{"id":46273,"date":"2025-07-02T02:41:46","date_gmt":"2025-07-02T02:41:46","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=46273"},"modified":"2025-07-02T02:41:48","modified_gmt":"2025-07-02T02:41:48","slug":"please-consider-the-mo-diagram-of-bh3-shown-below","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/please-consider-the-mo-diagram-of-bh3-shown-below\/","title":{"rendered":"Please consider the MO diagram of BH3 shown below"},"content":{"rendered":"\n

Please consider the MO diagram of BH3 shown below. node 2p, 2p, LGO(2) LGO(3) +# LGO() BH3, a) What are the symmetries of the LGO(1), LGO(2), and LGO(3) respectively? b) Assign symmetry to the atomic orbitals of Boron. c) Draw the shapes of the HOMO orbitals.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The molecular orbital (MO) diagram of BH\u2083<\/strong> (borane) involves the interaction between the atomic orbitals of boron and hydrogen atoms. To analyze the symmetries of the localized molecular orbitals (LMOs) and assign symmetries to the atomic orbitals of boron, let’s break down the question systematically.<\/p>\n\n\n\n

a) Symmetries of LGO(1), LGO(2), and LGO(3)<\/h3>\n\n\n\n

The LGO (Localized Molecular Orbitals) are typically constructed from linear combinations of the atomic orbitals (AOs) of boron and hydrogen atoms. The symmetries of these orbitals depend on the point group of the molecule. For BH\u2083<\/strong>, the molecule adopts D\u2083h<\/strong> symmetry, which affects how the atomic orbitals combine and the symmetries of the resulting molecular orbitals.<\/p>\n\n\n\n

    \n
  • LGO(1)<\/strong>: This orbital is the highest energy molecular orbital (HOMO) and is primarily anti-bonding. It has a1\u2019<\/strong> symmetry, meaning it is totally symmetric with respect to all symmetry operations in the D\u2083h group.<\/li>\n\n\n\n
  • LGO(2)<\/strong>: This is a bonding orbital with e\u2019\u2019<\/strong> symmetry, a doubly degenerate representation that is symmetric with respect to rotations around the principal axis (C\u2083 axis) but asymmetric under reflection in the horizontal mirror plane.<\/li>\n\n\n\n
  • LGO(3)<\/strong>: This is also a bonding orbital with e\u2019<\/strong> symmetry, which is another doubly degenerate orbital with a different phase and symmetry from LGO(2).<\/li>\n<\/ul>\n\n\n\n

    b) Symmetry of the Atomic Orbitals of Boron<\/h3>\n\n\n\n

    Boron has the electron configuration 1s\u00b2 2s\u00b2 2p\u00b9<\/strong>. In BH\u2083<\/strong>, boron\u2019s atomic orbitals contribute to the formation of molecular orbitals, and their symmetries are as follows:<\/p>\n\n\n\n

      \n
    • 2s orbital<\/strong>: This orbital belongs to the a1\u2019<\/strong> symmetry representation, which is totally symmetric in the D\u2083h point group.<\/li>\n\n\n\n
    • 2p orbitals<\/strong>: The 2p\u2093<\/strong> and 2p\u1d67<\/strong> orbitals belong to the e\u2019<\/strong> symmetry representation, while the 2p\ud835\udccf<\/strong> orbital is assigned to the a1\u2019<\/strong> symmetry representation.<\/li>\n<\/ul>\n\n\n\n

      Thus, boron\u2019s 2s<\/strong> and 2p\ud835\udccf<\/strong> orbitals contribute symmetrically in bonding interactions, while the 2p\u2093<\/strong> and 2p\u1d67<\/strong> orbitals contribute in degenerate pairs.<\/p>\n\n\n\n

      c) Shapes of the HOMO Orbitals<\/h3>\n\n\n\n

      The highest occupied molecular orbital (HOMO) in BH\u2083<\/strong> is typically the bonding orbital that has a1\u2019<\/strong> symmetry. This orbital has a non-degenerate<\/strong> shape, meaning it is symmetric about the molecule\u2019s center. Its shape resembles a spherical<\/strong> or lobed structure<\/strong> centered on boron and extending toward the hydrogen atoms.<\/p>\n\n\n\n

      For LGO(2)<\/strong> and LGO(3)<\/strong>, which are lower in energy but still occupied, these orbitals are degenerate<\/strong> and exhibit a pair of lobes<\/strong> with opposite phases, aligned along the axis of symmetry. The shapes of these orbitals are influenced by their specific symmetries (e\u2019<\/strong> and e\u2019\u2019<\/strong>).<\/p>\n\n\n\n

      These descriptions are a simplified representation based on molecular orbital theory and group theory applied to BH\u2083<\/strong>.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      Please consider the MO diagram of BH3 shown below. node 2p, 2p, LGO(2) LGO(3) +# LGO() BH3, a) What are the symmetries of the LGO(1), LGO(2), and LGO(3) respectively? b) Assign symmetry to the atomic orbitals of Boron. c) Draw the shapes of the HOMO orbitals. The Correct Answer and Explanation is: The molecular orbital […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-46273","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/46273","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=46273"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/46273\/revisions"}],"predecessor-version":[{"id":46275,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/46273\/revisions\/46275"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=46273"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=46273"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=46273"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}