Effect of substituents on ionization potentials of phosphorus compounds. Conjugation in radical cations

The first vertical ionization potentials (I) of phosphorus compounds P(X_i)₃, OP(X_i)₃, SP(X_i)₃, (4-XC₆H₄)₃P, and PCX are related to the inductive, resonance, and polarizability parameters of inorganic, organic, and organometallic substituents X by dependences of the type I = I _H + a_I + b_R ⁺ + c, where I _H is the I value for X = H. The I values are also affected by hyperconjugation. The ratio of the contributions of the resonance (b_R ⁺) and polarizability (c) effects to the I value is determined by the degree of delocalization of the unpaired electron and the positive charge in the radical cations formed upon ionization of neutral molecules. The _R ⁺ resonance parameters of organosilicon, organogermanium, and organotin substituents bound to the P ^·+ radical cation center were calculated for the first time.     

Preliminary calculations on excited states of the oxygen molecule

It is well known that the energy interval separating ³ _u ^– and ³ _u ⁺ states of O₂, as given by the conventional ASMO method, is too large. In order to resolve this difficulty, removal of the equivalence restrictions usually employed in the orbital theory is proposed. Thus the orbital exponent of one antibonding _g MO is allowed to take a different value from the other _g's. Variational calculations show that the resulting outermost orbital is much more diffuse than the others. This model of a single diffuse orbital brings about a considerable energy lowering for the ³ _u ^– state and thus the agreement of the ³ _u ^– - ³ _u ⁺ interval with experiment is improved.

---

Zusammenfassung Die konventionelle ASMO-Theorie liefert bekanntlich eine viel zu große Differenz der Terme ³ _u ^– und ³ _u ⁺ von O₂, weswegen der Vorschlag gemacht wird, die üblicherweise vorgenommene Äquivalenz-Einschränkung fallen zu lassen. Der Orbital-Exponent eines lockernden MO's kann von dem der übrigen _g's abweichen. Rechnungen zeigen, daß das äußerste MO viel diffuser als die anderen ist und daß die Energie des ³ _u ^– -Zustandes beträchtlich erniedrigt wird.

---

Résumé La séparation entre les états ³ _u ^{– 3} _u ⁺ de O₂ donnée par la méthode ASMO conventionnelle est connue pour être trop grande. Afin de résoudre cette difficulté la levée des restrictions d'équivalence ordinairement utilisées est proposée. Ainsi l'exposant orbital d'une des orbitales moléculaires antiliantes _g peut prendre une valeur différente de celui de l'autre orbitale antiliante _g. Des calculs variationnels montrent que l'orbitale la plus haute ainsi obtenue est beaucoup plus diffuse que les autres. Ceci a pour effet de diminuer considérablement l'énergie de l'état ³ _u ^– , améliorant la séparation entre les états ³ _u ^– et ³ _u ⁺ .

     

Theoretical electronic transition probabilities of heteronuclear diatomic molecules

Dipole strengths of various heteronuclear diatomic molecules are calculated for high and low energy transitions of one spectral type, 1-1, -. Through the use of increasingly accurate ground state wavefunctions it is possible to display the sensitivity of the transition probabilities to known approximations in the wavefunction. Selfconsistent field and configuration interaction effects are compared and contrasted.

---

Zusammenfassung Dipolstärken von zweiatomigen Molekülen mit verschiedenen Kernen wurden für Übergänge vom Typ 1-1, - mit großer und kleiner Energiedifferenz berechnet. In die Funktionen für den Grundzustand war eine unterschiedlich große Anzahl von Konfigurationen einbezogen worden, so daß die Abhängigkeit der Übergangswahrscheinlichkeiten vom Approximationsgrad verfolgt werden konnte. In der Diskussion wurden SCF- und CI-Effekte unterschieden.

---

Résumé Les forces d'oscilateurs dipolaires de diverses molécules diatomiques hétéronucléaires sont calculées pour les transitions de basse et haute énergie d'un type spectral 1-1, -. Par utilisation de fonctions d'onde de l'état fondamental de plus en plus précises il est possible de montrer la sensibilité des probabilités de transition aux approximations connues sur la fonction d'onde. Les effets liés au champ S.C.F. et à l'interaction de configuration sont comparés et différenciés.

---

---

Work Supported by the National Science Foundation.     

Some remarks on the periodical change of the stability constants of the lanthanide complexes

The correlations between the values of the lgK (K = stability constant of the lanthanide complex) and the reciprocal of the ionic radius 1/r or the sum of the ionization potentials ₁ ³ I for the lanthanide ions were reviewed for different ligands. A straight-line relationship (lgK – lgK)/lgK vs. (1/r – 1/r)/(1/r) or vs. ( ₁ ³ I – ₁ ³ I)/ ₁ ³ I was found within the tetrads La-Nd, Gd-Ho, and Er-Lu.

---

Bemerkungen zum periodischen Wechsel der Stabilitätskonstanten von Lanthaniden-Komplexen

Zusammenfassung Es wurde eine Übersicht der Korrelationen zwischen den Werten von logK (K = Stabilitätskonstante der Lanthanidenkomplexe) und den reziproken Ionenradien 1/r oder der Summe der Ionisierungspotentiale ₁ ³ I für die Lanthanidenionen für verschiedene Liganden gegeben. Dabei wurde eine lineare Korrelation für (lgK – lgK)/lgK gegen (1/r – 1/r)/(1/r) oder gegen ( ₁ ³ I – ₁ ³ I)/_1/3 I innerhalb der Tetraden La-Nd, Gd-Ho und Er-Lu aufgefunden.

     

Ab initio studies of ground and excited electronic states of MgAr,CdAr, and BeAr

Summary The ground state (X ¹⁺) and several excited state (A ³,c ³+,C ¹,D ¹⁺, andE ³⁺) potential energy surfaces for the diatomic molecules MgAr, CdAr, and BeAr have been computed using complete active space self-consistent field (CASSCF) wavefunctions and valence double- and triplezeta quality basis sets augmented with polarization and diffuse functions. Pump-and-probe laser experiments have examined the quenching, of excited singlet states of metal-rare gas complexes such as CdXe to produce triplets that dissociate to³ P _Jmetal atoms. This quenching, which is detected for CdXe but not for CdAr or MgAr, is thought to occur via a crossing or strong coupling of a repulsive triplet curve correlating to the underlying³ P state of the metal, with an attractive singlet curve that correlates to the higher¹ P state of the metal. The present work indicates that the attractiveC ¹ and repulsivec ³⁺ curves of MgAr and CdArdo not intersect in the energetically accessible region of theC ¹ surface, unlike the corresponding curves for the CdXe diatom. These data are consistent with the absence of³ P _J Cd atoms in the MgAr and CdAr experiments, respectively. However, an alternative quenching mechanism involving vibronic coupling between theC ¹ vibrational eigenstates and the continuum eigenstates of the underlying repulsive³⁺ surface may be operative; this possibility is examined qualitatively and predicted to be unlikely for MgAr (due to small spin-orbit coupling) and CdAr (due to unfavorable vibronic factors). BeAr, which has yet to be probed experimentally, is predicted to be bound by 770 and 900 cm^–1 in theD ¹⁺ state (which has metal 2s2p character) and theE ³⁺ state (which has Rydberg metal 2s3s character), respectively, and to display interesting potential curve intersections.Dedicated to Prof. Klaus Ruedenberg     

Simple molecular wavefunctions with correlation corrections II

The potential curves for the ground state of Li₂ (¹ _g ⁺ ) and FH (¹ _g ⁺ ) are computed. The correlation energy is calculated using a functional of the one- and two-electron density matrices derived from an MC SCF reference wavefunction and is added to the reference energy to obtain a correlated potential curve.     

An index of electrotopological state for atoms in molecules

A new method for molecular structure quantitation is described, in which both electronic and topological attributes are united. The method uses the hydrogen-suppressed skeleton to represent the structure and leads to a graph invariant index for the individual atoms and hydride groups of the molecular skeleton. An intrinsic atom value is calculated for each atom asI = ( + 1)/, in which and are the counts of valence and sigma electrons of atoms in the molecular skeleton, that is, exclusive of bonds to hydrogen atoms. The electrotopological state valueS _i for an atomi is defined asS _i =I _i + I _i, where the influence of atom j on atom i, I _i, is given as (I _i-j _j)/r ²;r is the graph separation between atoms i and j, counted as number of atoms, includingi andj. The information in the electrotopological state values is revealed by examples of various types of organic structures, including chain branching and heteroatom variation. The relation of the E-state value to NMR chemical shift is demonstrated for a series of carbonyl compounds.     

Theoretical study of the6Σ+,6Π, and4Σ+ van der Waals states of NO

Summary Potential energy curves for the weakly bound⁶⁺,⁶, and⁴⁺ states of NO are presented at various levels of correlation treatment. The binding energies for the van der Waals minima vary from about 30 cm^–1 for the⁶⁺ state to about 20 cm^–1 for the⁴⁺ and⁶ states. We investigate the importance of constraining the wave function to dissociate to a spherically symmetric O atom where the oxygen 2p orbitals are equivalent. For high levels of correlation treatment, we find that these restrictions have little effect on the potential, while greatly increasing the length of the CI expansion.     

Natural spin orbital analysis of diatomic molecular wave functions in terms of generalized diatomic orbitals

Starting from the demi-H ₂ ⁺ -model for Rydberg states, ab initio calculations of the energy and the wave function for some excited states of H₂ have been carried out with the help of diatomic orbitals. The potential curves and wave functions for the following states: 2¹ _g< ^/+ , 3¹ _g< ^/+ , 1³ _g< ^/+ , 2³ _g< ^/+ , 1¹ _u< ^/+ , 2¹ _u< ^/+ , 1³ _u< ^/+ , 2³ _u< ^/+ , 3³ _u< ^/+ , 1¹ _g , 1³ _g , 1¹ _u , and 1³ _u , have been calculated by a complete CI (configuration interaction) calculation in the sense that all configurations of the state symmetry have been used which can be formed from a given basis set. From the wave functions thus obtained the natural spin orbitals are calculated subsequently to the variational calculations. The dependence of the occupation numbers of the natural spin orbitals on internuclear distance is interpreted according to the model and is used for the explanation of the special features like double minima and maxima which occur in the potential curves of H₂. For the curves of the occupation numbers a non-crossing rule in analogy to that for potential curves is valid. The potential curves for the states 1³ _g and 1³ _u have been improved by the use of linear combinations of diatomic orbitals with different nuclear charges, which allow a flexible transition to linear combinations of atomic orbitals.Dedicated to Professor Iwan N. Stranski on the occasion of his 80th birthday.     

The ground state of TiC revisited

The ground state of TiC is ³⁺, as predicted by previous configuration interaction calculations. It is shown that there are two low-lying ¹⁺ states and that the density functional theory solution corresponds to the higher of the two ¹⁺ states.Contribution to the Björn Roos Honorary Issue     

Electronic–Rotational Coupling and c 1 Σ – u –b 1 Σ + g Transition Probability in the Oxygen Molecule

A theory was proposed for the formation of intensity of the forbidden singlet–singlet c ¹ _u ^– b ¹ _g ⁺ transition in the oxygen molecule. The dipole moments of transitions that contribute to the formation of the intensity of the c–b transition in the range of internuclear distances of 1.2–2.0 Å were calculated using the configuration interaction method with a valence triple-zeta basis set. Based on these results, the electric dipole moment for the c ¹ _u ^– b ¹ _g ⁺ transition was calculated.     

Ligand-structure effect on electrochemical reduction of copper(II) complexes

Summary Half-wave potentials for a one-electron reduction of copper(II) complexes containing polydentate ligands can be calculated using the equationE _1/2=E ⁰(Cu^2+/+)+ _{i j} E _i where E _i are contributions related to the electronic and steric properties of the ligands. The values of 18 E _i contributions are presented and explained, and the effect of the solvents on the half-wave potentials is exemplified.Dedicated to Prof. Dr. Viktor Gutmann to his 70th birthday     

Symmetry and other properties of second-order phenomenological coefficients and thier significance in a chemical system

Using a second-order phenomenological equationJ _i = _j L _ij X_j + _{j, k} L _ijk X_j X_kand assuming that the system is at a state near equilibrium, it has been shown that the symmetry ofL _ijk is retained with respect to the permutations of suffices i j and k Furthermore, using the second-order flux equations, the thermodynamic stability criterion is expressed. The symmetry is shown to be retained in a reaction scheme representing the emplate model. The significance of the stability criterion as expressed by the higher-order phenomenological coefficients is discussed.     

Computation of electronic transition moments: the length versus the velocity representation

Summary We have compared transition moments (TMs) obtained using the length and velocity representations for transitions from the ground state of H₂ to the lowest two¹ _u and two¹ _u ⁺ Rydberg states, theA ¹–X ¹⁺ transition in BH, and theA ¹ _u –X ¹ _g ⁺ transition in C₂. For H₂, the TMs in the length and velocity representations agree well even in cases where the one-particle basis is incomplete and the TM has not converged. For BH and C₂ the TM in the length representation converges rapidly with improvements in the one-particle basis set and is insensitive to inner-shell correlation. In contrast, in the velocity representation convergence with improvements in the one-particle basis is much slower, especially for C₂, and the TMs are significantly changed by inner-shell correlation. Thus the difference between the TMs in the length and velocity representations would not appear to be a viable diagnostic of TM convergence.     

Recherches théoriques sur la structure électronique de molécules contenant des atomes hybridés en sp:

Résumé La théorie L. C. A. O. améliorée est appliquée à l'étude de la molécule C₃. Afin de satisfaire l'égalité nécessaire entre les éléments de matrice non diagonaux L _pq et L _qp, nous avons introduit un déplacement électronique le long des liaisons . Les charges nettes portées par les atomes terminaux sont: + 0,09. La distance C-C calculée (1,286 Å) est en bon accord avec l'expérience. Les énergies des deux premières transitions NV: ¹ _g ^{+ 1} _u ^– et¹ _g ^{+ 1}_u sont: 4,7 et 4,8 eV. Ces valeurs ne sont pas en contradiction avec l'expérience qui situe ces transitions au delà de 4,1 eV, limite à partir de laquelle l'absorption de l'atmosphère terrestre rend impossible l'étude des spectres cométaires.

---

The improved LCAO theory is applied to the C₃ molecule. In order to satisfy the necessary equality between the non-diagonal matrix elements L _pq and L _qp, we have introduced an electron shift along the bonds. The net charges borne by the terminal atoms are: + 0.09. The computed C-C distance (1.286 Å) is in good agreement with experiment. The two first NV transition energies: ¹ _g ^{+ 1} _u ^– and ¹ _g ^{+ 1}_u are: 4.7 and 4.8 eV. These values are not in contradiction with experiment which places these transitions beyond 4.1 eV, limit from which the terrestrial atmospheric absorption makes impossible to study the comets' spectra.

---

Zusammenfassung Die verbesserte LCAO-Theorie wird auf die C₃-Molekel angewandt. Um die nötige Gleichheit der nicht-diagonalen Matrixelemente L _pq und L _qp zu erhalten, haben wir eine Elektronenverschiebung längs der -Bindungen eingeführt. Die Ladungen der Endatome sind: + 0,09. Die berechnete C-C-Bindungslänge (1,286 Å) stimmt mit der Erfahrung überein. Die berechneten Energien der zwei ersten NV-Übergänge: ¹ _g ^{+ 1} _u ^– und ¹ _g ^{+ 1}_u sind: 4,7 und 4,8 eV. Diese Werte sind nicht in Widerspruch mit der Erfahrung, die diese Übergänge über 4,1 eV ansetzt; denn das Stadium der Kometenspektren ist über dieser Grenze wegen der Luftabsorption unmöglich.

---

---

Nous remercions le Professeur P. Swings (Institut d'Astrophysique, Cointe-Sclessin, Belgique) ainsi que le Professeur Ch. Fehrenbach (Observatoire de Marseille), pour les échanges de vue que nous avons eu avec eux sur ce sujet.     

Adiabatic corrections for thei 3Π g state of the hydrogen molecule

Summary The adiabatic corrections of thei ³_g state of H₂ are calculated for a wide range of internuclear distances using an explicitly correlated wavefunction. The vibrational structure of this state is calculated in the adiabatic approximation. It is shown that forN=1 levels of the – substate, for which the nonadiabatic corrections are negligible, the agreement between theory and experiment is excellent; the small mass independent discrepancy of the order of 0.5–3 cm^–1 is due to the convergence error in the Born-Oppenheimer calculations. For higherN the discrepancy is much larger. However, it is mass andN-dependent and it is almost entirely due to the nonadiabatic effects caused by³_g-³_g interactions. The still larger discrepancy for the + substate of thei state is evidently caused by additional interactions of thei state with close-lying states of³ _g ⁺ symmetry.Dedicated to Prof. Klaus Ruedenberg on the occasion of his 70th birthday     

Error of Atomic Charges Derived from Electrostatic Potential

The purpose of this article is to show that CHELP, CHELPG, and Merz and Kollman undergo error for the charge on atoms of HCOO^– (H₂O) _n for n = 1 6. We also demonstrate that the CHELP, CHELPG, and Merz and Kollman show error for the tendency toward change in the charges on carbons for CH₃NH⁺ ₃ (CH₃)₂NH⁺ ₂ (CH₃)₃NH⁺ (CH₃)₄N⁺.     

Reactivity of coordinated O2? towards. One-electron oxidants

Ion-radical complexes Ti(IV) (O ₂ ^– ) are unreactive towards most oxidants except Ce(IV) and Cr₂O ₇ ^2– . The one-electron redox potential for the O_{2 coord.}/O _{2 coord.} ^– couple lies between 1 and 1.6 V.

---

- O ₂ ^– Ti(IV) , Ce(IV) Cr₂ O ₇ ^2– . - O_{2 .}/O ₂ ^– . 1 1,6 .

     

Lactam acetals

The dependence of pK _a (in nitromethane) and _I of methylene-group-substituted 1-methyl-2-methylenepiperidines is expressed by the equation pK _a =–0.41+11.8 _I. The basicities of tertiary enamines are more than five orders of magnitude greater than the basicities of the corresponding secondary enamines.See [1] for communication VII.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 385–388, March, 1974.     

Structural relationships in silatrane molecules

An updated compendium of silatrane structural data is presented. The relationships between nonplanarity at silicon (Si) andd(N-Si), the length of the dative bond, and nonplanarity at nitrogen N andd(N-Si) are examined. Excluding a platinum-substituted derivative: the Si relationship is strong and predicts the limiting length of a strong N Si bond, while the N relationship is weak. A good relationship between _I for the four (non-N) exo- and endocyclic substituents attached to Si holds for silatranes, methyl, keto, and diketo derivatives as well as for 2-carbasilatranes. The relationship fails for strong -donor exocyclic substituents, implicating resonance, and for benzo- and tribenzosilatranes, where steric effects dominate.On Leave of Absence from Academia Sinica, Beijing, People's Republic of China.