tailieunhanh - Ideas of Quantum Chemistry P23

Ideas of Quantum Chemistry P23 shows how quantum mechanics is applied to chemistry to give it a theoretical foundation. The structure of the book (a TREE-form) emphasizes the logical relationships between various topics, facts and methods. It shows the reader which parts of the text are needed for understanding specific aspects of the subject matter. Interspersed throughout the text are short biographies of key scientists and their contributions to the development of the field. | 186 4. Exact Solutions - Our Beacons Fig. . Various graphical representations of the hydrogen 3d. z2 orbital coordinates in Figs. a - c in . . The z axis is vertical x axis is horizontal. a Isolines of the xz section of the orbital. Gray means zero white means a high positive value black means a negative value. Note Figs. a b that 3d3z2 r2 orbitals are symmetric with respect to inversion. We may imagine xz section of the 3d3z2 r2 as two hills and two valleys b the hills are higher than the depth of the valleys the plateaus in Fig. b are artificial . Fig. c is similar to a but instead of isolines one has a mist with the highest concentration white on the North-South line and the smallest and negative black mist concentration on the East-West line. The orbital finally disappears exponentially with increasing distance r from the nucleus. Fig. d shows an isosurface of the absolute value of the angular part of the wave function yO . As for Y itself there are two positive lobes and a negative ring they touch each other at nucleus. To obtain the orbital we have to multiply this angular function by a spherically symmetric function of r. This means that an isosurface of the absolute value of the wave function will have also two lobes along the z axis as well as the ring but they will not touch in accordance with Fig. a . The lobes along the z axis are positive the ring is negative. Harmonic helium atom harmonium 187 Fig. . Summary schematic representation of 1s 2s 2p 3s 3p 3d orbitals of the hydrogen atom. 1s 2s 3s orbitals are spherically symmetric and increase in size 1s has no node 2s has one nodal sphere not shown 3s has two nodal spheres not shown . The shadowed area corresponds to the minus sign of the orbital. The 2p orbitals have a single nodal plane perpendicular to the orbital shape . 3p orbitals are larger than 2p and have a more complex nodal structure. Note that among 3d orbitals all except 3d3z2-r2 have identical shape but differ by orientation