{"id":36416,"date":"2022-10-04T14:27:39","date_gmt":"2022-10-04T06:27:39","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=36416"},"modified":"2022-10-06T18:25:33","modified_gmt":"2022-10-06T10:25:33","slug":"group-theory-for-chemistry-department-of-applied-chemistry-prof-chao-yuan-zhu","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-chemistry\/group-theory-for-chemistry-department-of-applied-chemistry-prof-chao-yuan-zhu","title":{"rendered":"Group Theory for Chemistry | Department of Applied Chemistry Prof. Chao-Yuan Zhu"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"36416\" class=\"elementor elementor-36416\">\n\t\t\t\t\t\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-10 elementor-section elementor-top-section elementor-element elementor-element-90a0113 elementor-section-boxed 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href=\"https:\/\/ocw.nycu.edu.tw\/\">Homepage<\/a><\/span><\/span><\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-20 elementor-section elementor-top-section elementor-element elementor-element-0025485 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0025485\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"penci-ercol-50 penci-ercol-order-1 penci-sticky-ct    elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-0446ed9\" data-id=\"0446ed9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2f5840a elementor-widget elementor-widget-penci-info-box\" data-id=\"2f5840a\" data-element_type=\"widget\" data-widget_type=\"penci-info-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"penci_info_box_65734\" class=\"penci-block-vc penci-info-box penci-ibox-float-left penci-view-default penci-shape-circle\">\r\n\t\t\t<div class=\"penci-ibox-inner\">\r\n\t\t\t\t\t\t\t\t<div class=\"penci-ibox-icon penci-ibox-icon--icon penci-icon penci-tibox-text\"><span class=\"penci-ibox-icon-fa\"><\/span><\/div>\t\t\t\t<div class=\"penci-ibox-content-wrap\">\r\n\t\t\t\t\t\t\t\t\t\t<h3 class=\"penci-ibox-title\">Group Theory for Chemistry<\/h3>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c6381f4 elementor-widget elementor-widget-eael-adv-tabs\" data-id=\"c6381f4\" data-element_type=\"widget\" data-widget_type=\"eael-adv-tabs.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t        <div 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\/><\/style><\/p><p style=\"margin-bottom: 10px; line-height: 28px; color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">\u672c\u8ab2\u7a0b\u662f\u7531\u00a0<a href=\"https:\/\/www.dac.nycu.edu.tw\/?lang=zh\" target=\"_blank\" rel=\"noopener\">\u570b\u7acb\u967d\u660e\u4ea4\u901a\u5927\u5b78\u61c9\u7528\u5316\u5b78\u7cfb<\/a>\u63d0\u4f9b\u3002<\/p><p class=\"text\">Group theory provides a systematic mathematical method for describing molecular symmetry. Actually each kind of symmetry corresponds to one of conservation law that is experimentally observable. Properties of a group, symmetry operations and symmetry elements, molecular symmetry groups, representations and characters all are used to describe molecular orbitals, molecular vibrations, selection rules, and so on.<br \/><br \/><\/p><p><span style=\"color: #3366ff; font-size: 16px;\">Textbook\uff1a<\/span><span style=\"font-size: 16px;\">Physical Chemistry 3rd edition, Mortimer, 2008.<br \/><\/span><span style=\"color: #ff00ff;\">For perfect learning results, please buy textbooks!<\/span><\/p><p>\u00a0<\/p><table style=\"color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\" border=\"1\"><tbody><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\" width=\"100\">Instructor(s)<\/th><td bgcolor=\"#EEEEEE\" width=\"518\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0Department of Applied Chemistry Prof. Chao-Yuan Zhu<\/span><\/span><\/span><\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Course Credits<\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a03\u00a0Credits<\/span><\/span><\/span><\/span><\/span><\/td><\/tr><tr><th class=\"text\" style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Academic Year<\/th><td class=\"text\" bgcolor=\"#EEEEEE\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a099 Academic Year<\/span><\/span><\/span><\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Level<\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0Third year university student<\/span><\/span><\/span><\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Prior Knowledge<\/th><td class=\"text\" bgcolor=\"#EEEEEE\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0Chemistry (I), Chemistry(II), Applied Mathematics, Physical Chemistry (II)<\/span><\/span><\/span><\/span><\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Related Resources<\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0<a href=\"#video\">Course Video<\/a>\u00a0 \u00a0<a href=\"#syllabus\">Course Syllabus<\/a>\u00a0 \u00a0<a href=\"#calendar\">Course Calendar<\/a><\/span><\/span><\/span><\/span><\/span><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"video-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"video-tab\">\n\t\t\t\t        \t\t\t\t\t        <p>\n<table id=\"tablepress-87\" class=\"tablepress tablepress-id-87\">\n<thead>\n<tr class=\"row-1 odd\">\n\t<th class=\"column-1\">Week<\/th><th class=\"column-2\">Course Content<\/th><th class=\"column-3\">Course Video<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-hover\">\n<tr class=\"row-2 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u55ae\u5143\u4e00 Introduction<br \/>\nConservation law via symmetry operation<br \/>\nElementary operations for molecule<br \/>\nApply symmetry operation to molecule<br \/>\nSummary<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=36424\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u55ae\u5143\u4e8c Definitions and theorems of group theory<br \/>\nDefinition of an abstract group<br \/>\nMultiplication table for a finite group<br \/>\nCyclic groups<br \/>\nSubgroups<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=38230\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u55ae\u5143\u4e09 Molecular symmetry and the symmetry groups<br \/>\nSymmetry planes and reflections<br \/>\nCenter of inversion<br \/>\nProper axes and proper rotations<br \/>\nImproper axes and improper rotations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=38236\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Products and relations of symmetry operations<br \/>\nThe symmetry point groups<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=38242\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Classes of point groups<br \/>\nSymmetry with multiple high-order axes<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=38248\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Summary of point groups<br \/>\nIllustrative examples<br \/>\nEXERCISES<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=38255\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u55ae\u5143\u56db Representation of groups<br \/>\nMatrix algebra<br \/>\nEigenvalue and eigenvector of matrix<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=38261\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Simultaneous diagonalization of matrices<br \/>\nIrreducible representations<br \/>\nGreat orthogonality theorem<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=38267\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Irreducible representations<br \/>\nRepresentation for cyclic group<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=38276\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Basis of representations<br \/>\nMulliken symbols<br \/>\n(x,y,z) basis for tetrahedron symmetry<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=38282\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u55ae\u5143\u4e94 Group theory with its applications in quantum chemistry<br \/>\nHydrogen atom as basis representation<br \/>\nGeneral wave functions for group representation<br \/>\nThe direct product<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=38288\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Identifying nonzero matrix elements<br \/>\nSymmetry-adapted basis<br \/>\nProjection operators<br \/>\nApplication of projection operators<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=38294\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Application of projection operators<br \/>\nSimplification<br \/>\nigma bonding in MH6<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=38300\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u55ae\u5143\u516d Molecular orbital theory and its applications in organic chemistry <br \/>\nBenzene<br \/>\nTetramethylenecyclobutane<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=38306\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Naphthalene<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=38312\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u55ae\u5143\u516b Molecular vibrations<br \/>\nCartesian coordinates<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=38319\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-18 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Normal-mode coordinates<br \/>\nInternal coordinates<br \/>\nFundamental vibrational transitions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=38326\">Watch Online<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/p>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"syllabus-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"syllabus-tab\">\n\t\t\t\t        \t\t\t\t\t        <p class=\"title\"><strong>\u8ab2\u7a0b\u76ee\u6a19<\/strong><\/p><p class=\"text\">Group theory provides a systematic mathematical method for describing molecular symmetry.<br \/>Actually each kind of symmetry corresponds to one of conservation law that is experimentally observable.<br \/>Properties of a group, symmetry operations and symmetry elements, molecular symmetry groups, representations and characters all are used to describe molecular orbitals, molecular vibrations, selection rules, and so on.<\/p><p>\u00a0<\/p><p class=\"title\"><strong>\u8ab2\u7a0b\u7ae0\u7bc0<\/strong><\/p><p>\u00a0<\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#e4d8b0\"><strong> \u7ae0\u7bc0<\/strong><\/td><td bgcolor=\"#e4d8b0\"><strong> \u7ae0\u7bc0\u5167\u5bb9<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u4e00<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Introduction<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u55ae\u5143\u4e8c<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Definitions and theorems of group theory<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u4e09<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\"> Molecular symmetry and the symmetry groups<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u55ae\u5143\u56db<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\"> Representations of groups<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u4e94<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Group theory with its applications in quantum chemistry<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u55ae\u5143\u516d<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\">Molecular orbital theory with its applications in organic chemistry<\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u4e03<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Molecular orbital theory with its applications in inorganic chemistry<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u55ae\u5143\u516b<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Molecular vibrations<\/span><\/td><\/tr><\/tbody><\/table><p>\u00a0<\/p><p class=\"title\"><strong>\u8ab2\u7a0b\u66f8\u76ee<\/strong><\/p><p class=\"text\">Physical Chemistry 3rd edition, Mortimer, 2008.<\/p><p class=\"title\"><strong>\u53c3\u8003\u66f8\u76ee<\/strong><\/p><p class=\"text\">Chemical Applications of Group Theory , Cotton, 3rd , (John Wiley and Sons) 2002.<br \/>Physical Chemistry,A Molecular Approach, McQuarrie and Simon, 1997.<br \/>Group theory with applications in chemical physics, Jacobs, 2005.<\/p><p>\u00a0<\/p><p class=\"title\"><strong>\u8a55\u5206\u6a19\u6e96<\/strong><\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#e4d8b0\"><strong>\u9805\u76ee<\/strong><\/td><td bgcolor=\"#e4d8b0\"><strong>\u767e\u5206\u6bd4<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u4f5c\u696d\u90e8\u5206\uff1a\u6bcf\u5802\u8ab2\u5f8c\u5747\u6709\u4f5c\u696d<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">25%<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u671f\u4e2d\u8003<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">35%<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u671f\u672b\u8003<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">40%<\/span><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"calendar-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"calendar-tab\">\n\t\t\t\t        \t\t\t\t\t        <p><span style=\"font-family: \u65b0\u7d30\u660e\u9ad4; font-size: 15px;\">\u672c\u8ab2\u7a0b\u884c\u4e8b\u66c6\u63d0\u4f9b\u8ab2\u7a0b\u9032\u5ea6\u8207\u8003\u8a66\u8cc7\u8a0a\u53c3\u8003\u3002<\/span><\/p><p>\u00a0<\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#e4d8b0\"><strong> \u7ae0\u7bc0<\/strong><\/td><td bgcolor=\"#e4d8b0\"><strong> \u7ae0\u7bc0\u5167\u5bb9<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u4e00<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Introduction<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u55ae\u5143\u4e8c<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Definitions and theorems of group theory<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u4e09<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\"> Molecular symmetry and the symmetry groups<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u55ae\u5143\u56db<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\"> Representations of groups<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u4e94<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Group theory with its applications in quantum chemistry<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u55ae\u5143\u516d<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\">Molecular orbital theory with its applications in organic chemistry<\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u4e03<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">Molecular orbital theory with its applications in inorganic chemistry<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u55ae\u5143\u516b<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Molecular vibrations<\/span><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t                    <\/div>\n        <\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d7723a8 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"d7723a8\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.13.3 - 28-05-2023 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class=\"elementor-item\" tabindex=\"-1\">College of Medicine<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118072\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-chinese-center\" class=\"elementor-item\" tabindex=\"-1\">Course of Chinese Center<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-120431\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/liberal-arts-college\" class=\"elementor-item\" tabindex=\"-1\">Forum Of Liberal Arts<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123746\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/speech-of-general-education-center\" class=\"elementor-item\" tabindex=\"-1\">Contemporary Civilization<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-128240\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/reading-of-classic-masterpiece\" class=\"elementor-item\" tabindex=\"-1\">Reading of Classic Masterpiece<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123745\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-general-education-center-2\" class=\"elementor-item\" tabindex=\"-1\">Course of General Education Center<\/a><\/li>\n<\/ul>\t\t\t<\/nav>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Group Theory 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