Raders DNA, eliminating any doubt that he was her murderer. High tech forensic computer detection was used to get evidence off of the disk Rader mailed to a Wichita television station in February 2005. This is how Rader was caught. Using this high tech computer, residual information left over on the disk identified the last person who had used the disk: someone named Dennis. It was also learned that the disk had been used on computers registered to two local organizations, Christ Lutheran Church and Park City Library. An internet search on the churchs name provided the name of the congregations president: Dennis Rader.14 Summary Its sad to say that if he had maintained his silence after his last murder in 1991, BTK would still be a free man today, writing citations and catching dogs for the city of Park City. He probably would have never been caught. But his ego was way too big for his own good, and he just had to let everyone know he was still at large. He wanted to taunt the police with the fact that BTK was still on the loose after 3 decades. His cockiness led to his downfall. Had these murders occurred today, I believe that he would have been caught before he got the chance to kill ten people. Today, we have much more advanced technologies than investigators had in the 70s and ways to gets results faster. Rader left entirely too many clues and had entirely way too much correspondence with the police over the years for them to not have caught him long ago. Some of his murders were way too sloppy and although he had a college education, he didnt appear to be intelligent enough to outsmart 3 decades worth o f police investigators. That is probably the reason why as soon as he re-emerged in 2004, he was caught. Although he planned to kill others, that same year, he never got the chance. Dennis Rader pled guilty to 10 counts of first degree murder and was found guilty and sentenced on August 18, 2005. He was sentenced to 10 consecutive life terms, which require a minimum of 175 years without a chance of parole. Because Kansas had no death penalty at the time the murders were committed, life imprisonment was the maximum penalty allowed by law. His earliest possible release date is February 26, 2180. Rader, 60, will spend the rest of his life at the maximum-security El Dorado Correctional Facility near Wichita. Other cold cases in Kansas were reopened to see if Raders DNA matched crime scenes, but Raders confession was limited to the 10 known victims and police and prosecutors do not believe there were any more victims because of the extensive records and memorabilia he kept on each of his victims.9 During Raders sentencing hearing, the families of the victims were given the chance to give victim impact statements describing how the murders have effected and continues to effect their lives. The families got a chance to speak on behalf of their loved ones who are no longer here because of BTK. C, Si, Ge Doped (6,3) Chiral BNNTs: A Computational Study C, Si, Ge Doped (6,3) Chiral BNNTs: A Computational Study The C, Si, Ge Doped (6,3) Chiral BNNTs: A Computational Study Mohammad Reza Zardoost a,*, Behnam Dehbandib , Marjan Dehbandib Abstract: Electronic structure properties including bond lengths, bond angles, dipole moments (Ã µ), energies, band gaps, NMR parameters of the isotropic and anisotropic chemical shielding parameters for the sites of various atoms were calculated using density functional theory for C , Si , Ge doped (6,3) Chiral BNNTs. The calculations indicated that average bond lengths were as: Ge-N > Si-N > C-N and Ge-B > Si-B > C-B. The dipole moments for C, Si, and Ge doped (6, 3) Chiral BNNTs structures show fairly large changes with respect to the pristine model. Keywords: NMR, Nanotube, DFT, Dipole moment 1. Introduction Since the early times that carbon nanotube (CNT) was discovered by Iijima , the physical, chemical and structural properties and applications of this material have been investigated extensively [2Ã¢â¬â4]. The properties of CNTs are mostly dependent on the tubular diameter, doped atoms in the structure and chirality, which make their synthesis for the specific purposes difficult. A lot of studies have been done in the investigation of stable structures of non-carbon based nanotubes, among them boron-nitride nanotubes (BNNTs) have a great importance . The stable tubular structure of BNNT was initially found by calculations  and later was successfully synthesized . After this time, a large growing number of experimental and theoretical studies, specifically ab initio calculations on carbon-, silicon- and germanium substituted BN nanotubes have been performed on the electronic structures of the BNNTs [8Ã¢â¬â11]. The results show that C, Si and Ge replacements can induce spontaneous magnetization with different deformation in the nanotube . At the present time, nuclear magnetic resonance (NMR) spectroscopy [13-14] is the best technique to study the electronic structure properties of materials. Doping of Chiral BNNTs by C, Si, Ge atoms changes their properties and so the interactions of the nanotube and foreign atoms or molecules. (see Fig. 1). In this work we studied the electronic structure properties, including bond lengths, bond angles, dipole moments (Ã µ), energies, band gaps, and NMR parameters in the C, Si, Ge doped Chiral BNNTs structures. a b c d e f g 2. Computational methods All calculations were performed using Gaussian 98 computational package  with density functional theory (DFT) method using BeckeÃ¢â¬â¢s three-parameter hybrid exchange functions with the correlation functions of Lee, Yang, Parr (B3LYP) [16,17] using 6-31G (d) basis set . Previously it has been found that the calculated NMR parameters at the B3LYP and B3PW91 levels have a good agreement with the experiment . It is shown that B3LYP gives reasonable and even accurate band gap values for nanotubes  so this function is chosen for band gap calculations. In the present study, we considered a pristine (6,3) chiral BNNTs of diameter 6.6 Ãâ¦ and 10.1 Ãâ¦ length. This BNNT model consists of 42 Boron, 42 Nitrogen and 18 hydrogens (B42N42H18) B and N sites of this BNNT are doped by C, Si, Ge (see Fig. 1). We have seven models, namely pristine (Fig. 1a), or with a B or N atom doped by C, i.e., the B-C-B or N-C-N model (Fig. 1b, c), doped by a Si atom, i.e., the B-Si-B or N-Si-N model (Fig. 1d, e), doped by a Ge atom, i.e., the B-Ge-B or N-Ge-N model (Fig. 1f, g). We investigated the influence of the C, Si, and Ge doping on the properties of the (6,3) Chiral BNNTs. The hydrogenated models of the pristine (6,3) Chiral BNNTs and the three atoms doped models of BNNTs consisted of 102 atoms with formulas of B42N42H18 (pristine), CB41N42H18 and CB42N41H18 (B-C-B or N-C-N model), SiB41N42H18 and SiB42N41H18 (B-Si-B or N-Si-N model), GeB41N42H18 and GeB42N41H18 (B-Ge-B or N-Ge-N model). The calculated CS tensors in the principal axis system (PAS) with the order of ÃÆ'33 > ÃÆ'22 > ÃÆ'11  for C, Si, and Ge doping for the investigated models of the (6,3) Chiral BNNTs were converted into measurable NMR parameters (isotropic chemical shielding (CSI) and anisotropic chemical shielding (CSA) p arameters) using Eqs. (1) and (2) , summarized in Tables 3-6. CSI(ppm)= (ÃÆ'11+ ÃÆ'22+ ÃÆ'33) (1) CSA(ppm)= ÃÆ'33(ÃÆ'11+ ÃÆ'22) (2) For NQR parameters, computational calculations do not directly detect experimentally measurable NQR parameters, nuclear quadrupole coupling constant (CQ), and asymmetry parameter (). Therefore, Eqns. (3) and (4) are used to convert the calculated EFG (electric field gradient) tensors in the principal axis system (PAS) with the order of |qzz| > |qyy| > |qxx| to their proportional experimental parameters; CQ is the interaction energy of nuclear electric quadrupole moment () with the EFG tensors at the sites of quadrupole nuclei (Nuclei with nuclear spin angular momentum greater than >1/2), but the asymmetry parameter () is a measure of the EFG tensors, which describes the deviation from tubular symmetry at the sites of quadrupole nuclei. The standard Q value (Q (11B) = 40.59 mb) reported by PyykkÃ ¶  is used in Eq. (3). The NQR parameters of 11B nuclei for the investigated models of the (6,3) BNNTs are summarized in Table 7. (3) (4) 3. Results and discussion 3.1. Structures of the (6,3) Chiral BNNTs The structural properties consisting of the B-N bond lengths, bond angles, dipole moments (Ã µ), energies, and band gaps for the investigated models of the (6,3) Chiral BNNTs are given in Table 1 and Table 2. R1, R2, and R3 are B-X-B and N-X-N bond lengths (doped atom and its neighbors). Ã ±, Ã ², and Ã ³ are B-X-B and N-X-N angles. There are Six forms of C, Si, Ge doped Chiral BNNTs for the (6,3) Chiral model. These calculations indicated that the average of the (X = C, Si, Ge) bond lengths of the B-X-B and N-X-N models is larger than those the pristine models. The reason seems to be increasing of atomic radius going from carbon to Ge. The bond angles produce some structural deformations that are responsible for deformation in structure by changing the doped atom size respect to carbon. For the B-X-B and N-X-N (X = C, Si, Ge) models, the diameter values are larger than those the pristine models. It has worth to be noted that the significant changes of geometries are just for those atoms placed in the nearest neighborhood of X atom and those of other atoms almost remained unchanged. 3.2. Energy band structure and density of states Table2. Energy, LUMO, HOMO, LUMO-HOMO gap, dipole moment Ã ¼, and electronegativity (Ãâ¡) of the studied structures at B3LYP/6-31G(d). The total densities of states (DOS) of these tubes are presented in Fig. 2. As can be seen from Fig. 2, the calculated HOMO-LUMO gap (band gap) of the (6,3) Chiral BNNTs is 6.2 (eV) and the calculated band gaps of the C , Si , Ge doped models molecular orbitalÃ¢â¬â¢s are 3.5,5.8 , 5.0 , 5.0 , 5.5 and 5.0 (eV) respectively (See Table 2). Doping of C, Si, and Ge in these tubes causes significant changes in the gaps of the DOS plots. In comparison with the pristine model, the band gaps of these models are reduced that increase their electrical conductance. These results indicated that the doping of C, Si, Ge atom by B, N atoms B-X-B and N-X-N model (X=C, Si, Ge) has more influence on the band gap of the Chiral BNNTs (see Table 2). By increasing atomic number and size polarizability increases that enhances dipole moment. Dipole moments (Ã µ) of the C, Si, Ge doped Chiral BNNTs structures (Fig. 1) indicate slightly changes with respect to the pristine model. 3.3. NMR parameters of the (6,3) Chiral BNNTs The NMR parameters for the investigated models of the (6,3) Chiral BNNTs are tabulated in Table 3, 4, 5 and Table 6. In the pristine model of the (6,3) Chiral BNNTs, there are 42 B atoms and 42 N atoms in the considered model and the NMR parameters are separated into five layers and six Columns, which means that the CS parameters for the atoms of each layer and Column have equivalent chemical environment and electrostatic properties. In Fig. 1b,c,d,e ,f,g the B and N atoms has been replaced by the C, Si, Ge atoms. Table 3 Isotropic shielding parameters of the studied structures at B3LYP/6-31G(d) The calculated results in Table 3 indicate that doping C, Si, and Ge slightly changes the NMR parameters of the various B and N atoms in (Fig.1bÃ¢â¬âg) of the Si, Ge, C doped(6,3) Chiral SWBNNTs except for the N25 and N27 atoms for which the changes are significant. Because among the atoms of (Fig.1bÃ¢â¬âe) BÃ¢â¬âX model (X= C, Si, Ge), the N25 and N27 atoms are the nearest neighbors of the C, Si, and Ge atoms; hence, both the CSI and CSA parameters show the most significant changes due to the C, Si, Ge doping. Also, changes in the CSI parameters of the N10 and N12 atoms, which are the next nearest neighbors of the C, Si, Ge atoms, are also notable. There are differences between the properties of the electronic structures of C, Si, Ge atoms. Comparison of the calculated NMR parameters in (Fig. 1bÃ¢â¬âg) indicates that the properties of the electronic structure of the Ge doped (6,3) Chiral SWBNNTs are more influenced than those of the SiÃ¢â¬âN model, where the N atom is doped by the Si atom. We studied the electronic energies of the models. The changes in the NMR parameter due to the C, Si, and Ge doping are more significant for the NÃ¢â¬âSi, NÃ¢â¬âGe, N-C models with the pristine model. 3.2. NQR parameters The 11B NQR parameters (Ã ·Q and CQ) in the geometrically optimized SWBNNT models were calculated from the EFG tensors. The results are tabulated in Table 7. A quick look at the results reveals that the calculated NQR parameters are not similar for various nuclei; therefore, the electrostatic environment of BNNT is not equivalent in length in all BNNT models. Since, in contrast with CNTs, the ends of BNNTs are different, the NQR values decrease from each end to the opposite end of the chiral model. It was proved before that the end nuclei in the SW-BNNTs are crucial to their growth and also field emission properties [22, 23]. Since no experimental NQR data for BNNTs are available in the literature, the tables do not include any reference experimental data for the calculated results. B17 and B46 in all models have the largest CQ that states greater orientation of the EFG tensor eigenvalues along the z-axis of the electronic distribution at the sites of the 11B17 and 11B46 nuclei. The electrostatic environments of atom B17 and B46 are stronger than in the other layers along the length of the tube. The largest change in CQ is due to B46, located in the layer of doped atoms, because doping changes the geometrical parameters and hence the electronic behavior of atoms. Table 8 The 11B NQR parametersThe highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) in the pristine, and CÃ¢â¬âX (X=B, N) models are plotted in Fig. 3. For the pristine model, HOMO and LUMO are uniformly distributed throughout the BÃ¢â¬âN bonds, whereas, in the CÃ¢â¬âX model (X=B, N) models, HOMO and LUMO are highly localized at the doped regions. (see Fig. 3) In comparison with the pristine model, band gaps of the C, Si, and Ge doped models increased their electrical conductance. Conclusion We studied the electronic structure properties including bond lengths, bond angles, dipole moments (Ã ¼), energies, band gaps, the NMR parameter of the six C, Si, Ge doped SWBNNTs models by means of DFT calculations. The calculated results indicated that the average Ge-B bond lengths of the Ge-N model are larger than those the pristine and the CÃ¢â¬âB, CÃ¢â¬âN, SiÃ¢â¬âB, Si-N and Ge-B models: GeÃ¢â¬âN>SiÃ¢â¬âN>GeÃ¢â¬âB>SiÃ¢â¬âB>CÃ¢â¬âN>Pure>C-B. The values of dipole moments (Ã ¼) of the six C, Si, Ge doped SWBNNTs are GeÃ¢â¬âN> SiÃ¢â¬âN> GeÃ¢â¬âB> CÃ¢â¬âN> Pure> SiÃ¢â¬âB > C-B. 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