and Applied Analysis 3 in the normal bundle T⊥M, and AN is the shape operator of the second fundamental form. Moreover, we have g ANX, Y g h X,Y ,N , 2.4 where g denotes the Riemannian metric onM as well as the metric induced onM. The mean curvature vector H on M is given by

Key points .................................................................................................................. 559 H

c o l o r e d l i g h t r e f l e c t i o n s p r o d u c e d b y h i s m o b i l e s . H i s s h o r t J a m e s E . D a v i s , " F i g u r e S t u d y , " p e n c i l o n p a p e r , 1 9 3 4 . f i l m s , a v e r a g i n g a b o u t t e n m i n u t e s i n l e n g t h , w e r e o f t e n a c c o m p a n i e d b y o r i g i n a l m u s i c , s o m e t i m e s c o m p o s e d a n d a r r a n g...

In this work, we augment the approximate density functional method SCC-DFTB (DFTB3) with the chemical-potential equalization (CPE) approach in order to improve the performance for molecular electronic polarizabilities. The CPE method, originally implemented for the NDDO type of methods by Giese and York, has been shown to significantly emend minimal basis methods with respect to the response pr...