Juergen Hinze

LiH Potential Curves and Wavefunctions for X 1Σ+, A 1Σ+, B 1Π, 3Σ+, and 3Π

Ab initio multiconfiguration self‐consistent‐field calculations are reported for the potential curves and electronic wave functions of the states X 1Σ+, A 1Σ+, B 1Π, 3Σ+, and 3Π of LiH. In this calculation, the outer two electrons are correlated, while the 1σ shell, essentially a K shell on Li, is left uncorrelated. The obtained dissociation energies, with the known experimental values in parentheses, are De(X 1Σ+)=2.411(2.5154) eV, De(A 1Σ+)=1.048 (1.0765) eV, De(B 1Π)=0.017 (0.035) eV and De(3Π)=0.226 eV.

Inverse perturbation analysis: Improving the accuracy of potential energy curves☆

Abstract The equation for the first-order energy correction is used inversely to find the perturbation responsible for the energy correction. In the specific application to the calculation of a potential energy curve from the spectroscopic term values, the sought perturbation is a correction to an approximate potential curve. Consequently, an approximate potential curve (e.g. an RKR (Rydberg-Klein-Rees) curve) can be improved until the eigenvalues calculated for this curve agree with the spectroscopic term values within the experimental uncertainty. Results are given for the X 2 Σ + state of HgH.

Valence excited states of CH. I. Potential curves

Ab initio CI calculations have been performed over a wide range of internuclear distances (1.00–20.00 bohr) to obtain the potential curves for the first five valence excited states of CH; X2Π, a4Σ−1, A2Δ, B2Σ−, and C2Σ+. Results, with known experimental values in parentheses, are Re(X2Π) = 2.113 (2.116) bohr, Re(a4Σ−) = 2.053 bohr, Re(A2Δ) = 2.083(2.083) bohr, Re(B2Σ−) = 2.216(2.20) bohr, Re(C2Σ+) = 2.100(2.105) bohr; De(X2Π) = 3.51(3.63) eV, De(a4Σ−) = 2.84 eV, De(A2Δ) = 1.90(2.01) eV, De(B2Σ−) = 0.23(0.40) eV, and De(C2Σ+) = 0.78(0.94) eV. Potential maxima of heights 1284 and 3228 cm−1 are calculated for the B2Σ− and C2Σ+ states, respectively. These maxima are attributed to avoided curve crossings. The a4Σ− state, not observed experimentally, is estimated to lie between 0.62 and 0.76 eV above the X2Π state.

MCSCF calculations for six states of NaH

Ab initio multiconfiguration self‐consisting‐field calculations are reported for the energies, electronic wavefunctions, and one‐electron properties of the X1Σ+, A1Σ+, B1Π, a3Σ+, b3Π, and c3Σ+ states of NaH over a wide range of internuclear distances. In these calculations, only the two valence electrons are correlated. Three states (X1Σ+, A1Σ+, and b3Π) were found to be bound, with the following dissociation energies and internuclear separations (with known experimental values in parentheses): De (X1Σ+) = 1.878 (2.12±0.20) eV, Rmin (X1Σ+) = 3.609 (3.566) bohr; De (A1Σ+) = 1.203 (1.41±0.20) eV, Rmin (A1Σ+) = 6.186 (6.062) bohr; and De (b3Π) = 0.109 eV, Rmin (b3Π) = 4.458 bohr.

Transition moments, band strengths, and line strengths for NaH

Electronic transition moments, as functions of internuclear separation, are calculated for the A1Σ+ → X1Σ+, B1Π → X1Σ+, B1Π → A1Σ+, c3Σ+ → a3Σ+, b3Π → a3Σ+, and b3Π → c3Σ+ transitions in NaH from ab initio molecular wavefunctions. Reduced line strengths, band strengths, band oscillator strengths, and band Einstein coefficients are calculated for the observed A1Σ+ → X1Σ+ transition, and are compared to experimental band intensities. Also calculated are Franck–Condon factors and R centroids, and the effects of various approximations used in treating experimental data are analyzed.

Valence excited states of CH. II. Properties

Expectation values of one‐electron operators and related molecular properties were calculated for the X2π, a4Σ−, A2Δ, B2Σ−, and C2Σ+ states of CH, using accurate ab initio electronic wavefunctions and potential curves. The calculated dipole moment for the ν = 0 vibrational level of the X2π state is 1.41 D, in excellent agreement with the experimental value of 1.46 ± 0.06 D. Other properties studied include dipole and quadrupole moments and field gradients at the nuclei. There are no known experimental values for these properties. Vibration‐rotational wavefunctions were obtained from the calculated potential curves by numerical solution of the radial Schrodinger equation for the nuclear motion. Vibration‐rotational analyses were carried out to yield spectroscopic constants which are in satisfactory agreement with known experimental values.

Calculated a4Σ−, A2Δ, B2Σ− States of CH

Ab initio CI calculations have been performed over a wide range of internuclear distances to obtain the potential curves for three low‐lying excited electronic states, a4Σ−, A2Δ, B2Σ−, of CH. With the computed potential curves, vibration‐rotational levels are obtained by numerical integration of the radial Schrodinger equations for the motion of the nuclei. The term values are analyzed to yield the conventional spectroscopic constants. Results, with known experimental values in parentheses, are Re(A 2Δ)=2.074(2.082) a.u., Re(B 2Σ−)=2.208(2.200) a.u., Re(a 4Σ−)=2.047 a.u.; De0(A 2Δ)=1.89(2.01) eV, De0(B 2Σ−)=0.17(∼ 0.40) eV, and De0(a 4Σ−)=2.88 eV. The computed spectroscopic constants are found to be within 4% of known experimental values. A potential maximum of height 1600 cm−1 occurs in the computed potential curve of the B2Σ− state. The a4Σ− state, not known experimentally, is estimated to lie between 0.52 eV and 0.75 eV above the X2II ground state.

Rotation–vibrational analysis for three states of NaH and NaD

We have carried out a rotation–vibrational analysis for the X1Σ+, A1Σ+, and b3Π states of NaH and NaD using accurate ab initio calculated potential curves. The calculated values of Be, αe, Re, ωe, and ωexe (with known experimental values in parentheses) are NaH X1Σ+ : Be = 4.748 (4.886) cm−1, αe = 0.126 (0.129) cm−1, Re = 3.625 (3.562) bohr, ωe = 1183.17 (1172.2) cm−1, and ωexe = 21.23 (19.72) cm−1; NaD X1Σ+ : Be = 2.475 (2.5575) cm−1, αe = 0.0474 (0.0520) cm−1, Re = 3.624 (3.565) bohr, ωe = 826.60 (826.10) cm−1 and ωexe = 9.44 cm−1; NaH b3Π : Be = 3.533 cm−1, αe = 0.853 cm−1, Re = 4.202 bohr, ωe = 419.39 cm−1 and ωexe = 50.25 cm−1; NaD b3Π: Be = 1.763 cm−1, αe = 0.265 cm−1, Re = 4.294 bohr, ωe = 311.95 cm−1 and ωexe = 28.68 cm−1. The anomalous behavior of the Bv′s and ΔGv+1/2′s of the A1Σ+ state is satisfactorily reproduced by these calculations: for NaH, Bv (max ) = 1.9717 (1.941) cm−1 at v = 6 (6) and ΔGv+1/2 (max) = 381.37 (360.3) cm−1 at v = 9 (8); for NaD, Bv (max) = 1.0274 (1.012) cm−1 at v = 8 (8)...

Frozen core approximation, a pseudopotential method tested on six states of NaH

A pseudopotential formulation, more appropriately called the frozen core approximation (FCA), is presented in detail. This FCA is tested by performing MCSCF calculations on the six low lying states, X1Σ+, A1Σ+, a3Σ+, c3Σ+, B1Π, and b3Π of NaH. The results obtained are compared with those of an analogous previous MCSCF calculation on these states without the use of FCA, i.e., with all orbitals optimized. It is found that energies are obtained rather accurately with FCA; however, calculated molecular properties are affected more strongly and the shapes of the potential curves appear to be distorted somewhat by FCA. It is argued that no pseudo‐ or model‐potential calculation can give errors less than FCA unless the potential is made valence shell dependent. This, however, would be analogous to a full calculation, and the savings due to a pseudopotential approximation would be lost.

Accuracy in determining the potential energy curve minimum

The symbol “re” commonly refers to two quantities: 1. (1) the location of the minumum of the actual rotationless potential energy function; 2. (2) the value calculated from spectroscopic data using the equation re = (h4πμcBe)12 Are the two quantities equivalent? To investigate this question, the exact quantum mechanical solutions of the Davidson potential, U(r) = ar2 + br2 − 2(ab)12, are analyzed analytically in order to determine the re of definition 2. Comparison is then possible with the re of definition 1. Disagreement is found between the two quantities called re for several of the spectroscopic analysis methods tested. These disagreements, generalized to diatomic potentials, indicate possible errors in the determination of the actual minimum up to 0.1% with three of the tested analysis methods and less than 10−5% with other, more appropriate methods.