TY - JOUR

T1 - Quantization of the dipole moment and of the end charges in push-pull polymers

AU - Kudin, Konstantin N.

AU - Car, Roberto

AU - Resta, Raffaele

PY - 2007/11/29

Y1 - 2007/11/29

N2 - A theorem for end-charge quantization in quasi-one-dimensional stereoregular chains is formulated and proved. It is a direct analog of the well-known theorem for surface charges in physics. The theorem states the following: (1) Regardless of the end groups, in stereoregular oligomers with a centrosymmetric bulk, the end charges can only be a multiple of 12 and the longitudinal dipole moment per monomer p can only be a multiple of 12 times the unit length a in the limit of long chains. (2) In oligomers with a noncentrosymmetric bulk, the end charges can assume any value set by the nature of the bulk. Nonetheless, by modifying the end groups, one can only change the end charge by an integer and the dipole moment p by an integer multiple of the unit length a. (3) When the entire bulk part of the system is modified, the end charges may change in an arbitrary way; however, if upon such a modification the system remains centrosymmetric, the end charges can only change by multiples of 12 as a direct consequence of (1). The above statements imply that-in all cases-the end charges are uniquely determined, modulo an integer, by a property of the bulk alone. The theorem's origin is a robust topological phenomenon related to the Berry phase. The effects of the quantization are first demonstrated in toy LiF chains and then in a series of trans-polyacetylene oligomers with neutral and charge-transfer end groups.

AB - A theorem for end-charge quantization in quasi-one-dimensional stereoregular chains is formulated and proved. It is a direct analog of the well-known theorem for surface charges in physics. The theorem states the following: (1) Regardless of the end groups, in stereoregular oligomers with a centrosymmetric bulk, the end charges can only be a multiple of 12 and the longitudinal dipole moment per monomer p can only be a multiple of 12 times the unit length a in the limit of long chains. (2) In oligomers with a noncentrosymmetric bulk, the end charges can assume any value set by the nature of the bulk. Nonetheless, by modifying the end groups, one can only change the end charge by an integer and the dipole moment p by an integer multiple of the unit length a. (3) When the entire bulk part of the system is modified, the end charges may change in an arbitrary way; however, if upon such a modification the system remains centrosymmetric, the end charges can only change by multiples of 12 as a direct consequence of (1). The above statements imply that-in all cases-the end charges are uniquely determined, modulo an integer, by a property of the bulk alone. The theorem's origin is a robust topological phenomenon related to the Berry phase. The effects of the quantization are first demonstrated in toy LiF chains and then in a series of trans-polyacetylene oligomers with neutral and charge-transfer end groups.

UR - http://www.scopus.com/inward/record.url?scp=36348974510&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36348974510&partnerID=8YFLogxK

U2 - 10.1063/1.2799514

DO - 10.1063/1.2799514

M3 - Article

C2 - 18035903

AN - SCOPUS:36348974510

VL - 127

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 19

M1 - 194902

ER -