CEPA calculations on open-shell molecules

Ab initio calculations at SCF and CEPA levels using large Gaussian basis sets have been performed for the two lowest electronic states,X ² Σ⁺ andA ² Π, of HeAr⁺. Spin-orbit coupling (SOC) effects have been added using a semiempirical treatment. The resulting potential curves for the three statesX,A ₁, andA ₂ have been used to evaluate molecular constants such as vibrational intervals ΔG(v + 1/2) and rotational constantsB _v as well as — by means of a Dunham expansion — equilibrium constants such asR _e , ω _e ,B _e etc. Comparison with the experimental data from UV emission spectroscopy shows that the calculated potential curves are slightly too shallow and have too large equilibrium distances:D _e = 242 cm^?1 andR _e = 2.66 Å compared to the experimental values of 262 cm^?1 and 2.585 Å, respectively, for theX ²Σ⁺ ground state. However, the ab initio calculations yield more bound vibrational levels than observed experimentally and allow for a more complete Dunham analysis, in particular for theA ₂ state. The experimental value of 154 cm^?1 for the dissociation energyD _e of this state is certainly too low; our best estimate is 180±5 cm^?1. For theA ₁ state our calculations are predictions since this state has not yet been observed experimentally.     

CEPA calculations on open-shell molecules. V. The vibration frequencies of SF and SCl

Ab initio calculations for the ² ground states of SF and SCl have been performed on Hartree-Fock level and with inclusion of valence shell correlation effects by means of the CI and CEPA approaches. The calculated properties are: Equilibrium distances, vibration frequencies, and dipole moment curves in the vicinity of the respective equilibrium geometries. Our best estimates for the 0 1 infrared absorption frequencies _o for SF and SCl are 786 cm^–1 and 520 cm^–1, respectively, both with an uncertainty of about 10 cm^–1. This confirms a recent experimental value obtained by Willner for SF (791 cm^–1), but indicates that for SCl both experimental values reported previously in the literature (617 cm^–1 and 574 cm^–1) are wrong. The S—F and S—Cl bonds in SF and SCl are very similar to the ones in SF₂ and SCl₂, being essentially single p-bonds in either case. In the analogous oxygen-halogen molecules the situation is different, the O—F and O—Cl bonds in the diatomic radicals OF and OCl have partial double bond character and are much stronger than those in OF₂ and OCl₂ or in HOF and HOCl.     

CEPA calculations of potential energy surfaces for open-shell systems

Potential energy surfaces for the collision of He atoms with NH radicals in the electronically excitedA ³ Π state have been calculated using quantum chemical ab initio methods. The NH distance was kept fixed to its equilibrium value, the range of the HN-He distancesR and HNHe angles γ was chosen to be 4.0≦R≦8.0a ₀, 0≦γ≦180°. The doubly degenerate NH(A ³ Π) state is split upon approach of He into two components, 1³ A′ and 2³ A″, which remain degenerate only for collinear geometries. The resulting two potential surfacesV _A′ andV _A″ are essentially repulsive with shallow van der Waals minima at large distances. An expansion of the sum and the difference potential,V _A′ +V _A″ andV _A′ ?V _A″, respectively, in terms of Legendre polynomials shows that the anisotropic componentsV ₁₀(R) andV ₂₂(R) which mainly govern rotational transitions and Λ-doublet mixing are of the same size. It is therefore expected that these processes as well as fine-structure transitions are similarly probable in NH(A ³ Π)-He collisions. This is in accord with recent experiments of Kaes and Stuhl.     

CEPA calculations on open-shell molecules. II. Singlet-triplet energy splitting in π2 configurations of diatomic molecules

The CEPA-PNO method is used for calculating the energy difference ΔE _ST between the³∑⁻ and the¹Δ states of diatomic molecules in electronic π² configurations. An analysis of the contribution of electron correlation to ΔE _ST is performed in terms of physically understandable effects such as direct correlation, dynamic spin polarization, semiinternal and internal excitations. It is shown that these effects are of completely different importance for the molecules treated in this study: For C₂ the direct correlation between the two singly occupied π-orbitals is the dominant correlation contribution to ΔE _ST; for O₂, S₂, SO the internal excitation π _u ² → π _g ² is predominant, whereas for NH and PH there is a close competition between the direct correlation and the spin polarization of the underlying σ-orbitals. The basis set dependence of these effects is investigated, in particular for NH. Our final results reproduce experimental values of ΔE _ST within 0.05–0.10 eV.     

CEPA calculations on open-shell molecules. III. Potential curves for the six lowest excited states of He2 in the vicinity of their equilibrium distances

CEPA-PNO and PNO-CI calculations have been performed for the potential energy curves of the He ₂ ⁺ ground state and the six lowest excited states of He₂ in the range of 1.4 a₀ ≤R ≤ 3.5 a₀. The calculated equilibrium distances as well as the spectroscopic constants are in very good agreement with molecular constants as derived experimentally from the rotation-vibration spectrum of He₂ by Ginter, except for thec ³∑ _g ⁺ state. This latter discrepancy is probably due to an “obligatory” hump in thec ³∑ _g ⁺ state occurring at 3.5 a₀ which cannot be properly treated in our calculation. The relative energetic positions of the six lowest states and their ionization energies are reproduced by our calculations with an accuracy of 0–400 cm⁻¹. Extrapolation of our results to infinite basis sets leads to estimates of the dissociation energies of He₂ excited states which cannot be measured spectroscopically because of the humps in all these states.     

CEPA calculations of potential energy surfaces for open-shell systems.: IV. Photodissociation of H2O in the A1B1 state

A three-dimensional potential energy surface for the photodissociation of H₂O in its lowest excited singlet state $\text{A}$¹B₁ in C_2v or $\text{A}$¹A″ in C₃ symmetry, respectively, has been calculated with quantum-chemical ab initio methods including electron correlation. The main features of the surface are discussed and qualitative explanations are given for the experimentally observed vibrational and rotational excitations of the product OH(²Π) radicals. The surface will be used in subsequent investigations of the dynamics of the H₂O photodissociation process.     

CEPA calculations of potential energy surfaces for open-shell systems.: III. Van der Waals interaction between O(3P) and He(1S)

Quantum-chemical ab initio calculations have been performed for the van der Waals interaction between helium and oxygen atoms in their respective ground states: He(¹S)+ O(³P). As long as fine-structure effects are neglected, there are two low-lying electronic states, ³Σ^? and ³Π resulting from the degeneracy of the O(³P) ground state. Both states are purely repulsive at the SCF level, after inclusion of electronic correlation by the CEPA method they exhibit shallow van der Waals (dispersion) minima at large interatomic separation: R_? = 3.61 Å, ? = 1.0 meV (³Σ^?) and R_? = 3.05 Å, ? = 2.3 meV (³Π). The analysis of the results shows the very slow convergence of the dispersion interaction with increasing basis size, while SCF repulsion and the repulsion due to the change of the intra-atomic correlation are obtained reasonably accurately with moderate basis stes. Van der Waals coefficients C₆, C₈, C₁₀, potential curves of the type HFD (i.e. Hartree-Fock plus damped dispersion) and the influence of fine-structure effects (mainly spin-orbit coupling) on the shape of the adiabatic potential curves are discussed as well.     

Integral invariants for high-symmetry open-shell molecules.

A numerical procedure for expanding electron repulsion integrals 〈mm|nn〉 on degenerate molecular orbitals of γ symmetry (γ=e, t, g, h) into integral invariants (reduced matrix elements) H^k(γ, γ) is suggested. The latter are analogous in their sense to Slater-Condon parameters F^k(l, l) for atoms with an electronic configuration l^N. The method is applicable to nonlinear molecules of arbitrary symmetries, including “not readily reducible” groups. G. K. Boreskov Institute of Catalysis, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 1, pp. 3–17, January–February, 1998. This work was supported by RFFR grants No. 96-03-01167 and 96-03-34035.     

CEPA Calculations of potential energy surfaces for open-shell systems. II. The reaction of C+ Ions with molecular hydrogen

Ab initio calculations including electron correlation effects (mainly on CEPA-PNO level) have been performed for the potential energy surface (PES) of the reaction of ²P carbon ions with molecular hydrogen. For the collinear abstraction reactions (C_∞v symmetry: ²σ⁺, ²Π-2) the minimum energy paths have been determined. The vertical insertion reaction (C_2v; ²A₁,B₁, ²B₂) has been investigated with particular emphasis (minimum energy path, barrier heights, intersystem crossing). The influence of the size of the orbital basis and of electron correlation has been studied in some detail. The interaction of the ²A₁, and ²B₂ surfaces has been analyzed, leading to the conclusion that close to C_2v symmetry a low energy path exists by which CH₂⁺(²A₁)can be easily formed, with a barrier (²B₂ → ²A₁) ≈ 18 kcal/mol below the asymptote. The analysis of electron correlation effects reveals that it is compulsory to correlate the whole valence shell if one wants to obtain reliable surfaces. The influence of singly excited configurations for getting the correct behaviour of the PES is generally small.     

K-shell ionization energies in molecules by SCF GF calculations

Energies of CH₄, NH₃, H₂O and C₂H₄ K-ionized molecules are calculated by means of a Group Function method using minimal or near minimal basis sets of STO's. Further results from very large basis sets are reported for CH₄, NH₃, and H₂O. Results seemingly do not suffer the shortcomings of a previous SCF MO treatment.     

A.M.O. calculations for some first row diatomic molecules

AMO wavefunctions for LiH, Li₂, HF, F₂ are presented. An explicit formula for computing the energy of a closed shell system composed by doubly occupied MO's and singly filled AMO's is given.     

All electron calculations of open-shell polyatomic molecules. III. Perturbation treatment of the spin polarization in vinyl and methyl radicals

A first order perturbation treatment starting with SCF-MO 'S in canonical or equivalent quasi-localized form is presented for the hyperfine coupling constants of vinyl and methyl radicals. The spin-polarisation contribution to hyperfine splittings is found to be large, negative for the proton of the radical center in both radicals and positive for the β protons of vinyl.     

Chemical ionization mass spectrometry of complex molecules—VI: Peptides

The chemical ionization mass spectra of a series of simple peptides containing six or fewer amino acids have been studied. Using methane as the reactant gas we found cleavage of the peptide bond occurs in two ways, yielding either the acyl carbonium ion or the complementary ammonium ion. The observation of both types of fragments permits the determination of the amino acid sequence of the peptide. The ammonium ions provide an additional sequence determining route compared to that available from electron-impact spectra. ‘Sequence-determing ions,’ especially the quasimolecular ion at m/e [M+1] are usually more intense than in the electron-impact mass spectra.     

Convergence optimization of restricted open-shell self-consistent field calculations

Different self-consistent field (SCF) iteration schemes for open-shell systems are discussed. After a brief summary of the well-known level shifting and damping procedure, we describe the quadratically convergent SCF (QCSCF) approach based on the gradient and the Hessian matrix in a space of orbital rotation parameters. An analytical expression for the latter is derived for the general many-shell case. Starting from the expression for the energy change obtained by the QCSCF method, we then present a simplified direct procedure avoiding matrix diagonalization but also the difficulties of the QCSCF method in handling the Hessian matrix. Numerical calculations on some open-shell systems involving transition-metal complexes show that this method leads to rapid and reliable convergence of the iteration process in cases where the usual SCF procedure of iterative diagonalization tends to diverge. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 617–637, 1997     

Analysis of wave functions for open-shell molecules

During the past decade we have looked at several ways to track the distribution of unpaired electrons during chemical reactions and in different spin states. These methods were inspired by our previous work on singlet di-radicals where the spin density is zero yet there are clearly singly occupied orbitals. More recently we have been concerned with analysis of wave functions for single molecule magnets. This review discusses the mathematical framework by which open-shell systems can be described, in addition to methods that extract the effectively unpaired electron density, the spin state of atoms in a molecule, and other useful properties from a molecular wave function. Some of the difficulties associated with using broken spin Slater determinants to evaluate the exchange coupling parameters in the Heisenberg Hamiltonian are also mentioned.     

Density-functional theory with effective potential expressed as a mapping of the external potential: applications to open-shell molecules

In this paper we apply the direct-mapping density-functional theory (DFT) to open-shell systems, in order to get many-electron wave functions having the same transformation properties as the eigenstates of the exact Hamiltonians. Such a case is that of spin, where in order to get the magnetic properties, the many-particle states must be eigenstates not only of S(z) but also of S2. In this theory the Kohn and Sham [Phys. Rev. A 140, 1133 (1965)] potential is expressed directly as a mapping of the external potential. The total energies of the molecules calculated were satisfactory as their relative deviations (deltaEE) from the exact Hartree-Fock ones were of the order of 10(-4). This accuracy is much higher than that of the standard DFT in its local exchange potential approximation. This method does not need an approximate density as input, as the effective potential is derived directly from the external potential.     

The first ionization potential of uranium and thorium measured in a d.c. arc plasma

Tha Saha relationship was used to derive the ionization potentials of uranium and thorium from measurements of temperature or of electron density in a plasma in thermodynamic equilibrium. Introducing into the plasma elements with well defined ionization potentials, such as Ba, Al, V, Cr, Zr, Mo, Cu, Si and some of the rare-earths, as matrices, the temperature and electron density were measured in the central region of the arc plasma. A relation was established between the different ionization potentials and the plasma temperature or the electron density. From this relation the values of 6.3 ± 0.3 and 7.5 ± 0.3 eV were found for the ionization potentials of U and Th respectively.