DTIC ADA440631: Ab Initio Quantum Chemical Study of Electron Transfer in Carboranes

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2005 Journal Article Postprint 2005
4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
Ab initio quantum chemical study of electron transfer in
carboranes 5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S) 5d. PROJECT NUMBER
Ranjit Pati*, Andrew C. Pineda**, Ravindra Pandey*, Shashi P. Karna† 2305
5e. TASK NUMBER
RP
5f. WORK UNIT NUMBER
AA
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT
AND ADDRESS(ES) NUMBER
**Air Force Research Laboratory
Michigan Technological Space Vehicles
University 3550 Aberdeen Ave SE
1400 Townsend Dr Kirtland AFB, NM 87117-5776
Houghton, MI 49931

10. SPONSOR/MONITOR’S ACRONYM(S)
AFRL/VSSE

11. SPONSOR/MONITOR’S REPORT
NUMBER(S)

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Approved for public release; distribution is unlimited.

13. SUPPLEMENTARY NOTES
Published in Chemical Physics Letters 406 (2005) 483-488
Government Purpose Rights
†U.S. Army Research Laboratory, AMSRD-ARL-WM-BD, Aberdeen Proving Ground, MD 21005
14. ABSTRACT
The electron transfer (ET) properties of 10- and 12-vertex carboranes are investigated by the
ab initio Hartree-Fock method within the Marcus-Hush (MH) two-state model and the Koopman
theorem (KT) approach. The calculated value of the ET coupling matrix element, V is
AB,
consistently higher in the KT approach than in the MH two-state model. For the carborane
molecules functionalized by –CH groups at C-vertices, V strongly depends on the relative
2 AB
orientation of the planes containing the terminal –CH groups. The predicted conformation
2
dependence of V offers a molecular mechanism to control ET between two active centers in
AB
molecular systems.
15. SUBJECT TERMS
Space Vehicles, carboranes, ab initio Hartree-Fock, ET, electron transfer, KT, Koopman
theorem, molecular systems
16. SECURITY CLASSIFICATION OF: 17. LIMITATION 18. NUMBER 19a. NAME OF RESPONSIBLE PERSON
OF ABSTRACT OF PAGES Andrew C. Pineda
a. REPORT b. ABSTRACT c. THIS PAGE Unlimited 7 19b. TELEPHONE NUMBER (include area
Unclassified Unclassified Unclassified code)
505-853-2509
Standard Form 298 (Rev. 8-98)
Prescribed by ANSI Std. 239.18
ChemicalPhysicsLetters406(2005)483–488
www.elsevier.com/locate/cplett
Ab initio quantum chemical study of electron transfer in carboranes
Ranjit Pati a,*, Andrew C. Pineda b,c, Ravindra Pandey a, Shashi P. Karna d,*
aDepartmentofPhysics,MichiganTechnologicalUniversity,1400TownsendDrive,Houghton,MI49931,USA
bTheCenterforHighPerformanceComputingandtheDepartmentofChemistry,TheUniversityofNewMexico,
MSC011190,1UniversityofNewMexico,Albuquerque,NM87131-0001,USA
cUSAirForceResearchLaboratory,SpaceVehiclesDirectorate,3550AberdeenAve,SE,KirtlandAirForceBase,NM87117-5776,USA
dUSArmyResearchLaboratory,WeaponsandMaterialsResearchDirectorate,ATTN:AMSRD-ARL-WM-BD;
AberdeenProvingGround,MD21005-5069,USA
Received3January2005;infinalform7March2005
Availableonline31March2005
Abstract
The electron transfer (ET) properties of 10- and 12-vertex carboranes are investigated by the ab initio Hartree–Fock method
withintheMarcus-Hush(MH)two-statemodelandtheKoopmantheorem(KT)approach.ThecalculatedvalueoftheETcoupling
matrixelement,V ,isconsistentlyhigherintheKTapproachthanintheMHtwo-statemodel.Forthecarboranemoleculesfunc-
AB
tionalized by –CH groups at C-vertices, V strongly depends on the relative orientation of the planes containing the terminal
2 AB
–CH groups. The predicted conformation dependence of V offers a molecular mechanism to control ET between two active
2 AB
centersin molecularsystems.
(cid:1)2005Elsevier B.V.All rightsreserved.
1. Introduction also offera unique opportunity inthearea ofmolecular
engineering for their potential application as a molecu-
Carboranes are animportant class ofboron-contain- laranchorbetweentwoactivereactioncenters,andhave
ing rigid structures that have potential applications in beenthe subject ofnumerousexperimental andtheoret-
medicinal drug design as hydrophobic pharmacophores icalstudies[8–11].Ithasbeenfoundthatelectrontrans-
[1], as antisense agents for antisense oligonucleotide fer (ET) across the carborane cage plays an important
therapy (AOT) [2], as boron carriers for boron neutron role in controlling the redox process in Ni-carboranes
capture therapy (BNCT)[3–5],andasmolecularprobes [12]. Therefore, an understanding of the electron trans-
for molecular medical diagnostics [6], among others. fer process across the carborane cages and its relation-
Recently, heteroisomeric diodes, based upon the chemi- ships to molecular geometry and electronic structure is
calvapordepositionofdifferentisomersofcloso-dicarb- deemedimportant.Suchanunderstandingisalsocrucial
adodecaborane, namely closo-1,2-dicarbadodecaborane for the future application of carboranes in molecular-
(orthocarborane, C B H ) and closo-1,7-dicarbado- scale electronics. It has recently been predicted [13–16]
2 10 12
decaborane (metacarborane, C B H ), which have that r-bonded carbon cage structures can be used as
2 10 12
important applications as solid state neutron detectors an effective electron tunnel barrier in molecular-scale
have also been fabricated [7]. Due to their axially direc- electronic circuits.
tedterminalbondsandrigidcagestructures,carboranes In this Letter, we present ab initio investigations of
the electronic structure and ET coupling strengths in
closo-1,10-dicarbadecaborane (C B H ), and closo-
* Correspondingauthors. 2 8 10
1,12-dicarbadodecaborane (C B H ) and their –CH
E-mail addresses: [email protected] (R. Pati), [email protected] 2 10 12 2
(S.P.Karna). derivatives,namely,1,10-dimethylene-1,10-dicarba-closo-
0009-2614/$-seefrontmatter (cid:1)2005ElsevierB.V.Allrightsreserved.
doi:10.1016/j.cplett.2005.03.039
484 R.Patietal./ChemicalPhysicsLetters406(2005)483–488
decaborane (H C-CB H C-CH ), and 1,12-dimethylene- and
2 8 8 2
1,12-dicarba-closo-dodecaborane (H C-CB H C-CH ).
2 10 10 2 S ¼hW jW i: ð6Þ
AB A B
These carborane molecules will be referred to in the rest
of this Letter as 10-vertex and 12-vertex carborane Here,SABistheoverlapmatrixelement.Histheelec-
molecules, respectively. The ET coupling strength is tronic Hamiltonian of the system, and WA and WB are
calculated using the MH two-state model [17–21] within the localized many-electron wave-functions of the two
ab initio Hartree–Fock theory. The effects of basis states A and B, respectively.
sets and geometrical parameters on the ET coupling In the present study, the ab initio unrestricted
strength are also investigated. For comparison, the ET Hartree–Fock (UHF) method was used to generate the
coupling strength is also estimated using the KT ap- localized states of the molecules. These localized wave-
proach [17]. functions were subsequently used as the initial guess in
In Section 2, the computational approach employed the self-consistent evaluation of the ET coupling matrix
in the present study is briefly described. The results element.Thenuclearconfigurationusedforthecalcula-
and discussions follow in Section 3. The main findings tion of the ET matrix element was taken to be the geo-
of the present study are summarized in Section 4. metric average of the two localized structures, where
H =H .ItisimportanttonotethatEq.(2)assumes
AA BB
thevalidityoftheCondonapproximation(i.e.,V isa
AB
weakfunctionofthenuclearcoordinates)inthevicinity
2. Computational approach of the transition state [17].
For the parent 10- and 12-vertex carboranes (i.e.,
Ab initio Hartree–Fock (HF) and density functional C B H and C B H ), a symmetry-constrained opti-
2 8 10 2 10 12
theory (DFT) calculations of equilibrium geometry mizationwasperformedtoobtaintherespectiveequilib-
and electronic structure were performed with the rium structures. A model p-cage-p structure containing
GAUSSIAN quantum chemistry program package [22]. two active reaction centers was then constructed by
The geometrical parameters were obtained with the use replacingtheterminalHatomsby–CH groupsyielding
2
of a minimal basis set (STO-3G) as well as an extended atwo-statesystem.Theresultingstructuresofthederiv-
basis set consisting of a double zeta augmented by one ative carboranes are shown in Fig. 1 where the –CH
2
pandonedpolarizationfunctions(DZP)asimplemented groups are the active reaction centers. The derivative
intheGaussian[22]basissetlibrary.Theextendedbasis molecules were then optimized in the singly positively
setisreferredtoastheDZPbasissetintheremainderof charged doublet state. A pair of equilibrium structures,
the Letter. In the DFT calculations, the B3LYP [23] whichbyconventionwetermasleft-localizedandright-
exchange-correlationfunctionalwasemployed. localized structures, were obtained by varying the C–C
Theelectrontransfercouplingstrength,VAB,iscalcu- bond distance between the cage and each of the –CH2
lated using the MH two-state (TS) model the details of end groups, keeping the cage structure fixed.
which can be found in various review articles [17–21]. The localized wavefunctions obtained for the deriva-
Briefly, the ET rate constant for a weak coupling (i.e., tive carboranes (i.e., [C B H ]+) and (i.e., [C B H ]+)
4 8 12 4 10 14
non-adiabatic limit) between electron donor and accep- were used as the initial guess for the calculation of the
torcenterscan beobtainedfromtheFermi Golden rule ET coupling element at the average of the left-localized
as [17] and right-localized asymmetric configurations. In order
2p to examine the effects of nuclear configurations on
Ket ¼ (cid:1)h jVABj2FCWD; ð1Þ VAB, two-state model calculations were also performed
at one of the localized geometries, namely the left-
where FCWD represents a Franck–Condon-weighted
localized asymmetric configuration. Calculations of
density of states, which reflects the nuclear modes of V in the two-state model were performed with the
AB
the system. The ET coupling matrix element, V ,
AB HONDO-8 electronic structure suite [24].
which plays a major role in the ET process, represents The V of a singly-charged positive ion can also be
AB
the strength of the interaction between the two active
calculated within the KT approach as [17]
reaction sites, and is given by [21]
V ¼1=2ðe (cid:1)e Þ; ð7Þ
AB HOMO HOMO(cid:1)1
V ¼ð1(cid:1)S2 Þ(cid:1)1½H (cid:1)S ðH þH Þ=2(cid:2); ð2Þ
AB AB AB AB AA BB
where e and e are energies of the highest
HOMO HOMO(cid:1)1
where
occupied molecular orbital (HOMO) and the nexthigh-
H ¼hW jHjW i; ð3Þ est occupied molecular orbital in the triplet state of the
AB A B
neutral molecule. The HOMO and HOMO-1 orbitals
H ¼hW jHjW i; ð4Þ correspondtothesymmetricandanti-symmetriccombi-
AA A A
nation of the p-orbitals of the terminal end groups,
H ¼hW jHjW i; ð5Þ respectively. The KT approach has been successfully
BB B B
R.Patietal./ChemicalPhysicsLetters406(2005)483–488 485
Fig.1. Theequilibriumstructuresof(a)10-and(b)12-vertexcarboranemoleculesobtainedusingtheabinitioHartree–Fockmethod.
used to study ET properties of a wide range of organic the geometrical parameters for C B H and C B H ,
2 8 10 2 10 12
structures [25–28] and generally yields V values com- the structural parameters for similar systems, B H(cid:1)2
AB 10 10
parabletomorerigorousmethods[29].However,itwas and B H(cid:1)2, have been reported [30,31]. For the bond
12 12
notedinapreviousstudy[13]thatthemagnitudeofV length between a pair of B atoms generated by single
AB
obtained in the KT approach is generally larger than 4- and 5-fold proper rotations, such as the bonds be-
that obtained using the MH two-state approach at a tween B(8)–B(9) in Fig. 1a and B(3)–B(11) in Fig. 1b,
similar level of theory. the reported values are 1.88 and 1.77A˚ for the 10- and
3. Results and discussion
Table1
3.1. Geometry Calculatedlengthsoftypicalbondsin10-and12-vertexcarboranes
Molecule Bondlength HF HF DFT-B3LYP
The equilibrium structural parameters, in this case (A˚) (STO-3G) (DZP) (DZP)
the bond lengths of the cage portions, of the parent
C BH C(1)–B(8) 1.603 1.601 1.607
2 8 10
10- and 12-vertex carboranes (C2B8H10 and C2B10H12) B(8)–B(9) 1.869 1.869 1.869
showninFig.1arepresentedinTable1.Onenotesthat B(5)–B(9) 1.829 1.834 1.825
the optimized geometrical parameters are relatively
C B H C(4)–B(3) 1.710 1.710 1.711
2 10 12
insensitive to the choice of the basis set. The HF and B(3)–B(11) 1.789 1.797 1.797
DFT(B3LYP) methods are also in good accord with B(2)–B(3) 1.760 1.780 1.780
each other. While there are no experimental reports on ThelabelingoftheatomsisshowninFig.1.
486 R.Patietal./ChemicalPhysicsLetters406(2005)483–488
12-vertexboranes,respectively.Thesevaluesareingood HFapproachwithDZPbasisset)oftheory.Similardif-
agreement with the calculated HF (DZP) values of 1.87 ferences in the calculated values of V in the KT and
AB
and 1.80A˚ in the corresponding carboranes. The bond MH approaches were noted in our previous study
length between a pair of B atoms related by a single 8- [13,14] on carbon cage structures.
fold improper rotation in the 10-vertex carborane, such Between the 10-vertex and 12-vertex carboranes, a
asthebondsbetweenB(5)–B(9)inFig.1aandB(2)–B(3) decreaseintheETcouplingwithanincreaseincagesize
in Fig. 1b, has been reported [30] to be 1.82A˚, which is is observed. This is consistent with our previously re-
close to the corresponding bond distance (1.84A˚) ob- ported results [13] for carbon-based spacers. We also
tained in our ab initio HF (DZP) calculation. note here that the ET coupling matrix element for the
In the degenerate ionized configurations (i.e., left- 10-vertex carborane is nearly the same as that for the
localizedandright-localizedasymmetric configurations) smaller carbon-based cage structured bicyclo[1.1.1]pen-
of the derived 10- and 12-vertex carboranes, the tane [13]. This suggests that it is possible to control
C(CH )–C(cage) bond length is found to be shorter, the ET coupling strength between a pair of active reac-
2
by approximately 0.06A˚, on the side of the cage on tioncentersnotonlybystructuralmodificationbutalso
which the single positive charge is localized. For exam- by the chemical nature of the spacer element, as also
ple, the respective values of R and R are noted by others [25–29].
(C1–C20) (C2–C19)
1.41 and 1.47A˚ in the 10-vertex carborane molecule at
the HF(DZP) level of theory. Similarly, the HF(DZP) 3.3. Dependence of V on the orientation of the end
AB
values of R and R are 1.43 and 1.49A˚, groups of the molecules
(C1–C6) (C4–C5)
respectively, in the 12-vertex carborane molecule.
In orderto investigate the effect of therelativeorien-
3.2. Computation of the ET matrix element tation of the end groups on ET, we calculated V as a
AB
function of the angle, /, between the planes of the two
The values of V calculated in the MH model with terminal –CH groups. Calculations were performed on
AB 2
theuseoftheminimalandtheextendedbasissetsarepre- structures obtained by rotating one of the –CH groups
2
sented in Table 2. In the calculations, the –CH end in steps of 10(cid:2) about the C(cage)–CH bond while
2 2
groups of the carborane molecules were kept co-planar. keeping the rest of the molecule fixed. The calculated
It is clear from the table that the choice of the basis set variation of V with the twist angle (/) is shown in
AB
has a small but noticeable effect on the calculated value Fig. 2 and can be represented by a simple cosine func-
of V . The DZP basis set used in the study yields tion of /. It is clear that the value of V is maximal
AB AB
(cid:3)10% larger value for V than the STO-3G basis set. when the two –CH groups attached to the carborane
AB 2
However,negligible,ifany,differenceisnotedintheva- cagearecoplanarandisminimalwhentheyareperpen-
lue of V between the localized (i.e., H 6¼H ) and dicular to each other. This conformation dependent,
AB AA BB
the average (i.e., H =H ) structure, justifying the through-bond electron tunneling between the donor
AA BB
validityofCondonapproximation[17,18]usedinderiv- and acceptor groups can be explained in terms of the
ingEq.(2). super-exchange model. In the planar orientation of
The values of V estimated using the KT approach the two end groups, a strong coupling between the
AB
Eq. (7) from the one-electron energy levels are 70.9 and p-orbitals of the –CH end groups and the vertex
2
64.7kJ/mol for the 10-vertex and 12-vertex carboranes, C-atoms of the cage is inherent. The orbitals of thever-
respectively. These values are (cid:3)36% and 38% larger tex C-atoms subsequently couple to the cage-centered
than the corresponding values obtained from the MH MO providing a pathway for the electron tunneling.
two-state approach (Table 2) at the same level (i.e., This indirect interaction, in which the electron transfer
between two reaction centers is mediated by intermedi-
ate bonds, is generally referred to as super-exchange
interaction. For the perpendicular relative orientation
Table2
of the two –CH groups, the coupling between the
TheETcouplingelement(V )calculatedwiththeMarcus–Hushtwo- 2
AB
statemodelforthe10-and12-vertexcarboranemolecules p-orbitals of the –CH2 end groups and the vertex
Molecule Basisset V a(kJ/mol) V b(kJ/mol) C-atoms of the cage vanishes, breaking the super-ex-
AB AB
change pathway for electron tunneling, thereby yielding
C B Hþ STO-3G 48.3 48.3
4 8 12 a nearly vanishingvalue forV .As proposed inapre-
DZP 52.6 53.7 AB
vious study [13,16], and also observed experimentally
C B Hþ STO-3G 37.6 37.5
4 10 14 [32], the conformational dependence of ET offers an
DZP 46.7 46.7
effective intrinsic mechanism for the control of electron
a V calculated using the asymmetric (localized) geometry of the
AB transport in molecular systems – a property that can be
molecule.
b V calculated using the symmetric (average) geometry of the of immense value in developing molecular-scale
AB
molecule. electronics.
R.Patietal./ChemicalPhysicsLetters406(2005)483–488 487
(a) 60
STO-3G
50 DZP
40
ol)
M
J/ 30
K
(B
A
V
20
10
0
0 20 40 60 80 100
Twist Angle, φ (degrees)
50
(b)
45 STO-3G
DZP
40
35
ol) 30
M
J/ 25
K
(B
VA 20
15
10
5
0
0 20 40 60 80 100
Twist Angle, φ (degrees)
Fig.2. The variationoftheETcouplingelement(|V |)asafunctionoftwist-angle(/) in(a)10-and(b)12-vertexcarboranemoleculesusing
AB
STO-3GandDZPbasissets.
4. Conclusion for V . Any other orientation between p-end groups
AB
leads toafiniteorbitaloverlapandafinite ETcoupling
Ab initio electronic structure calculations have been between the two reaction centers. The conformational
performed to obtain the equilibrium structure and V dependenceofET,alsoobservedinourpreviousstudies
AB
of –CH derivatized 10-vertex and 12-vertex carborane on carbon cage systems [13], offers an effective mecha-
2
molecules. The value of V is calculated to be larger nism for developing molecular switches [16].
AB
by more than 35% in the KT approach than in the
MH two-state model. The strength of the calculated
ET coupling between the two active reaction centers is Acknowledgments
found to be only weakly dependent on the nuclear con-
figuration of the carboranes considered here. We thank Professor Josef Michl, Professor Mark
The switching characteristics with respect to rotation Ratner,andDr.JohnMillerforhelpfuldiscussionsdur-
of the p-end groups can be simply described in terms of ingthiswork.GenerouscomputertimeattheUniversity
the cosine dependence on the twist angle between the of New Mexico Center for High Performance Comput-
terminal moieties, as also predicted for carbon cage ing and the Army Research Laboratory Major Shared
systems [13]. The perpendicular orientation of the two Resource Center is gratefully acknowledged. This re-
p-end groups yields a nearly vanishing value of V , search was partly funded by DARPA through contract
AB
while the parallel orientation gives the maximum value number 6197-99S11335.
488 R.Patietal./ChemicalPhysicsLetters406(2005)483–488
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