Although chiroptical methods have been used in chemistry for some 150 years, and the basic theory was developed by Rosenfeld 50 years ago, their success in determining absolute conformation rests mainly on empirical rules. Some of these can be proved theoretically; however, in the case of more complex molecules this is not yet always possible. In what follows, an attempt is made to bridge the wide gap between theory and empiricism: “qualitative MO-theory”, which has already been successfully used to explain reaction mechanisms, the shape of molecules, or photoelectron spectra, can also be applied to circular dichroism (CD). In general we shall have to be content with a reasonable interpretation of the experimentally determined sign correlation, but even this will be of great value since it can yield general relations between the geometry of molecules and the sign of CD. Such relations become particularly important when only a few examples of a given chromophore are known. If first and second sphere of a molecule are achiral then sector rules can be put forward, and in other cases helicity or chirality rules.

Circular Dichroism and Absolute Conformation: Application of Qualitative MO Theory to Chiroptical Phenomena†

Modern computers have made possible the evaluation of higher order terms of perturbation series. Apart from the empirical work involving numerical calculations, much formal mathematical work has been done on the convergence properties of perturbation series and of Pade approximants which represent them. Some of the modern work in perturbation theory is reviewed in the context of traditional results from the theory of real and complex variables. The two major versions of time-independent perturbation theory, the Rayleigh-Schrodinger (RS) and Brillouin-Wigner (BW) theories, are compared and contrasted, and the alternative techniques for evaluating the terms in the energy series are discussed. The sum-over-states method, the differential equation method and the variational principle method are treated, with emphasis on their inter-relations.

https://iopscience.iop.org/article/10.1088/0034-4885/40/9/001/pdf

Quantum-mechanical perturbation theory

Single photon induced symmetry breaking of H 2 dissociation F. Mart´ 1 , J. Fern´ ndez 1 , T. Havermeier 2 , L. Foucar 2 , Th. Weber 2 , in a K. Kreidi 2 , M. Sch¨ ﬄer 2 , L. Schmidt 2 , T. Jahnke 2 , O. Jagutzki 2 , A. o Czasch 2 , E.P. Benis 4 , T. Osipov 5 , A. L. Landers 3 , A. Belkacem 5 , M. H. Prior 5 , H. Schmidt-B¨ cking 2 , C. L. Cocke 4 , and R. D¨ rner 2 o o Departamento de Qu´ mica, C-9, Universidad Aut´ noma de Madrid, 28049-Madrid, Spain o Institut f¨ r Kernphysik, University Frankfurt, u Max von Laue Str 1, D-60438 Frankfurt Germany Department of Physics, Auburn University Auburn AL-36849 Dept of Physics, Kansas State Univ, Cardwell Hall, Manhattan KS 66506 Lawrence Berkeley National Lab., Berkeley CA 94720 Abstract H 2 , the smallest and most abundant molecule in the universe, has a perfectly symmetric ground state. What does it take to break this symmetry? Here we show that the inversion symmetry can be broken by absorption of a linearly polarized photon, which itself has inversion symmetry. In particular, the emission of a photoelectron with subsequent dissociation of the remaining H + fragment shows no symmetry with respect to the ionic H + and neutral H atomic fragments. This result is the consequence of the entanglement between symmetric and antisymmetric H + states resulting from autoionization. The mechanisms behind this symmetry breaking are general for all molecules.

/pdf/single-photon-induced-symmetry-breaking-of-h2-dissociation-371hbxf08b.pdf

Single photon induced symmetry breaking of H2 dissociation - eScholarship

Chemistry remains an experimental science. The theory of chemical bonding leaves much to be desired. Yet, the past 20 years have been marked by a fruitful symbiosis of organic chemistry and molecular orbital theory. Of necessity this has been a marriage of poor theory with good experiment. Tentative conclusions have been arrived a t on the basis of theories which were such a patchwork on approximations that they appeared to have no right to work; yet, in the hands of clever experimentalists, these ideas were transformed into novel molecules with unusual properties. In the same way, by utilizing the most simple but fundamental concepts of molecular orbital theory we have in the past 3 years been able to rationalize and predict the stereochemical course of virtually every concerted organic reaction.' In our work we have relied on the most basic ideas of molecular orbital theory-the concepts of symmetry, overlap, interaction, bonding, and the nodal structure of wave functions. The lack of numbers in our discussion is not a weakness-it is its greatest strength. Precise numerical values would have to result from some specific sequence of approximations. But an argument from first principles or symmetry, of necessity qualitative, is in fact much stronger than the deceptively authoritative numerical result. For, if the simple argument is true, then any approximate method, as well as the now inaccessible exact solution, must obey it. The simplest description of the electronic structure of a stable molecule is that i t is characterized by a finite band of doubly occupied electronic levels, called bonding orbitals, separated by a gap from a corresponding band of unoccupied, antiboding levels as well as a continuum of higher levels. The magnitude of the gap may range from 40 kcal/mole for highly delocalized, large aromatic systems to 250 kcal/mole for saturated hydrocarbons. It should be noted in context that socalled nonbonding electrons of heteroatoms are in fact bonding. Consider a simple reaction of two molecules to give a third species, proceeding in a nonconcerted manner through a diradical intermediate I. A + B + [I] + C

The Conservation of Orbital Symmetry (福井謙一とフロンティア軌導理論) -- (参考論文)

Obwohl chiroptische Methoden seit etwa 150 Jahren in der Chemie benutzt werden und die zugrundeliegende Theorie bereits vor 50 Jahren von Rosenfeld entwickelt worden ist, beruht ihr Erfolg zur Bestimmung der absoluten Konformation weitgehend auf empirischen Regeln. Einige lassen sich theoretisch begrunden, bei komplexeren Molekulen ist dies haufig noch nicht moglich. Im folgenden soll versucht werden, die grose Kluft zwischen Theorie und Empirie zu uberbrucken: Die „qualitative MO-Theorie”, die sich bereits zur Erklarung von Reaktionsmechanismen, der Molekulgestalt oder von Photoelektronenspektren als nutzlich erwiesen hat, kann auch auf den Circulardichroismus (CD) angewendet werden. Im allgemeinen wird man sich hierbei damit begnugen mussen, plausible Deutungen fur experimentell gefundene Vorzeichen-Korrelationen zu bekommen, aber auch dies ist schon von grosem Wert, da man daraus allgemeine Zusammenhange zwischen Molekulgeometrie und CD-Vorzeichen ableiten kann. Solche Zusammenhange sind insbesondere dann wichtig, wenn es fur einen bestimmten Chromophor nur wenige Beispiele gibt. Sind erste und zweite Sphare eines Molekuls achiral, so lassen sich Sektorregeln aufstellen, andernfalls Helicitats- oder Chiralitatsregeln.

Circulardichroismus und absolute Konformation: Anwendung der qualitativen MO‐Theorie auf die chiroptischen Phänomene

Die optische Aktivitat von Methanderivaten in Abhangigkeit von den Eigenschaften der Substituenten wird entsprechend einer algebraischen Theorie fur diese Molekulklasse [17] quantenmechanisch diskutiert Mit geeigneten Festsetzungen uber die Begriffe „formal gebundener Ligand“ und uModelloperator fur die Energie“ und mit den Mitteln einer Storungsrechnung, bei der die Wechselwirkung zwischen den Liganden als Storung betrachtet wird, last sich der Ansatz nach der sogenannten zweiten Methode exakt bestatigen, wenn man die Storungsrechnung mit der zweiten Ordnung abbricht Da storungstheoretische Korrekturen nullter und erster Ordnung nur Zusatzbeitrage liefern, die auf geometrische Abweichungen von der sogenannten Td-Situation zuruckzufuhren sind, wird der einzige Beitrag, der bei allen Methanderivaten mit vier verschiedenen Liganden auftritt und bei kleinen Abweichungen von der Td-Situation den Hauptbeitrag zum optischen Drehwinkel darstellt, erst in zweiter Ordnung beschrieben Die Korrekturen nullter und erster Ordnung werden ebenfalls besprochen Mit vereinfachenden Annahmen uber die Form der Storung gelingt die Interpretation des Resultats durch Dipolmomente und elektromagnetische Polarisierbarkeiten der Liganden und geometrische Parameter Schlieslich werden weitere Naherungsannahmen mit dem Ziel einer Vereinfachung der gefundenen Formel diskutiert

Quantenmechanische Theorie der optischen Aktivität der Methanderivate im Transparenzgebiet

The boron rotor B 13 + 11 consists of a tri-atomic inner "wheel" that may rotate in its pseudo-rotating ten-atomic outer "bearing"-this concerted motion is called "contorsion." B 13 + 11 in its ground state has zero contorsional angular momentum. Starting from this initial state, it is a challenge to ignite contorsion by a laser pulse. We discover, however, that this is impossible, i.e., one cannot design any laser pulse that induces a transition from the ground to excited states with non-zero contorsional angular momentum. The reason is that the ground state is characterized by a specific combination of irreducible representations (IRREPs) of its contorsional and nuclear spin wavefunctions. Laser pulses conserve these IRREPs because hypothetical changes of the IRREPs would require nuclear spin flips that cannot be realized during the interaction with the laser pulse. We show that all excited target states of B 13 + 11 with non-zero contorsional angular momentum have different IRREPs that are inaccessible by laser pulses. Conservation of nuclear spins thus prohibits laser-induced transitions from the non-rotating ground to rotating target states. We discover various additional constraints imposed by conservation of nuclear spins, e.g., laser pulses can change clockwise to counter-clockwise contorsions or vice versa, but they cannot stop them. The results are derived in the frame of a simple model.

Nuclear spin blockade of laser ignition of intramolecular rotation in the model boron rotor B13+11.

Charge migration moves electrons from one molecular site to another, in the typical time domain from few hundred attoseconds to few femtoseconds. On this timescale, the nuclei stand practically sti...

Attosecond Charge Migration Can Break Electron Symmetry While Conserving Nuclear Symmetry.

Quantum simulations of the electron dynamics of oriented benzene and Mg-porphyrin driven by short (<10 fs) laser pulses yield electron symmetry breaking during attosecond charge migration. Nuclear motions are negligible on this time domain, i.e., the point group symmetries G = D6h and D4h of the nuclear scaffolds are conserved. At the same time, the symmetries of the one-electron densities are broken, however, to specific subgroups of G for the excited superposition states. These subgroups depend on the polarization and on the electric fields of the laser pulses. They can be determined either by inspection of the symmetry elements of the one-electron density which represents charge migration after the laser pulse, or by a new and more efficient group-theoretical approach. The results agree perfectly with each other. They suggest laser control of symmetry breaking. The choice of the target subgroup is restricted, however, by a new theorem, i.e., it must contain the symmetry group of the time-dependent electronic Hamiltonian of the oriented molecule interacting with the laser pulse(s). This theorem can also be applied to confirm or to falsify complementary suggestions of electron symmetry breaking by laser pulses.

Electron Symmetry Breaking during Attosecond Charge Migration Induced by Laser Pulses: Point Group Analyses for Quantum Dynamics

Fur zeitunabhangige Hamiltonoperatoren ℋ
0 und ℋ=ℋ
0 + V mit einem diskreten Spektrum, den Eigenwerten und Eigenvektoren E

 (o)
 , ¦s〉(o) bzw. E
s, ¦s〉 von ℋ
0 und ℋ sei die Behandlung nach der RS-Storungstheorie gewahrleistet. Dann existiert ein Operator 
$$\mathfrak{p}$$

 mit der Eigenschaft 
$$\left| s \right\rangle ^{(n + 1)} = \frac{1}{{n + 1}}\mathfrak{p}\left| s \right\rangle ^{(n)} , E_s^{(n + 1)} = \frac{1}{{n + 1}}\mathfrak{p}E_s^{(n)} $$

 , wobei ¦s〉(n) und E

 ()
 die storungstheoretischen Korrekturen n-ter Ordnung beschreiben, falls E
s
(0) nicht entartet ist. Im Entartungsfall bleibt die Operation 
$$\mathfrak{p}$$

 definiert und kann zur Bestimmung storungstheoretischer Korrekturen der quantenmechanischen Ausdrucke verwendet werden, die in nullter Naherung invariant sind gegenuber Basistransformationen in den entarteten Teilraumen von ℋ
0. Die Gleichungen 
$$\left| s \right\rangle = \sum\limits_n^{0,\infty } {\left| s \right\rangle ^{(n)} = e^\mathfrak{p} \left| s \right\rangle ^{(0)} } , E_s = \sum\limits_n^{0,\infty } {E_s^{(n)} } = e^\mathfrak{p} E_s^{(0)} $$

 entsprechen einer Basistransformation, bei der nichtentartete Eigenvektoren ¦s〉(o) und Eigenwerte E

 (o)
 von ℋ
0 in Eigenvektoren ¦s〉 und Eigenwerte E
s von ℋ ubergehen. Beispiele zeigen den Nutzen dieser Formulierung.

Dietrich Haase

Papers

Quantenmechanische Theorie der optischen Aktivität der Methanderivate im Transparenzgebiet

Nuclear spin blockade of laser ignition of intramolecular rotation in the model boron rotor B13+11.

Attosecond Charge Migration Can Break Electron Symmetry While Conserving Nuclear Symmetry.

Electron Symmetry Breaking during Attosecond Charge Migration Induced by Laser Pulses: Point Group Analyses for Quantum Dynamics

Bemerkung zur Rayleigh-Schrödinger-Störungstheorie