Kraitchman has shown that a single isotopic substitution on an atom is sufficient to determine directly the coordinates of that atom with respect to the principal axes of the original molecule. Kraitchman's formulas represent exact solutions of the equations for the equilibrium moments of inertia. However, the effects of the zero‐point vibrations are such that the coordinates obtained by substitution from the ground state moments of inertia I0 are systematically less than r0. These coordinates have here been called r (substitution) or rs, and it is found that rs≃(r0+re)/2, and Is= ∑ imirsi2≃(I0+Ie)/2.In the usual method of solution, the coordinate of one atom is determined from the equation for I0, and therefore the difference I0—Is must be made up by this one coordinate. This introduces a large error in the structures normally determined from ground state constants, and results in variations of 0.01 A in structures determined from different sets of isotopic species. If instead, we obtain the structure on...

A new criterion for the determination of molecular structures from ground state rotational constants

Two-component relativistic pseudopotentials (i.e., scalar-relativistic and spin–orbit (SO) potentials) of the energy-consistent variety have been adjusted for the group 11 and 12 atoms Cu, Zn; Ag, Cd; Au, Hg, replacing the 1s–2p; 1s–3d; and 1s–4f cores, respectively. The adjustment has been done for the valence-energy spectrum of (near-)neutral atoms, to reference data from numerical all-electron four-component multi-configuration Dirac–Hartree–Fock (MCDHF) calculations, including the two-electron Breit interaction. For use in molecular calculations, the potentials have been supplemented by energy-optimized (12s12p9d3f2g)/[6s6p4d3f2g] valence basis sets. First benchmark applications of the potentials and basis sets are presented for atomic excitation energies and SO splittings at a correlated level, and for ground and excited state spectroscopic properties of group 11 monohalides and group 12 dimers.

Energy-consistent pseudopotentials for group 11 and 12 atoms: adjustment to multi-configuration Dirac–Hartree–Fock data

Many light-induced molecular processes involve a change in spin state and are formally forbidden in non-relativistic quantum theory. To make them happen, spin–orbit coupling (SOC) has to be invoked. Intersystem crossing (ISC), the nonradiative transition between two electronic states of different multiplicity, plays a key role in photochemistry and photophysics with a broad range of applications including molecular photonics, biological photosensors, photodynamic therapy, and materials science. Quantum chemistry has become a valuable tool for gaining detailed insight into the mechanisms of ISC. After a short introduction highlighting the importance of ISC and a brief description of the relativistic origins of SOC, this article focusses on approximate SOC operators for practical use in molecular applications and reviews state-of-the-art theoretical methods for evaluating ISC rates. Finally, a few sample applications are discussed that underline the necessity of studying the mechanisms of ISC processes beyond qualitative rules such as the El-Sayed rules and the energy gap law. © 2011 John Wiley & Sons, Ltd.

Spin–orbit coupling and intersystem crossing in molecules

The heat of formation of NCO has been determined rigorously by state‐of‐the‐art ab initio electronic structure methods, including Mo/ller–Plesset perturbation theory from second through fifth order (MP2–MP5) and coupled‐cluster and Brueckner methods incorporating various degrees of excitation [CCSD, CCSD(T), BD, BD(T), and BD(TQ)]. Five independent reactions were investigated to establish a consistent value for ΔHf,0○(NCO): (a) HNCO(X 1A’)→H(2S)+NCO(2Π), (b) HNCO(X 1A’)→H++NCO−, (c) N(4S)+CO→NCO(2Π), (d) HCN+O(3P)→H(2S)+NCO(2Π), and (e) NH(3Σ−)+CO→H(2S)+NCO(2Π). The one‐particle basis sets employed in the study were comprised of as many as 377 contracted Gaussian functions and ranged in quality from [4s2p1d] to [14s9p6d4f] on the (C,N,O) atoms and from [2s1p] to [8s6p4d] on hydrogen. After the addition of bond additivity corrections evaluated from related reactions of precisely known thermochemistry, all five approaches were found to converge on the value ΔHf,0○(NCO)=31.4(5) kcal mol−1. Appurtenant refi...

The heat of formation of NCO

http://theop11.chem.elte.hu/main_index_files/1990_Allen_ChemPhys_145_427_LinMol.pdf

A systematic study of molecular vibrational anharmonicity and vibration-rotation interaction by self-consistent-field higher-derivative methods. Linear polyatomic molecules

Thirteen pure rotational transitions of CH2 in its X 3B1 ground vibronic state have been measured and assigned using the technique of far‐infrared laser magnetic resonance (LMR) spectroscopy. The energy levels thus determined led to the prediction and subsequent detection by microwave spectroscopy of a further rotational transition 404–313, at lower frequency (∼70 GHz). The analysis of these observations yields precise rotational constants as well as spin–spin, spin‐rotation, and hyperfine interaction parameters for gas phase CH2. Its rotational spectrum may enable interstellar CH2 to be detected by radio astronomy. Two rotaional transitions within the v1=1 excited vibrational state have also been identified in the LMR spectrum. Future observations of vibrationally excited CH2 may afford a means of determining the singlet–triplet splitting in methylene, and studies of CD2 and CHD will result in improved structural determinations.

The rotational spectrum and hyperfine structure of the methylene radical CH2 studied by far‐infrared laser magnetic resonance spectroscopy

Lines in the b3Σ+-a3II and c3Σ+-a3II systems of AlF show partially resolved hyperfine structure. This structure has been attributed to magnetic interactions involving the 27Al nucleus for which I = 5/2. About twenty unblended lines from the (0, 0) bands of the two systems have been analysed in detail, using a computer programme to simulate the profiles by calculating the frequencies and intensities of individual hyperfine transitions. For low values of the rotational quantum number, the lines show a simple triplet structure, which reflects the case (bβS) coupling in the 3Σ states. Analysis of these lines gives values for the Fermi contact parameters in the two states involved (bF = 0.049 cm-1 and 0.057 cm-1 in the b3Σ+ and c3Σ+ states respectively). As the rotational quantum number increases, the hyperfine patterns become less regular, indicating a departure from case (bβS) coupling in the 3Σ states and from case (aβ) coupling in the 3II state. By reproducing the details of these line-shapes, it has also proved possible to determine values for the electron spin-spin and spin-rotation parameters in the two 3Σ states: b3Σ+ λ = -0.025(10)cm-1 γ = 0.0000(3)cm-1 c3Σ+ λ = 0.00(1)cm-1 γ = 0.0015(10)cm-1 The experimental values for the Fermi contact parameter of AlF in the a3II and b3Σ+ states are well produced by a simple single configuration molecular orbital calculation but the value for the c3Σ state is rather larger than expected on this basis.

An Analysis of Hyperfine Interactions in the Electronic Spectrum of AIF

Several lines in the lambda-doubling spectrum of the CH radical in its ground 2Π state have been recorded by the technique of microwave-optical double resonance. Individual lines in the (0, 0) band...

John M. Brown

Papers

The rotational spectrum and hyperfine structure of the methylene radical CH2 studied by far‐infrared laser magnetic resonance spectroscopy

An Analysis of Hyperfine Interactions in the Electronic Spectrum of AIF

A measurement of the lambda-type doubling spectrum of the CH radical by microwave-optical double resonance: further characterization of the A2Δ state

The far-infrared Laser Magnetic Resonance Spectrum of the OH radical

The far-infrared laser magnetic resonance spectrum of the CF radical and determination of ground state parameters☆