Aage E. Hansen

NMR SHIELDING CALCULATIONS BEYOND COUPLED HARTREE-FOCK : SECOND-ORDER CORRELATION EFFECTS IN LOCALIZED-ORBITAL/LOCAL-ORIGIN CALCULATIONS OF MOLECULES CONTAINING PHOSPHORUS

Abstract The localized-orbital/local-origin (LORG) method and the second-order polarization propagator approximation (SOPPA) are combined to form a local gauge theory of nuclear magnetic shielding that includes electron-correlation effects through second order in the fluctuation potential. Calculations are presented for the NMR shielding tensors of a set of molecules spanning the range of 31 P shieldings. The results show that correlation effects on the shielding can be significant, and that the use of local gauge origins yields marked improvement over common-origin calculations.

Calculation, display, and analysis of the nature of nonsymmetric nuclear magnetic resonance shielding tensors: Application to three‐membered rings

The components of the full nuclear shielding tensor are analyzed with particular regard to the origins of the antisymmetric component of the shielding of nuclei at low‐symmetry molecular sites. As an aid we propose the study and display of the shielding response vector, i.e., the nuclear shielding field per unit applied magnetic field. The analysis is based on ab initio calculations in the localized orbital‐local origin method for cyclopropane, cyclopropene, ethylene oxide, ethylene imine, and diazirine, and also includes a discussion of the mechanism for the large antisymmetric component predicted for the unsaturated nuclei in cyclopropene and diazirine, both in terms of bond and lone pair contributions and in terms of a decomposition of the dominant paramagnetic contributions into molecular point group species. Display of the component of the shielding vector parallel to the applied field is shown to be a valuable alternative to the common ellipsoid representations. Display of the components perpendicul...

Correlation effects in the calculation of ordinary and rotatory intensities

A mixed dipole length-dipole velocity expression for the oscillator strength of an electronic transition is shown to be rather less sensitive to ground state correlation effects than are the ordinary dipole length and dipole velocity formulae. Similar considerations for rotatory strengths show that, in certain, symmetry favoured, cases the results of the dipole length expression are likewise significantly less affected by ground state correlation than are the results of the dipole velocity expression. Some comments are made on the importance of correlation errors in the excited states.

Ab initio calculation and display of the rotary strength tensor in the random phase approximation. Method and model studies

Abstract The theory of the rotatory strength tensor describing circular dichroism (CD) of electronic excitations in oriented molecules is summarized in length and velocity formulations, and we outline an ab initio implementation of the calculation of this tensor and its electric dipole — magnetic dipole and electric dipole — electric quadrupole components in the random phase approximation. Results are presented for the predominantly π → π ∗ and σ → π ∗ type transitions in an ethylene molecule twisted into chiral D2 conformations demonstrating the origin-sensitivity of the electric dipole-magnetic dipole and electric dipole-electric quadrupole contributions to the tensor, and demonstrating origin-invariance of the total tensor in the velocity formulation. The electric dipole-electric quadrupole contribution is small, but not insignificant for both transitions. We present a pictorial representation of the CD response, and its application to the total tensor and its components for the π → π ∗ excitation.

Abinitio calculations of oscillator and rotatory strengths in the random‐phase approximation: Twisted mono‐olefins

Ab initio (STO‐nG) computations of ordinary and rotatory intensities of low‐lying electronic transitions are presented for twisted ethylene and twisted trans‐2‐butene in the random‐phase approximation (RPA). The intensities are computed in both dipole length and dipole velocity forms, as well as the mixed form for the oscillator strength, and the convergence of these formally equivalent results is examined in the RPA and several other methods for constructing the electronic excitation: the virtual orbital, or single‐transition, approximation (STA), the monoexcited configuration‐interaction, or Tamm–Dancoff, approximation (TDA), and one version of the higher RPA (HRPA). We show that the RPA has consistent advantages over the TDA for calculation of CD as well as ordinary intensities. Our computations confirm that a localized, ethylenic chromophore is indeed adequate to account for the low‐lying CD spectrum in mono‐olefins. Further, even with minimal valence‐shell basis sets, our RPA rotatory strengths agree...

Hypervirial relations as constraints in calculations of electronic excitation properties: the random phase approximation in configuration interaction language

Off-diagonal hypervirial relations (for example, the equivalence of the dipole length and dipole velocity forms of the electronic transition moment for exact wavefunctions) are imposed upon two approximate configuration interaction (CI) representations of the ground and excited states of interest in an atomic or molecular system. It is shown that, if the ground state is approximated by the exact Hartree-Fock function correlated by double excitations and the excited state is represented by mono-excited CI, the hypervirial constraint on the transition moments leads directly to the random phase approximation (RPA) equations. No second-quantized formulation or assumed excitation operator is invoked. The same constraint, applied to an uncorrelated ground state, leads to non-variational mono-excited CI schemes, which are related to Hartree-Fock instability conditions. The methods are illustrated by 5–31/G computations of the chiroptical properties, in dipole length, velocity and acceleration forms, of two low-l...

Iterative LORG calculations of nuclear magnetic shieldings. 13C shielding tensors in 2-norbornenone

Abstract A computationally efficient new implementation of the LORG (localized orbital-local origin) method for nuclear magnetic shieldings is described, in which the paramagnetic response term is obtained by means of a reduced linear equations method instead of by explicit diagonalization of the A–B matrix. Comparative timings for calculations on a number of molecules are presented, and nuclear shieldings are calculated for 2-norbornenone, a computationally demanding case.

Ab initio calculation of electronic circular dichroism fortrans-cyclooctene using London atomic orbitals

SummaryThe second-quantization magnetic dipole operator that arises when London atomic orbitals are used as basis functions is derived. In atomic units, the magnetic dipole operator is defined as the negative of the first derivative of the electronic Hamiltonian containing the interaction with the external magnetic field. It is shown that for finite basis sets, the gauge origin dependence of the resulting magnetic dipole operator is analogous to that of the exact operator, and that the derived operator converges to the exact operator in the limit of a complete basis set. It is also demonstrated that the length expression for the rotatory strength in linear response calculations gives gauge-origin-independent results. Sample calculations ontrans-cyclooctene and its fragments are presented. Compared to conventional orbitals, the basis set convergence of the rotatory strengths calculated in the length form using London atomic orbitals is favourable. The rotatory strength calculated fortrans-cyclooctene agrees nicely with the corresponding experimental circular dichroism spectrum, but the spectra for the fragment molecules show little resemblance with that oftrans-cyclooctene.

On the hypervirial relation in the random phase approximation and the sum rules for ordinary and rotatory intensities in finite bases

Abstract It is shown that a one-electron hypervirial relation for transition amplitudes in the random phase approximation (RPA) follows immediately from the double commutator RPA formulation proposed by Rowe. For the transition energy-independent expressions for the ordinary and rotatory intensities it is shown that, in finite basis calculations, the sums of these intensities are independent of whether the single-transition approximation, the Tamm—Dancoff approximation or the RPA method is used. Specific results are quoted for a ab-initio minimal basis calculations on twisted ethylene.

Electronic spectra of mono-olefins. RPA calculations on ethylene, propene, and cis- and trans-2-butene

Abstract We present ab initio extended basis set calculations on the electronic spectra of ethylene, propene, and cis- and trans-2-butene in the random-phase approximation (RPA). All computed singlet excitations correlating with ethylene states below 9.3 eV are assigned and discussed with reference to experiment with an overall agreement better than 0.2 eV. The effects of methyl substitution and diffuse basis sets are discussed, and it is shown that the quantization axes of the Rydberg p and d orbitals in the substituted olefins are not the same as those in ethylene.