Applied Biomathematics for Nucleic Acid Chemistry and Protein Folding: Quantitative Simulations

A Theoretical Investigation on 10-12 Potential of Hydrogen-Hydrogen Covalent Bond

Author(s): Sencer Taneri * .

Pp: 65-73 (9)

DOI: 10.2174/9789815179965123010009

* (Excluding Mailing and Handling)

Abstract

In Appendix, we have an analytical investigation of the well-known 10-12 potential of hydrogen-hydrogen covalent bond. In this research, we will make an elaboration of the well-known 6-12 Lennard-Jones potential in case of this type of bond. Though the results are illustrated in many text books and literature, an analytical analysis of these potentials is missing almost everywhere. The power laws are valid for small radial distances, which are calculated to some extent. The internuclear separation as well as the binding energy of the hydrogen molecule are evaluated with success. 

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      • 13. app/Models/UserAccess/UserAccess.php:1266
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      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Trial Access" as access_base_text, CASE j.type WHEN 111 THEN true ELSE false END as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_trail` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59650778 and j.to_ip >=59650778 )) and ((j.from_date <= 1739847149 and j.to_date >= 1739847149 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 20979) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Subscribed" as access_base_text, false as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_corporate` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59650778 and j.to_ip >=59650778 )) and ((j.from_date <= 1739847149 and j.to_date >= 1739847149 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 20979) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Token Based Access" as access_base_text, false as terms_popup, "R" as content_download_type, j.uc_id as restricted_user_access_key, "v" as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_token` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59650778 and j.to_ip >=59650778 )) and ((j.from_date <= 1739847149 and j.to_date >= 1739847149 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 20979)
      610μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
      Backtrace
      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1549
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` where `b`.`banner_ebook` = 1 and `bd`.`content_type` = 'B' and `bd`.`content_id` = 3625 and `b`.`banner_from_date` <= 1739847149 and `b`.`banner_to_date` >= 1739847149 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.08msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 3625
      • 3: 1739847149
      • 4: 1739847149
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='b4a8d9e8a41802df405302dd53ba352a'
      220μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Ebook
    1Ebook.php#?
        _token
        o9BqD3HCjOQAbA2ONnavFEPzRfWOud2Gh8EhngwX
        uc_cart_id
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        _previous
        array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/20979" ]
        _flash
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        PHPDEBUGBAR_STACK_DATA
        []
        path_info
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        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
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        request_cookies
        0 of 0
        array:3 [ "wayfindertarget" => null "_ga_9F3B5VV3T3" => null "_ga" => null ]
        response_headers
        0 of 0
        array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Tue, 18 Feb 2025 02:52:29 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IlhpTGllS3B5TUJaVk53R3lXdXF5YkE9PSIsInZhbHVlIjoiTHBPZnlGOHVuY25SQnJLVmU3OFd3QS9RUmZkdUhqL0tEZHBJUUlKOE1yMFB6YlhLZVp4SFNmcm5ON0JudGYxb1ZiV2lSQ0JoNyt1MFFDUzV5VGF1WlFPNDJYVy8rdW4rVGNRZW5IMXptSE5TWHlqM1ZqUi9XeXNKWmtaaWNyaHgiLCJtYWMiOiIzN2Y0ZjgxNTBkZDMzNjI3MDlkZWFlOTM2NzZlMzlmNzAxMjlhMzZmNjgzOGMxMTY1OWZkMTllZWUwNWJkZDYyIiwidGFnIjoiIn0%3D; expires=Thu, 20 Feb 2025 14:52:29 GMT; Max-Age=216000; path=/; secure; samesite=laxXSRF-TOKEN=eyJpdiI6IlhpTGllS3B5TUJaVk53R3lXdXF5YkE9PSIsInZhbHVlIjoiTHBPZnlGOHVuY25SQnJLVmU3OFd3QS9RUmZkdUhqL0tEZHBJUUlKOE1yMFB6YlhLZVp4SFNmcm5ON0JudGYxb1ZiV2lSQ" 1 => "alphaeurekaselectnet_session=eyJpdiI6Im9QNHJNdHRoUzdLbjlmbnZnbWVDelE9PSIsInZhbHVlIjoic1YzcUF5azNhcXE5TGtjbHlhMWcwNElNZkNGNUtXa0t0RVV4bmh4NkJHYlZSZGEvOGJ4Y0Z3ejFMRHptaGdRcXBrTjRCKzVBY2tXZWVaN3pjUWgwYjVkQ2VDejl4OHFqMENBRU5ZZmh2UEhZbThtcVNHZnllUGs5cmNpNERTTXYiLCJtYWMiOiJiOWU5NTc5YzY4NjY0Y2FjOTVjNmYzZWIyMTBkYmIzOGVlNGYzZGJkMzE4MTMwNjkzNmVhZWQyNmM3Mjg4Y2JlIiwidGFnIjoiIn0%3D; path=/; secure; httponly; samesite=laxalphaeurekaselectnet_session=eyJpdiI6Im9QNHJNdHRoUzdLbjlmbnZnbWVDelE9PSIsInZhbHVlIjoic1YzcUF5azNhcXE5TGtjbHlhMWcwNElNZkNGNUtXa0t0RVV4bmh4NkJHYlZSZGEvOGJ4Y0Z3ejF" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IlhpTGllS3B5TUJaVk53R3lXdXF5YkE9PSIsInZhbHVlIjoiTHBPZnlGOHVuY25SQnJLVmU3OFd3QS9RUmZkdUhqL0tEZHBJUUlKOE1yMFB6YlhLZVp4SFNmcm5ON0JudGYxb1ZiV2lSQ0JoNyt1MFFDUzV5VGF1WlFPNDJYVy8rdW4rVGNRZW5IMXptSE5TWHlqM1ZqUi9XeXNKWmtaaWNyaHgiLCJtYWMiOiIzN2Y0ZjgxNTBkZDMzNjI3MDlkZWFlOTM2NzZlMzlmNzAxMjlhMzZmNjgzOGMxMTY1OWZkMTllZWUwNWJkZDYyIiwidGFnIjoiIn0%3D; expires=Thu, 20-Feb-2025 14:52:29 GMT; path=/; secureXSRF-TOKEN=eyJpdiI6IlhpTGllS3B5TUJaVk53R3lXdXF5YkE9PSIsInZhbHVlIjoiTHBPZnlGOHVuY25SQnJLVmU3OFd3QS9RUmZkdUhqL0tEZHBJUUlKOE1yMFB6YlhLZVp4SFNmcm5ON0JudGYxb1ZiV2lSQ" 1 => "alphaeurekaselectnet_session=eyJpdiI6Im9QNHJNdHRoUzdLbjlmbnZnbWVDelE9PSIsInZhbHVlIjoic1YzcUF5azNhcXE5TGtjbHlhMWcwNElNZkNGNUtXa0t0RVV4bmh4NkJHYlZSZGEvOGJ4Y0Z3ejFMRHptaGdRcXBrTjRCKzVBY2tXZWVaN3pjUWgwYjVkQ2VDejl4OHFqMENBRU5ZZmh2UEhZbThtcVNHZnllUGs5cmNpNERTTXYiLCJtYWMiOiJiOWU5NTc5YzY4NjY0Y2FjOTVjNmYzZWIyMTBkYmIzOGVlNGYzZGJkMzE4MTMwNjkzNmVhZWQyNmM3Mjg4Y2JlIiwidGFnIjoiIn0%3D; path=/; secure; httponlyalphaeurekaselectnet_session=eyJpdiI6Im9QNHJNdHRoUzdLbjlmbnZnbWVDelE9PSIsInZhbHVlIjoic1YzcUF5azNhcXE5TGtjbHlhMWcwNElNZkNGNUtXa0t0RVV4bmh4NkJHYlZSZGEvOGJ4Y0Z3ejF" ] ]
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        ClearShow all
        Date ↕MethodURLData
        #12025-02-18 02:52:29GET/chapter/20979112192