|
[×ÊÔ´]
ʹÓÃMultiwfn×öÍØÆË·ÖÎöÒÔ¼°¼ÆËã¹Â¶Ôµç×ӽǶÈ
ʹÓÃMultiwfn×öÍØÆË·ÖÎöÒÔ¼°¼ÆËã¹Â¶Ôµç×ӽǶÈ
ÎÄ/Sobereva 2011-Dec-1
Multiwfn³ÌÐò(http://multiwfn.codeplex.com)´Ó2.1°æ¿ªÊ¼Ö§³Öµç×ÓÃܶȵÄÍØÆË·ÖÎö£¬ÔÚ¸Õ¸Õ·¢²¼µÄ2.2°æÖнøÒ»²½Ö§³ÖELF¡¢LOL¡¢µç×ÓÃܶÈÀÆÕÀ˹º¯Êý¡¢¹ìµÀ²¨º¯ÊýµÄÍØÆË·ÖÎö¡£±¾ÎĽ«¼òÒª½éÉÜMultiwfnÍØÆ˹¦ÄܵĻù±¾Ê¹Ó÷½·¨¡£
µç×ÓÃܶȺ¯Êý´ó¼Ò¶¼ºÜÊìϤ£¬Èç¹û²»ÊìϤELF¡¢LOLºÍÀÆÕÀ˹º¯Êý£¬¿ÉÒԲο´¡¶µç×Ó¶¨ÓòÐÔµÄͼÐηÖÎö¡·Ò»ÎÄ£¬¼ûhttp://hi.baidu.com/sobereva/blo ... e99b0c4a90a7d6.html¡£
1 ÍØÆË·ÖÎö¼ò½é
ÏÞÓÚƪ·ù£¬ÕâÀïÖ»ÊǶÔÍØÆË·ÖÎö×ö¼«¼òµ¥µÄ˵Ã÷£¬»òÕß˵Êǻعˡ£¶ÔÓÚÍêÈ«²»Á˽âAIMÀíÂÛµÄÈË£¬²»·Á¿´¿´The Quantum Theory of Atoms in Molecules-From Solid State to DNA and Drug DesignÒ»ÊéµÄµÚÒ»Õ£¬¶Ôµç×ÓÃܶȵÄÍØÆË·ÖÎöÓмò½é¡¢Çå³þ¡¢Ò׶®µÄ½éÉÜ¡£
ʵ¿Õ¼äº¯Êý£¨ÒÔÈýά¿Õ¼ä×ø±êΪ±äÁ¿µÄº¯Êý£©µÄÍØÆË·ÖÎöÖ÷ÒªÊÇÖ¸»ñÈ¡ÁÙ½çµã£¬ÒÔ¼°»ñµÃÁ¬½ÓÁÙ½çµãµÄÍØÆË·¾¶¡£µç×ÓÃܶȵÄÍØÆË·ÖÎöÊÇÓÉBaderÊ×ÏÈÌá³öµÄ£¬ÊÇAIMÀíÂÛÖеÄÖØÒª×é³É²¿·Ö£¬ºóÀ´ÍØÆË·ÖÎöµÄ˼·ÓÖ±»Silvi¡¢SavinµÈÈËÓÃÓÚ·ÖÎöELF£¨µç×Ó¶¨Óò»¯º¯Êý£©¡£
ÁÙ½çµã(Critical point, CP)ÊǺ¯ÊýµÄÌݶȵÄģΪ0µÄµã£¬·ÖËÄÀ࣬ÒÔ(3,X)±íʾ¡£¼ÙÉèʵ¿Õ¼äº¯ÊýµÄHessian¾ØÕó£¨3*3µÄ¶þ½×µ¼Êý¾ØÕ󣩵ı¾Õ÷ÖµÓÐM¸öÕýÖµºÍN¸ö¸ºÖµ£¬ÔòX=M-N¡£
(3,-3)¶ÔÓ¦º¯ÊýµÄ¾Ö²¿¼«´óµã¡£¶ÔÓÚµç×ÓÃܶȺ¯Êý£¬Í¨³£³öÏÖÔÚÀëÔ×Ӻ˺ܽüµÄλÖ᣶ÔÓÚELFº¯Êý£¬Í¨³£³öÏÖÔÚ¹²¼Û¼üÇøÓò¡¢¹Â¶Ôµç×ÓÇøÓò¡¢Ô×Ӻ˴¦¡£
(3,-1)¶ÔÓ¦º¯ÊýµÄ¶þ½×°°µã¡£º¯ÊýÔÚÒ»¸ö·½ÏòÇúÂÊΪÕý£¬ÁíÁ½¸ö·½ÏòΪ¸º¡£¶ÔÓÚµç×ÓÃܶȺ¯Êý£¬Í¨³£³öÏÖÔÚÓÐÏ໥×÷ÓõÄÁ½¸öÔ×ÓÖ®¼ä£¬Ò²±»³ÆΪ¼üÁÙ½çµã(BCP)¡£¶ÔÓÚELFº¯Êý£¬Î»Öò»ÉõÈ·¶¨£¬¾³£Æ«ÀëÁ½¸öÏà¹ØµÄ(3,-3)µÄÁ¬Ïߺܶࡣ
(3,+1)¶ÔÓ¦º¯ÊýÒ»½×°°µã£¬ÈçͬÊÆÄÜÃæÉϵĹý¶É̬¡£¶ÔÓÚµç×ÓÃܶȺ¯Êý£¬Í¨³£³öÏÖÔÚ»·ÌåϵƽÃæÖУ¬Èç±½»·µÄÖÐÐÄ¡£¶ÔÓÚELF£¬(3,+1)ºÍÏÂÃæµÄ(3,+3)ͨ³£½ÏÉÙÌÖÂÛ¡£
(3,+3)¶ÔÓ¦º¯ÊýµÄ¾Ö²¿¼«´óµã¡£¶ÔÓÚµç×ÓÃܶȺ¯Êý£¬Í¨³£³öÏÖÔÚÁý×´ÌåϵÖУ¬ÀýÈçC60µÄÖÐÐÄ¡£
Ñ°ÕÒÁÙ½çµãͨ³£Ê¹ÓÃÅ£¶Ù·¨¡£¸ø³öÒ»¸ö³õ²Âµã£¬Í¨¹ý·´¸´µü´ú£¬¾ÍÄÜÕÒµ½ÓëÖ®×îÁÚ½üµÄÁÙ½çµã¡£µ«Å£¶Ù·¨²»Ò»¶¨Ã¿´Î¶¼³É¹¦£¬ÓпÉÄÜÒ»Ö±²»ÊÕÁ²£¬Ò²¿ÉÄܵü´ú¹ý³ÌÖÐÅöµ½Hessian¾ØÕóΪÆæ¾ØÕóµÄÇé¿ö£¬»òÕßÊÕÁ²µ½ÒÑÕÒµ½µÄÁÙ½çµãλÖ㬴Ëʱ¾ÍÒª³¢ÊÔ´ÓÏÂÒ»¸ö³õ²Âµã¿ªÊ¼ÁË¡£³õ²ÂµãÓëÆÚÍûµÄÁÙ½çµãλÖÃÔ½½üÔ½ÈÝÒ׳ɹ¦ÊÕÁ²µ½ÏàÓ¦µÄÁÙ½çµã¡£
µç×ÓÃܶȺ¯ÊýµÄ½á¹¹ºÜ¼òµ¥£¬Ò»°ã¶¼ÊÇÔÚÔ×Ӻ˴¦ÏñÒ»¸öɽ·åËÊÁ¢£¬Ïò×ÅËÄÖܳÊÖ¸Êý½µµÍ£¬µäÐÍÌåϵµÄ¸÷ÖÖÁÙ½çµãλÖö¼ÄÜ´óÖ²³öÀ´£¬ÕýÈçÉÏÃæÒѾÌáµ½µÄ¡£Ñ°ÕÒ(3,-3)µãµÄʱºò³õ²Âµã¶¼Ñ¡ÔÚÔ×ÓºËλÖá£Ñ°ÕÒ(3,-1)µãµÄʱºò£¬³õ²Âµã¶¼Ñ¡ÔÚÁ½¸öÔ×Ó»òÕßÁ½¸öÒÑÕÒµ½µÄ(3,-3)µãÁ¬ÏßµÄÖе㣬ÔÚÕâ¸ö¹ý³ÌÖÐÒ²¿ÉÄÜ˳±ãÕÒµ½(3,+1)ºÍ(3,+3)µã¡£ÁíÍâÒ²³£³£½«Èý¸öÔ×Ó»òËĸöÔ×ӵļ¸ºÎÖÐÐÄ×÷Ϊ³õ²Â£¬Õâ·Ö±ðÊʺϽøÒ»²½Ñ°ÕÒÉÐδÕÒµ½µÄ(3,+1)ºÍ(3,-3)µã¡£¼ÙÉèÀûÓÃÕ⼸ÖÖ³õ²Â·½Ê½»¹ÊÇûÕÒµ½Ò»Ð©ÆÚÍûµÄÁÙ½çµã£¬µ«Í¨¹ý¾Ñé¿ÉÒÔ¹À¼Æ³öÆÚÍûµÄµã³öÏֵĴóÖ¿ռ䷶Χ£¬ÄÇô¾ÍÓ¦µ±ÔÚÕâ¸ö¿Õ¼ä·¶Î§ÄÚÉ趨һ´ó¶Ñ³õ²ÂµãÀ´³¢ÊÔÑ°ÕÒÄǸöÁÙ½çµã¡£
¶ÔÓÚELF¡¢LOLºÍµç×ÓÃܶÈÀÆÕÀ˹º¯Êý£¬Ñ°ÕÒ¶ÔÓ¦Ô×ÓÄں˴¦µÄÁÙ½çµã£¨¶ÔÓ¦¸ß¶È¶¨ÓòµÄ1s¹ìµÀµç×Ó£©»¹ÊÇÓÃÔ×ÓºËλÖÃ×÷Ϊ³õ²Â¡£µ«ÊǶÔÓÚ¼Û²ãµÄELFÁÙ½çµã£¬ÓÉÓÚÆä·Ö²¼½ÏÄÑÔ¤ÁÏ£¬¶øÇÒÊýÄ¿Öڶ࣬×îºÃµÄ°ì·¨¾ÍÊÇÖ±½ÓÔÚÿ¸öÔ×Ó¸½½ü¶¼ÉèÒ»´ó¶Ñ³õ²ÂµãÀ´Ñ°ÕÒ¸÷¸öÁÙ½çµã¡£²»¹ý£¬ÓÉÓÚELFÁÙ½çµãÌ«¶à¶øÇÒ·Ö²¼Ì«¸´ÔÓ£¬ÏëÕÒÈ«ËùÓÐÁÙ½çµã¾ø·ÇÒ×Ê£¬ËùÒÔ£¬Ö»Òª¿´µ½»¯Ñ§ÒâÒåÏÔÖøµÄÁÙ½çµã£¨ËùÓеÄ(3,-3)£¬ÒÔ¼°²¿·Ö(3,-1)£©¶¼ÒѾÕÒµ½ÁË£¬ÁÙ½çµãµÄËÑË÷¾Í¿ÉÒÔÍ£µôÁË¡£³ýÁËÅ£¶Ù·¨£¬»¹ÓÐÒ»ÖÖ»ùÓÚÁ¢·½¸ñµãµÄÁÙ½çµãËÑË÷·½·¨£¬ÔÚTopModÖÐÓõľÍÊÇÕâÖÖ£¬µ«ÊýÖµ¾«¶ÈÉÏÁî±ÊÕ߱ȽϱÉÒÄ£¬ÎÒ²»´òËãÔÚÕâÀïϸ̸£¨Á¢·½¸ñµã·½·¨ºÍÅ£¶Ù·¨Ïà½áºÏµ¹ÊÇ¿ÉÄܲúÉú³ö¸ßЧÇÒ׼ȷµÄ·½·¨£©¡£
ÍØÆË·¾¶ÊÇÁ¬½ÓÁÙ½çµãµÄ·¾¶¡£Ò»°ã±È½Ï¹Ø×¢µÄÊÇ(3,-1)Óë(3,-3)Ö®¼äµÄ·¾¶£¬ÑØ×Å(3,-1)µÄHessian¾ØÕó±¾Õ÷ֵΪÕýµÄ±¾Õ÷ÏòÁ¿·½Ïò·Ö±ðÏòÇ°ºÍÏòºó³ö·¢£¬Ë³×ÅÌݶȷ½Ïò²»¶ÏÇ°½ø¾ÍÄÜÕÒµ½Á½¸ö(3,-3)£¬¶ø¾¹ýµÄ¹ì¼£¾ÍÊÇÍØÆË·¾¶¡£¶ÔÓÚµç×ÓÃܶȺ¯Êý£¬ÕâÑùµÄÍØÆË·¾¶½üËÆÓÚ»¯Ñ§¼ü£¬Òò´Ë³ÆΪ¼ü¾¶¡£¶ÔÓÚELF£¬Í¨¹ýÉú³ÉÍØÆË·¾¶Ôò¿ÉÒÔ½«(3,-1)Óë(3,-3)ÁÙ½çµãÖ®¼äµÄ¹ØϵÇåÎúµØ±íÏÖ³öÀ´¡£
2 µç×ÓÃܶÈÍØÆË·ÖÎöÔÚMultiwfnÖеIJÙ×÷
ÕâÀïÏȽéÉܵç×ÓÃܶÈÍØÆË·ÖÎöµÄ²Ù×÷£¬ÒÔGaussianÔÚHF/6-31G*ÏÂÓÅ»¯²¢Éú³É²¨º¯ÊýÎļþµÄ¶à°Í°··Ö×ÓΪÀý¡£ÏÈÆô¶¯³ÌÐò£¬È»ºóÒÀ´ÎÊäÈë
dopamine.wfn //²¨º¯ÊýÎļþ
2 //ÍØÆË·ÖÎö¹¦ÄÜ
2 //ÒÔËùÓÐÔ×ÓºË×÷Ϊ³õ²Âµã£¬Ä¿µÄÊÇÑ°ÕÒËùÓкËÁÙ½çµã
3 //ÒÔÿһ¶Ô¶ù¾àÀë²»ºÜÔ¶µÄÔ×ÓºËÁ¬ÏßÖеã×÷Ϊ³õ²Âµã£¬Ö÷ÒªÓÃÀ´Ñ°ÕÒ¼üÁÙ½çµã
8 //Éú³É¼ü¾¶
0 //¹Û¿´½á¹û
´ËʱÎı¾½çÃæ»áÊä³öËùÓÐÁÙ½çµãºÍ¼ü¾¶µÄÐÅÏ¢£¬×îºóÌáʾÄãFine, Poincare-Hopf relationship is satisfied£¬ÕâÊÇËùÓÐÁÙ½çµã¶¼ÒÑÕÒµ½µÄ±ØÒª·Ç³ä·ÖÌõ¼þ£¬Èç¹ûÕâ¸öÌõ¼þûÂú×㣬¿Ï¶¨ÁÙ½çµãûÕÒÈ«¡£Í¬Ê±±Ä³öÀ´Ò»¸öͼÐνçÃ棬ÈçÏÂËùʾ
×ÏÉ«µÄÇòÊÇ(3,-3)£¬ÓëÔ×ÓºËλÖûù±¾Ò»Ö¡£½Û»ÆÉ«ÊǼüÁÙ½çµã£¬»ÆÉ«ÊÇ»·ÁÙ½çµã¡£×ØÉ«µÄÏßÊǼü¾¶¡£Í¨¹ýͼÐνçÃ棬¿ÉÒÔÑ¡ÔñÏÔʾÄÄЩ¡¢²»ÏÔʾÄÄЩ£¬ÒÔ¼°ÐýתËõ·ÅµÈ²Ù×÷¡£Æ¾½è»¯Ñ§Ö±¾õ£¬ÒÔ¼°Poincare-Hopf¹Øϵ¿ÉÖªÆÚÍûµÄÁÙ½çµã¶¼ÒѾÕÒµ½ÁË£¬¾Íû±ØÒªÔÙÓÃÑ¡Ïî4£¨Èý¸öÔ×ÓÖÐÐÄ×÷Ϊ³õ²Â£©¡¢Ñ¡Ïî5£¨ËĸöÔ×ÓÖÐÐÄ×÷Ϊ³õ²Â£©»òÑ¡Ïî6£¨ÔÚij¸öλÖø½½üËæ»úÉèÒ»´ó¶Ñµã£©À´½øÒ»²½ÕÒÁÙ½çµãÁË¡£
¼ò¶øÑÔÖ®£¬¶ÔÓÚÒ»°ãµÄÌåϵ£¬ÕÒµç×ÓÃܶȵÄÁÙ½çµã¾ÍÊǽøÈëÍØÆË·ÖÎö½çÃæºó£¬ÒÀ´ÎÑ¡2¡¢3¡¢4¾ÍÐÐÁË£¬¼òµ¥ÖÁ¼«£¡
ÖµµÃ˵Ã÷µÄÊÇMultiwfnµÄ´úÂë¾¹ý³ä·ÖÓÅ»¯£¬²¢ÇÒÖ§³ÖSMP²¢ÐУ¬ÕâʹµÃÆäÍØÆË·ÖÎöËٶȼ«¿ì¡£ÔÚÒ»°ãµÄÖ÷Á÷Ëĺ˻ú×ÓÉÏ£¬ÉÏÃæµÄÈÎÎñÔÚMultiwfnÀïÕ£ÑÛ¼ä¾ÍÍê³ÉÁË¡£ÎÒÔø±È½Ï¹ýAIM2000ºÍMultiwfn·ÖÎöÒ»¸öº¬900¸ö¸ß˹º¯ÊýµÄC60Ìåϵ£¬ÔÚËĺ˲¢ÐеĻú×ÓÉÏ£¬MultiwfnÑ°ÕÒÁÙ½çµãµÄËÙ¶ÈÊÇAIM2000µÄÔ¼100±¶£¬Éú³É¼ü¾¶ËÙ¶ÈÊÇÆ佫½ü30±¶£¬¶ø½á¹ûÍêÈ«Ò»Ö¡£AIMALLµÄËٶȱÈAIM2000Òª¿ì£¬²»¹ýÓÉÓÚËã·¨²»ºÜÒ»Ö£¬Ò²²»ºÃ¹«Æ½µØ±È½Ï£¬µ«´Óʵ¼ÊÓ¦ÓýǶÈÉÏÀ´Ëµ£¬Multiwfn±ÈAIMALLÒª¿ìÒ»¸öÊýÁ¿¼¶¡£ÁíÍâAIMALLµÄ²Ù×÷Ô¶²»ÈçMultiwfnÕâÖÖ½»»¥Ê½³ÌÐò±ãÀû£¬Æä½á¹û¿ÉÊÓ»¯³ÌÐòaimstudio»¹ÒªÊÕ·Ñ¡£¿ÉÒÔ˵£¬ÏëÒª²Ù×÷¼òµ¥¡¢ÄÜÖ±½Ó¿ÉÊÓ»¯¡¢Ãâ·Ñ¶øÇÒËٶȷɿìµÄAIMÍØÆË·ÖÎö³ÌÐò£¬MultiwfnÊDz»¶þ֮ѡ¡£
ÓÐЩÁÙ½çµã±È½ÏÌØÊ⣬ÔÚĬÈϵÄÉ趨Ï£¬Óø÷ÖÖËÑË÷·½·¨¿ÉÄܶ¼ÕÒ²»µ½ÁÙ½çµã£¬Õâ¾ÍÐèÒªÈËΪµ÷ÕûһϲÎÊýÁË£¬ÔÚMultiwfnÀïÌṩÁ˷ḻµÄ¿Éµ÷²ÎÊý¡£±È½ÏµäÐ͵ľÍÊÇÖØÔ×ÓµÄÔ×Ӻ˵ÄÁÙ½çµãÕÒ²»µ½£¬ÕâÊÇÒòΪÔ×Ӻ˴¦µç×ÓÃܶȼ«´óÖµ¶ÔÓ¦µÄ·åÌ«¼âÈñ£¬ÄÑÒÔ¶¨Î»¡£½â¾ö°ì·¨ÊÇÊʵ±½µµÍÊÕÁ²±ê×¼£¬Ò²¾ÍÊǽøÈëÑ¡Ïî-1£¬½«ÌݶȺÍλÒƵÄÊÕÁ²±ê×¼½µµÍ£¬È»ºóÖØÐÂÓÃÑ¡Ïî2ÒÔºËΪ³õ²ÂÀ´ËÑË÷ÁÙ½çµã¡£ÁíÒ»ÖÖÇé¿ö¾ÍÊÇÖØÔ×ÓºÍÇâÁ¬ÏßÉϵļüÁÙ½çµãÕÒ²»µ½£¬Õâ¾ÍÐèÒªÔÚ²ÎÊýÉ趨½çÃæÖн«Set scale factor for stepsizeÒ»ÏîÉèµÍ£¬½¨ÒéÉèΪ0.5£¬È»ºóÔÙÖØÐÂÕÒÁÙ½çµã¡£ÆäËüÑ¡ÏîÔÚMultiwfnÊÖ²áµÚÈýÕµÄÍØÆË·ÖÎöÒ»½ÚÀﶼÓÐ˵Ã÷¡£
Multiwfn»¹ÌṩÁËһЩѡÏîÓÃÓÚ·ÖÎö¡¢±à¼½á¹û¡£ÓÃÑ¡Ïî7²¢ÇÒÊäÈëÁÙ½çµãµÄ±àºÅ£¬¾Í¿ÉÒÔ»ñÖªÕâ¸öÁÙ½çµãµÄÒ»ÇÐÐÅÏ¢£¬°üÀ¨MultiwfnÖ§³ÖµÄ¸÷ÖÖʵ¿Õ¼äº¯ÊýµÄÊýÖµºÍµç×ÓÃܶȵÄÌݶÈÏòÁ¿ºÍHessian¾ØÕó¡£ÀûÓÃ-9¿ÉÒÔ·½±ãµØ¼ÆËãÁÙ½çµã¼ä¡¢Ô×Ó¼äµÄ¾àÀë¡¢½Ç¶È¡£½øÈë-4Ôò¿ÉÒÔµ¼Èëµ¼³öÒÑÕÒµ½µÄÁÙ½çµã¡¢É¾³ý»òÈËΪµØÔö¼ÓÁÙ½çµã¡£½øÈë-5Ôò¿ÉÒÔÏÔʾÍØÆË·¾¶µÄÏêϸÐÅÏ¢£¨Â·¾¶¹ì¼£µÄ×ø±ê¡¢Â·¾¶³¤¶ÈµÈ£©²¢½øÐб༺͵¼Èëµ¼³ö¡£ÔÚMultiwfnÀÍØÆË·¾¶ÊµÖÊÉÏÊÇÒÔÒ»Á¬´®µÄµãÀ´±íʾµÄ¡£
³ýÁËÑ°ÕÒÁÙ½çµãºÍÉú³ÉÍØÆË·¾¶£¬MultiwfnµÄÍØÆË·ÖÎöÄ£¿é»¹ÄÜÉú³É²¢»æÖÆÅè·Ö½çÃ棬¶ÔÓÚµç×ÓÃܶȷÖÎö£¬¾Í¶ÔÓ¦ÓÚÔ×Ó¼ä·Ö½çÃæ(Interatom surface, IAS)¡£ÔÚIASÃæÉÏûÓеç×ÓÃܶÈÌݶÈÏß´©¹ý£¬Ò²³ÆÁãͨÁ¿Ãæ(zero-flux surface)£¬Ã¿¸öIAS¶¼¾¹ýÒ»¸ö¼üÁÙ½çµã¡£IAS½«Õû¸ö·Ö×ÓÇøÓò·Ö¸ô³ÉÒ»¸ö¸öÔ×ӿռ䣬Ҳ½ÐÔ×ÓÅè¡£´ÓÍØÆË·ÖÎöÖ÷½çÃæ½øÈëÑ¡Ïî10ºó£¬ÊäÈë(3,-1)µÄ±àºÅ£¬¾ÍÄÜÉú³É´©¹ýÕâ¸ö(3,-1)µÄIAS¡£¶øÔÚ±àºÅÇ°¼ÓÉϸººÅ£¬¾Í˵Ã÷½«ÒѾÉú³ÉµÄ´©¹ýÕâ¸ö(3,-1)µÄIASɾµô¡£Èç¹ûµ±Ç°ÉÐδÉú³ÉÈκÎIAS£¬ÊäÈë0¾Í¿ÉÒÔÉú³ÉËùÓÐIAS¡£Èç¹ûÒѾÓÐÁËIAS£¬ÊäÈë0¾Í»áɾµôËùÓÐIAS¡£ÏÂͼÖÐÉú³ÉÁ˲¿·ÖIAS
3 ELFÍØÆË·ÖÎöÔÚMultiwfnÖеIJÙ×÷
ÕâÒ»½Ú̸̸ELFµÄÍØÆË·ÖÎö²Ù×÷£¬ÒÔ±½·ÓΪÀý¡£
phenol.wfn // HF/6-31G*ÏÂÓÅ»¯ºóµÃµ½µÄ²¨º¯Êý
2 //½øÈëÍØÆË·ÖÎöÄ£¿é
-11 //Çå¿ÕÒÑÓÐÍØÆË·ÖÎöÊý¾Ý²¢Ñ¡ÔñеÄʵ¿Õ¼äº¯Êý¡£Ä¬Èϵĺ¯ÊýÊǵç×ÓÃܶÈ
9 //Ñ¡ÔñELF
6 //ÔÚÖ¸¶¨°ë¾¶ºÍÖÐÐĵÄÇòÀïËæ»ú·Ö²¼Ö¸¶¨ÊýÄ¿µÄ³õ²ÂµãÀ´ËÑË÷ÁÙ½çµã
-1 //½«Ã¿¸öÔ×ÓºËÒÀ´Î×÷ΪÇòÖÐÐÄ¡£ÓÉÓÚ´Ë·Ö×ÓÓÐ13¸öÔ×Ó£¬Èç¹ûÌáʾÖÐ"Points:"´ËʱÏÔʾµÄÊDZÈÈç1000£¬×ܹ²¾Í»áÒÔ13*1000=13000¸ö³õ²ÂµãÀ´ÕÒÁÙ½çµã¡£ÔÚÎÒµÄi7-2630QM»ú×ÓÉÏÒÔËĺ˲¢ÐÐģʽÔËÐУ¬½ö15ÃëÖÓ¾ÍÍê³ÉÁËËÑË÷¡£
-9 //·µ»ØÉÏÒ»¼¶²Ëµ¥
0 //¹Û¿´½á¹û
Äã»á¿´µ½½á¹ûÔ¶±Èµç×ÓÃܶȷÖÎöʱ¸´ÔÓ£¬×ܹ²ÕÒ³öÁË126¸öÁÙ½çµã£¬ºÜ»¨ÉÚ¡£ÎªÁËʹ½á¹û¸üÇå³þ£¬¿ÉÒÔ½«ÒâÒå²»´óµÄ(3,+1)ºÍ(3,+3)ÁÙ½çµãͨ¹ýÓҲิѡ¿ò¹Øµô¡£ÁíÍ⣬Ô×ÓÇòµ²×¡ÁËһЩÁÙ½çµã£¬½«Ratio of atomic size»¬¶¯ÌõÍϵ½×îС£¬Ô×ÓÇò¾Í²»ÏÔʾÁË£¬·Ö×Ó´ËʱÏ൱ÓÚÒÔ¹÷°ôÄ£ÐÍÏÔʾ¡£ÈçÏÂͼËùʾ¡£
ÒÀÈ»ÊÇÿһ¸ö×ÏÇò¶ÔÓ¦Ò»¸ö(3,-3)¡£¿ÉÒÔ¿´µ½Ã¿¸öÔ×Ӻ˶¼ÓÐÒ»¸ö(3,-3)£¨¶ÔÓÚÇâÔ×Ó»áÆ«ÀëЩ£©¡£Èç¹ûÄã·¢ÏÖÔ×Ӻ˴¦Ã»ÓÐ×ÏÇò£¬ËµÃ÷ËüÃÇËÑË÷ÖЩ¹ýÈ¥ÁË£¬¿ÉÒÔÓÃÑ¡Ïî2ÒÔÔ×ÓºËλÖÃΪ³õ²ÂÔÙÕÒһϣ¬Ò»°ã¶¼ÄÜÕÒµ½¡£C-CºÍC-O¼üÖ®¼ä¶¼ÓÐ×ÏÇò£¬Õâ¶ÔÓ¦ÓÚ¹²¼Û¼üÇøÓòµç×Ó¶¨Óò³Ì¶È¾Ö²¿×î¸ßµã¡£ÔÚÑõÔ×ÓÅԱ߻¹ÓÐÁ½¸öÐü×ŵÄ×ÏÇò£¬ËüÃǶÔÓ¦ÓÚÑõµÄÁ½¸ö¹Â¶Ôµç×ӵĵç×Ó¶¨ÓòÐÔ¾Ö²¿×î´óµã¡£´ÓλÖÃÉÏ¿´£¬°´ÕÕ´«Í³ÔÓ»¯ÀíÂÛ¿ÉÒÔÈÏΪÑõÊÇ´¦ÓÚsp3ÔÓ»¯×´Ì¬¡£
ÔÚÏÔʾ½á¹ûµÄʱºò£¬ÃüÁîÐд°¿Ú»áÌáʾWarning: Poincare-Hopf relationship is not satisfied, some CPs may missing£¬Õâ±íÃ÷ÕâÒ»´ÎËÑË÷²¢Ã»Óн«ËùÓÐÁÙ½çµãÕÒÈ«¡£²»¹ýûÓйØϵ£¬ÒòΪ´ÓͼÖпɼûËùÓÐÓÐÏÔÖø»¯Ñ§ÒâÒåµÄÁÙ½çµã¶¼ÕÒµ½ÁË¡£Èç¹ûÄãÏë³¹µ×ÕÒÈ«£¬ÄÇô¾ÍÔٴνøÈëÑ¡Ïî6£¬Êʵ±Ñ¡Ôñ²ÎÊýºóÖØнøÐÐÁÙ½çµãËÑË÷£¬½«»áÕÒ³öÁãÐÇÊý¸öÊ£ÓàµÄÁÙ½çµã¡£³¹µ×ÕÒÈ«ËùÓÐÀàÐÍELFµÄÁÙ½çµã£¬¶ÔÓÚ²»ÊǺÜСµÄÌåϵÊǺÜÀ§ÄѵÄÊ£¬Ò»°ãûÓбØҪȥ×ö¡£¶ÔÓÚ×îÖØÒªµÄÁÙ½çµãÀàÐÍ£¬¼´(3,-3)£¬»ù±¾ÉÏ×öÒ»´Îÿ¸öÔ×ÓÖÜΧÓÐ1000¸ö³õ²ÂµãµÄËÑË÷£¨¼´±¾ÀýµÄ²Ù×÷£©ºó¾Í¶¼ÄÜÕÒµ½¡£
ÏÖÔÚµãRETURN¹Ø±ÕͼÐνçÃæ»Øµ½ÍØÆË·ÖÎöÖ÷²Ëµ¥£¬Ñ¡8À´Éú³É(3,-1)ºÍ(3,-3)¼äµÄÍØÆË·¾¶£¬ÔÙ´ÎÏÔʾ½á¹û£¬ÈçÏÂͼËùʾ
Ô±¾¿´ÆðÀ´ÊýÄ¿ÖڶࡢºÜÂҵĽۻÆɫСÇò£¬¼´(3,-1)µã£¬Í¨¹ýÍØÆË·¾¶Óë(3,-3)ÏàÁ¬ºó£¬´Ëʱ¹Øϵ±äµÃ±È½ÏÇåÎúÁË¡£
¶ÔÓÚ¸ö±ðÌåϵ£¬ÓÐʱºò»á·¢ÏÖ±¾¸Ã³öÏÖµÄ(3,-1)Óë(3,-3)¼äµÄ·¾¶Ã»ÓгöÏÖ£¬ÕâºÜ¿ÉÄÜÊÇÒòΪÉú³ÉÍØÆË·¾¶µÄĬÈϲÎÊý²»Ì«Êʺϡ£±È½ÏÓÐЧµÄ½â¾ö·½·¨ÊǽøÈëÑ¡Ïî-2£¬½«StepsizeÉèµÃСһЩ£¬±ÈÈ罫ĬÈÏÖµ¼õСһÁ½±¶¡£×¢Òâ·¾¶µÄ×î´ó³¤¶ÈÊÇ"²½³¤*·¾¶µÄ×î´óµãÊý"£¬Èç¹ûÉú³É·¾¶¹ý³ÌÖУ¬µü´ú´ÎÊý³¬¹ýÁË×î´óµãÊý»¹Ã»Óö¼ûÁíÍâÒ»¸öÁÙ½çµã£¬¾Í˵Ã÷Õâ´Î·¾¶Éú³Éʧ°Ü¡£Òò´Ë£¬²½³¤ÉèСÁË£¬ÄÇô·¾¶×î´ó³¤¶È¾Í»á¼õС£¬Èç¹ûÌåϵÖÐÓÐһЩºÜ³¤µÄ·¾¶£¬ÕâЩ·¾¶¿ÉÄÜÔÚ´Ëʱ¾Íû·¨Éú³ÉÁË¡£Òò´Ë¼õС²½³¤µÄͬʱҲӦµ±Í¬Ê±¼Ó´ó·¾¶×î´óµãÊý¡£²½³¤Ô½Ð¡Ô½ÈÝÒ׳ɹ¦Éú³É¸´Ôӵķ¾¶£¨±ÈÈçÇúÂÊÌرð´óµÄ·¾¶£©£¬µ«ÊÇÓÉÓÚÐèÒª¼Ó´ó·¾¶×î´óµãÊý£¬Õâ¾Í»áÔì³É¼ÆËãºÄʱԽ¶à¡£Ä¬ÈϵÄ·¾¶Éú³É²ÎÊýÊÇÕÛÖп¼ÂǾ«¶ÈºÍЧÂʵĽá¹û¡£
LOLºÍµç×ÓÃܶÈÀÆÕÀ˹º¯ÊýÓëELFÓкܴóÏàËÆÖ®´¦£¬´Ë½ÚµÄ×ö·¨Ò²Í¬ÑùÊʺÏÕâÁ½ÖÖº¯Êý£¬Ö»ÒªÔÚÑ¡Ïî-11ÀïÑ¡ÔñÏàÓ¦µÄº¯ÊýÈ»ºóÒÔ±¾ÀýͬÑùµÄ·½·¨²Ù×÷¼´¿É¡£ÁíÍ⻹¿ÉÒÔÓÃÕâÖÖ·½·¨À´»ñµÃ¹ìµÀ²¨º¯ÊýµÄÁÙ½çµã¡£
4 ̸̸¹Â¶Ôµç×ӽǶÈÔõôËã
ºÃ¼¸´Î¿´µ½ÓÐÈËÎʹ¶Եç×Ӽнǡ¢¶þÃæ½ÇÔõôË㣬ÓÉÓÚMultiwfnµÄÍØÆË·ÖÎö¹¦ÄÜÕýºÃÄܽâ¾öÕâ¸öÎÊÌ⣬ËùÒÔ˳±ã̸̸¡£Èç¹û¶Ô´ËÎÊÌâûÐËȤ£¬¿ÉÒÔÌø¹ýÕâ½Ú¡£
ÔÚÌÖÂÛÔõô¼ÆËã½Ç¶ÈÕâ¸ö¾ßÌåÎÊÌâÇ°£¬ÏÈÒª¸ãÇå³þ¹Â¶Ôµç×ÓÓ¦¸ÃÈçºÎÑϸñµØÃèÊö¡£Ê×ÏÈÒªÃ÷È·µÄÊÇ£¬¹Â¶Ôµç×Ó±¾Éí²»Êǿɹ۲âµÄ£¬Ö»ÊǸö¸ÅÄҲû·¨Î¨Ò»µØÈ¥¶¨Ò壬ֻÄÜ˵ÄÄÖÖ·½Ê½µÄÃèÊö¸üÓÐÎïÀíÒâÒå¡£Ò»°ãÒâÒåÉϵŶԵç×ÓÖ¸µÄ¾ÍÊÇÔ×Ó¼Û²ãij¾Ö²¿¿Õ¼äÄÚÔ˶¯µÄÁ½¸ö×ÔÐý»¥ÏàÅä¶ÔµÄµç×Ó¡£Ò»ÖÖ½«Õâ¸ö¸ÅÄî¾ßÏÖ»¯µÄ·½·¨ÊǹìµÀ¶¨Óò»¯·½·¨£¬Ëüͨ¹ý¶ÔÕ¼¾ÝµÄ·Ö×Ó¹ìµÀ£¨ÍùÍùÓкÜÇ¿ÀëÓòÌØÕ÷£©½øÐÐÓϱ任£¬»ñµÃÄܹ»Ó뻯ѧ¼ü¡¢¹Â¶Ôµç×ÓÏà¶ÔÓ¦µÄ¹ìµÀ£¬ºÜ´ó³Ì¶ÈÉÏÖØÏÖÁËlewisÄ£ÐÍ¡£ÕâÀà·½·¨×î´óȱµãÊÇÎïÀíÒâÒå²»Ñϸñ£¬Óϱ任¹ý³ÌÊÇËæÒâµÄ£¬ÒÔʲô±ê׼ȥ×öÓϱ任ÒòËã·¨¶øÒ죬²»Í¬µÄ³£ÓõĶ¨Óò»¯·½·¨ËäÈ»Äܵõ½ÏàËƵÄͼ¾°£¬µ«ÊÇÔÚ¶àÖؼü¡¢¹Â¶Ôµç×ÓµÄÃèÊöÉÏÈ´¿ÉÄܺܲ»Ïàͬ£¬ËùÒÔÎÒ²¢²»½¨ÒéÓÃÕâÀ෽ʽÌÖÂ۹¶Եç×Ó¡£NBOÒ²ÊÇÊôÓÚ¶¨Óò»¯¹ìµÀÒ»À࣬ËäÈ»²»ÊÇͨ¹ýÓϱ任µÃµ½£¬µ«½á¹ûÉÏ¿´Ò²Í¨³£²î²»¶à¡£´ÓËã·¨ÉÏNBO·ÖÎö¶Ô¹Â¶Ôµç×ÓµÄÃèÊöÔÚ¹ÑÈË¿´À´Ò²Óе㲻ºÏÀíÐÔ£¬ÔÚNBO·ÖÎöÖÐÊÇÏÈ´ÓÃܶȾØÕóµÄÔ×ӶԽǿéËÑË÷ÍêCR¡¢LPÐÍNBO²Å¿ªÊ¼Ñ°ÕÒË«ÖÐÐÄNBO£¬µÈÓÚ˵Éú³ÉLPµÄÓÅÏȼ¶Òª¸ßÓÚË«ÖÐÐÄNBO£¬È»¶øʵ¼ÊÉϹ¶Եç×Ӻͻ¯Ñ§¼üÊÇͬʱÐγɵģ¬Ó¦µ±Í¬²½¿¼ÂÇ¡£ÕâÒ²µ¼ÖÂÁËNBOµÄ¹Â¶Ôµç×Ó¹ìµÀ¿´ÆðÀ´ºÍÔÓ»¯ÀíÂÛÏÔʾµÄͼ¾°²»·û¡£
ÏÂÃæÊÇHF/6-31G*ϵı½·ÓµÄ16ºÅºÍ22ºÅNLMO¹ìµÀͼÐΣ¬ÒÔ¼°Á½¸ö¹ìµÀ²¨º¯ÊýÏà¼ÓºÍÏà¼õºóµÄͼÐΡ£Ë³´øÒ»ÌᣬNLMOÊÇNBO·ÖÎö·½·¨¿ò¼ÜÄÚµÄÒ»²¿·Ö£¬ËüÊÇÓÉNBO½øÒ»²½±ä»»µÃµ½µÄ£¬Í¨³£ºÍNBOºÜÏàËÆ£¬Ö»ÊÇÀëÓòÐÔ±ÈNBOÉÔ´ó¡£NLMOÒ²¿ÉÒÔÊÓΪÊÇÖ±½Óͨ¹ý¶ÔÕ¼¾ÝµÄ·Ö×Ó¹ìµÀÓϱ任µÃµ½µÄ¡£
16ºÍ22ºÅNLMO¶ÔÓ¦ÑõµÄ¹Â¶Ôµç×Ó£¬Õ§¿´ÉÏÈ¥ºÃÏñÑõÊÇsp2ÔÓ»¯£¬Ò»¸ö¹Â¶Ôµç×ÓÔÚƽÃæÉÏ£¬Ò»¸ö´¹Ö±ÓÚƽÃæ¡£µ«Êµ¼ÊÉÏÎÒÃÇ¿ÉÒÔ½«ÕâÁ½¸ö¹ìµÀÈËΪµØ»ìºÏÐγÉÁ½¸öеĹìµÀ£¬¼´16+22ºÍ16-22£¨ÎªÁËÊ¡ÊÂδ¿¼ÂǹéÒ»»¯£¬Õâ¶Ô¶¨ÐÔ·ÖÎöûӰÏ죩¡£ÕâÁ½¸öеĹìµÀÒ²¿ÉÒÔ˵ÊǶÔÓ¦¹Â¶Ôµç×ӵģ¬ÕâÑùÒ»À´Ñõ¾Í³ÉÁËsp3ÔÓ»¯ÁË£¬ÓëELF·ÖÎöµÄ½á¹ûÒ»Ö¡£»òÐí»áÓÐÈËÎÊ£¬½«16ºÍ22ºÅ¹ìµÀÄÇô»ìºÏÓеÀÀíô£¿ÕâÑù»ìºÏÊÇûÎÊÌâµÄ£¬ÒòΪNLMO¼ä¶¼ÊÇÕý½»µÄ£¬Òò´Ë16+22ÒÔ¼°16-22¹ìµÀÒ²ÓëÆäËü¹ìµÀÕý½»£¬ÕâµÈÓÚÊǶÔÕ¼¾Ý¹ìµÀÔÙÓϱ任һÏ°ÕÁË£¬ÍêÈ«ÊÇÔÚ¹ìµÀ¶¨Óò»¯µÄ¿ò¼ÜÄÚÔÊÐíµÄ²Ù×÷¡£ËùÒÔ˵¶¨Óò»¯¹ìµÀÄ£ÐÍÓÐÑÏÖصÄÈÎÒâÐÔ£¬Á¬¹Â¶Ôµç×Ó¹ìµÀ¶¼²»ÄÜΨһȷ¶¨£¬¸ü±ÂÌáÔÙ½øÒ»²½¼ÆËã¹Â¶Ôµç×ӽǶÈÁË¡£
ÎïÀíÒâÒå±È½ÏÑϸñµÄÊÇͨ¹ýʵ¿Õ¼äº¯Êý·ÖÎö£¬¾ßÌåÀ´ËµÊÇELF»òLOLº¯Êý£¬½á¹ûͨ³£½ÏÏàËÆ¡£µç×ÓÃܶÈÀÆÕÀ˹º¯ÊýÒ²ÄÜ·ÖÎö£¬µ«ËüÓëµç×Ó¶¨Óò»¯µÄ¹ØϵֻÊǼä½ÓµÄ£¬º¯ÊýÐÐΪÉÏÒ²²»ÈçELFºÍLOLÊæ·þ¡£ELF½Ï´óµÄÇøÓò£¬±íÃ÷ÏàÓ¦ÇøÓòÄڵĵç×Ó¶¨ÓòÐÔ½ÏÇ¿£¬¿ÉÒÔÍƶϵç×ӵķÑÃ×ѨÖ÷Òª·Ö²¼ÔÚÕâ¸öÇøÓòÄÚ£¬¼´×ÔÐýÏàͬµç×Ó¼ä¾àÀë»á½ÏÔ¶£¬¶ø×ÔÐýÏà·´µÄµç×ÓÏà¶ÔÀ´Ëµ¾ÍÈÝÒ×´ôÔÚÒ»Æ𣬼´Ëµµç×ÓÔÚÕâ¸öÇøÓòÄÚÅä¶Ô£¬ÕâÕýÊǹ¶Եç×Ó¸ÅÄîÑϸñµÄÎïÀí½âÊÍ¡£Èç¹û¶Ôµç×Ó¶¨ÓòÐÔÎÊÌâÏëÓнøÒ»²½Á˽⣬¿É²ÎÔıÊÕߵġ¶µç×ӵĶ¨ÓòÐÔÓëÏà¹ØѨ¡·Ò»ÎÄ£¨http://hi.baidu.com/sobereva/blo ... 7954dca7ef3f8e.html£©¡£Òò´Ë£¬Î»ÖÃÊʵ±µÄELF½Ï´óµÄÇøÓò¾Í¿ÉÒÔ˵Êǹ¶Եç×ÓµÄÇøÓò£¬ÄÇôͨ¹ýÍØÆË·ÖÎö¸ø³öµÄELF½Ï´óÇøÓòµ±Öеļ«´óµã£¬¾Í¿ÉÒÔ˵Êǹ¶Եç×Ó³öÏÖλÖõÄ×î´ó³Ì¶ÈµÄ³éÏó£¬ÀûÓÃÕâ¸öµã¾Í¿ÉÒÔºÜÈÝÒ׵ؼÆËã³ö¹Â¶Ôµç×ӽǶÈÁË¡£
±ÈÈ磬°´ÕÕµÚÈý½ÚµÄ·½·¨ÕÒÍêÁÙ½çµãºó£¬ÎÒÃÇÏë¼ÆËãCP93-O12-CP83µÄ¼Ð½Ç£¨±êºÅ¼ûÏÂͼ¡£ÔÚͼÐνçÃæÑ¡ÔñCP labels¾ÍÄÜÏÔʾ¸÷¸öÁÙ½çµãµÄ±àºÅ£©£¬¾ÍÔÚÍØÆË·ÖÎöÖ÷½çÃæÀïÃæÑ¡Ñ¡Ïî-9ÒÔ½øÈë½Ç¶È²âÁ¿µÄ½çÃ棬ȻºóÊäÈëa c93 a12 c83£¬½á¹ûÏÔʾΪ88.228¶È¡£ÕâÀïa´ú±íangle£¬c´ú±ícritical point£¬a´ú±íatom£»ÏëÔÙ²âÁ¿CP83-O12-C4-C5µÄ¶þÃæ½Ç¾ÍÊäÈëd c83 a12 a4 a5£¬½á¹ûÊÇ130.496¶È¡£°´q¿ÉÒÔ·µ»ØÖ÷²Ëµ¥¡£ÖµµÃÒ»ÌáµÄÊÇÿ´ÎËÑË÷ÁÙ½çµã¸ø³öµÄÁÙ½çµãµÄ±àºÅ¿ÉÄܲ»Í¬£¬ËùÒÔ¶ÔÒ»¸öÌåϵÖظ´·ÖÎöʱ£¬Ã¿´Î¶¼Ó¦ÔÚͼÐνçÃæÀï¿´Çå³þ¸÷¸öÁÙ½çµãµÄµ±Ç°±àºÅ¡£
ÎÒÃÇÒ²¿ÉÒÔ¿´¿´ÓÃLOLºÍÀÆÕÀ˹º¯ÊýÑо¿Õâ¸öÎÊÌâÄܵõ½Ê²Ã´½á¹û¡£ÔÚÍØÆË·ÖÎöµÄÖ÷²Ëµ¥Ñ¡Ôñ-11È»ºóÑ¡ÔñLOLº¯Êý£¬´ËʱËùÓиղÅELFµÄÍØÆË·ÖÎö»á×Ô¶¯Çå¿Õ£¬È»ºóÖØÐÂËÑË÷ÁÙ½çµã£¬ÎÒÃǻῴµ½¸÷¸ö(3,-3)µÄλÖúÍELF·ÖÎöʱ¶¼²î²»¶à¡£ÔٴμÆËãÑõµÄÁ½¶Ô¶ù¹Â¶Ôµç×Ó¼äµÄ¼Ð½Ç£¬µÃµ½µÄ½á¹ûÊÇ119.895¶È£¬Ã÷ÏÔ´óÓÚELF¸ø³öµÄÊýÖµ¡£¸ÄÓõç×ÓÃܶÈÀÆÕÀ˹º¯ÊýÔÙËãÒ»´Î£¬½á¹ûÊÇ131.244¶È£¬¸ü´óÁË¡£°´ÕÕÒ»°ã¹ÛÄ¹Â¶Ôµç×Ó¼äÏ໥»¥³â±È½ÏÇ¿£¬Ò²Ó¦µ±´óÓÚsp3ÔÓ»¯µÄ109¶È28·Ö¡£½á¹ûÔÚÒ»¶¨³Ì¶ÈÉÏÏÔʾELF¿ÉÄÜ»áµÍ¹À¹Â¶Ôµç×ӵļнǡ£Êµ¼ÊÉÏÓÐʱµÍ¹ÀµÃ¸üÀ÷º¦£¬ÄËÖÁÓÚLOLµÄ½áÂÛÊÇÓÐÁ½¶Ô¶ù¹Â¶Ôµç×Ó³öÏÖµÄʱºò£¬ELFÈ´ÈÏΪÁ½¶Ô¶ù¹Â¶Ôµç×ÓºÏÔÚÁËÒ»Æð¡£ÎҵĽ¨ÒéÊÇʹÓÃLOLÀ´Ñо¿¹Â¶Ôµç×Ó£¬LOL±ÈELFÐÎʽ¸ü¼òµ¥£¬¼ÆËãËÙ¶ÈÉԿ죬¶øÇÒһЩÎÄÕÂÖ¸³öLOLÒ²Äܸø³ö±ÈELF¸üÇå³þµÄ»¯Ñ§Í¼¾°£¬¶øLOLÔÚÎïÀíÒâÒåÉÏÒ²ºÍELF²î²»¶à¡££¨LOLÒ²²¢·Ç¸÷·½Ã涼±ÈELFºÃ£¬µÈÓлú»áÔÙϸ̸£©
5 ÁÙ½çµãÓëµÈÖµÃæͼ
ÎÒÃǽÓÏÂÀ´½«Í¨¹ýµÈÖµÃæͼÌÖÂÛELFµÄÓò(Domain)¡¢·ÖÆçµã(Bifurcation point)Óë(3,-3)¼°(3,-1)ÁÙ½çµãµÄ¹Øϵ£¬ÕâÓÐÖúÓÚÀí½âÒÔ¼°ÑéÖ¤ÍØÆË·ÖÎöµÄ½á¹û¡£
ÏÈ°´ÕÕµÚÈý½ÚµÄ¹ý³ÌËÑË÷ÍêELFÁÙ½çµã£¬È»ºóÖ±½ÓÍ˻ص½Ö÷²Ëµ¥£¬²¢ÊäÈëÒÔÏÂÃüÁî
5 //Éú³É¸ñµãÎļþ
9 //ELFº¯Êý
2 //ÖеȾ«¶È¸ñµã£¬¶ÔÓÚСÌåϵ¶¨ÐÔ·ÖÎöÕâ¾Í¹»ÁË¡£Õâʱ¿ªÊ¼¼ÆËã
-1 //ÏÔʾµÈÖµÃæ
ÓÉÓÚÒѾËÑË÷¹ýÁËÁÙ½çµã£¬ËùÒÔÁÙ½çµãÒ²ÔÚµÈÖµÃæͼÉÏÒ»ÆðÏÔʾÁ˳öÀ´¡£À¶¯µÈÖµÃæÊýÖµµÄ»¬¶¯Ìõ£¬¿ÉÒÔ¿´µ½Ëæ×ÅÊýÖµÓÉСµ½´ó£¬µÈÖµÃæÈçÏÂͼ±ä»¯£¨À¶É«Êý×ÖÊǵÈÖµÃæ¶ÔÓ¦µÄÊýÖµ£©
ÓÉͼ¿É¼û£¬ÔÚÊýÖµºÜСʱ£¬µÈÖµÃæÁ¬³ÉÒ»¸ö´óÓò£¨»òÕß½Ð×öÅ裬ÊÇÖ¸µÈÖµÃæ°üº¬µÄ·â±Õ¿Õ¼ä£©£¬Ò²±íÃ÷Äܳ¬¹ýÕâ¸ö¶¨ÓòÐÔ±ê×¼µÄÇøÓò·Ç³£¹ã¡£Ëæ×ÅÊýÖµÔö¼Ó£¬µÈÖµÃ濪ʼÖð½¥¼õС¡£ÔÚ0.52ʱ£¬ÈçºìÉ«¼ýÍ·ËùÖ¸£¬Ç¡ºÃÁ½¸ö(3,+1)¸Õ¸Õ³öÏÖ¡£ËüÃǵijöÏÖÈÝÒ×Àí½â£¬ÒòΪ(3,+1)´ú±íÕâ¸öµãÔÚÁ½¸ö·½ÏòÉÏÊǺ¯ÊýÖµ¼«Ð¡µã£¬¶øÁíÒ»¸ö·½ÏòÊǼ«´óµã£¬ÓɵÈÖµÃæËæÊýÖµµÄ±ä»¯¹ý³Ìͼ¿ÉÒÔÏëÏó£¬ÄÇÁ½¸ö×÷Ϊ¼«Ð¡µãµÄ·½Ïò¾ÍÊÇ˳×ŵÈÖµÃæµÄÁ½¸öÕý½»·½Ïò£¬¶ø×÷Ϊ¼«´óµãµÄ·½ÏòÊÇ»ù±¾ÉÏ´¹Ö±ÓÚµÈÖµÃæµÄ·½Ïò¡£½øÒ»²½Ôö¼ÓµÈÖµÃæÊýÖµ£¬µÈÖµÃæ»á½øÒ»²½Î®Ëõ£¬²¢ÇҺܶàµØ·½µÈÖµÃ濪ʼ·ÖÀ룬ÁªÍ¨µÄ´óÓòÖð½¥·Ö½âΪСÓò¡£ÔÚ0.66ʱ£¬ºìÉ«¼ýÍ·ËùÖ¸µÄµØ·½¾ÍÊÇÒ»¸öÓò¿ªÊ¼·ÖÆçµÄµØ·½£¬³ÆΪ·ÖÆçµã£¬·²ÊÇÕâÖֵط½¶¼¶ÔÓ¦ÓÚÒ»¸ö(3,-1)µã£¬¶øÍØÆË·ÖÎöʱ»ñµÃµÄÏàÓ¦(3,-1)µãµÄELFÊýÖµ£¬Ò²¾ÍÕý¶ÔÓ¦ÓÚELFÓòÔÚ´Ë´¦·ÖÆçʱµÄÊýÖµ¡£µÈÖµÃæÊýÖµÔö¼Óµ½±È½Ï¸ßµÄÇé¿ö£¬Èç0.84£¬´ÓͼÖпɼûELFÓòÒѾ³ä·Ö·ÖÀëÁË£¬¶ÔӦÿ¸ö³É¼üÇøÓòÒÔ¼°ÇâµÄ¸ß¶¨ÓòÐÔÇøÓòÒѾºÜÇåÎúÃ÷ÀÊ£¬µ«ÊÇÑõµÄÁ½¶Ô¶ù¹Â¶Ôµç×ӵĸ߶¨ÓòÐÔÇøÓò»¹ÊÇû·Ö¿ª¡£¼ÌÐøÔö¼Óµ½0.915ʱ£¬·¢ÏÖÁ½¶Ô¶ù¹Â¶Ôµç×ÓµÄÓòÇ¡ºÃ·ÖÀ뿪£¬ºì¼ýÍ·Ö¸³öÁË·ÖÆçµã¡£Èç¹û½øÒ»²½Ôö¼ÓÊýÖµ£¬Ôòÿ¸öÓò¶¼Ö»»á½øÒ»²½ËõСֱÖÁÏûʧ£¬µ«²»»áÔÚÕâ¸ö¹ý³ÌÖзÖÆç³ÉΪ¸üСµÄÓò£¬ÕâÖÖ²»ÄÜÔÙ·ÖÆçµÄÓò³ÆΪ²»¿ÉÔ¼Óò¡£Ã¿¸ö²»¿ÉÔ¼ÓòÀïÃ涼°üº¬Ò»¸ö(3,-3)ÁÙ½çµã£¬¶ÔÓ¦ÓÚÓòËæ×ŵÈÖµÃæÊýÖµÔö¼ÓÔ½±äԽС×îºóÏûʧµÄλÖá£
µÈÖµÃæͼ±È½ÏÖ±¹ÛÇå³þ£¬¸÷¸ö¸ß¶¨ÓòÐÔÇøÓòһĿÁËÈ»£¬Í¨¹ý²»¶Ïµ÷½ÚµÈÖµÃæÊýÖµ£¬»¹¿ÉÒÔÖ±½ÓÈ·¶¨³ö(3,-1)ºÍ(3,-3)µÄλÖúÍÕâЩÁÙ½çµãµÄÊýÖµ¡£µ«ÊǵÈÖµÃæͼ²»±ãÓÚ׼ȷµØ¶¨Á¿·ÖÎö£¬ÎÞ·¨µÃµ½ºÜ¾«È·µÄÁÙ½çµãµÄλÖúͺ¯ÊýÊýÖµ¡£¶øÇÒ£¬ÕâÖÖÕÒÁÙ½çµãµÄ·½·¨Ò²±È½ÏÀÛ£¬ÓÈÆäÊÇͨ¹ý¹Û²ìµÈÖµÃæµÄ±ä»¯À´È·¶¨(3,+1)ºÍ(3,-3)ÁÙ½çµãÊǺÜÀ§Äѵġ£Ö±½ÓÓÃÍØÆË·ÖÎöËäȻ׼ȷ¿ìËÙ£¬µ«µç×ӽṹ¸´ÔÓʱ£¬ÁÙ½çµã·Ö²¼·×·±¸´ÔÓ£¬²»ÄÜ´ÓͼÉÏÖ±¹ÛµØ»ñÖª¸÷¸ö¿Õ¼äλÖõç×Ó¶¨ÓòÐԵĴóС¡¢¸ß¶¨ÓòÐÔÇøÓòµÄ·Ö²¼·¶Î§¡£ËùÒÔ£¬ÍØÆË·ÖÎöºÍµÈÖµÃæ·ÖÎö½¨Òé½áºÏʹÓã¬Ç°ÕßÓÃÓÚ¾«È·¶¨Á¿·ÖÎö£¬ºóÕßÓÃÓÚ¿ìËÙ¶¨ÐÔ·ÖÎö¡£ÁíÍ⣬ͨ¹ýµÈÖµÃæͼ¹Û²ì²»¿ÉÔ¼ÓòµÄλÖã¬Ò²ÓÐÖúÓÚÈ·¶¨ÊÇ·ñÔÚÍØÆË·ÖÎöÖЩµôÁËһЩ(3,-3)ÁÙ½çµã£¬Èç¹ûij²»¿ÉÔ¼ÓòµÄ·¶Î§ÄÚûÕÒµ½(3,-3)£¬¾ÍÓ¦µ±ÔÚËÑË÷ÉèÖÃÖн«ÇòµÄÖÐÐÄÉèÔÚÄǸöÇøÓò£¬ÈôóÁ¿ÔÚÇòÌåÄÚËæ»ú·Ö²¼µÄµã×÷Ϊ³õ²ÂµãÀ´Ñ°ÕÒÄǸö(3,-3)¡£ |
» ÊÕ¼±¾ÌûµÄÌÔÌùר¼ÍƼö
» ²ÂÄãϲ»¶
» ±¾Ö÷ÌâÏà¹Ø¼ÛÖµÌùÍƼö£¬¶ÔÄúͬÑùÓаïÖú:
|