Partial Triple Excitations Research Articles

Relativistic Coupled-Cluster Calculations of Isotope Shifts for the Low-Lying States of Ca II in the Finite-Field Approach

We have evaluated the isotope shift (IS) constants of the first five low-lying fine-structure states of the singly charged calcium ion (Ca II) by adopting a finite-field (FF) approach in the relativistic coupled-cluster (RCC), a method developed by us and by using a code also developed by us. A similar previous calculation using singles and doubles approximation RCC theory (RCCSD method), gives results for the individual states in the FF approach that deviate substantially, while the differential values (the shifts of the spectral lines) agree reasonably well with other theoretical results and with experiments. However, we find a contrasting trend from the FF approach using our RCCSD method although calculations with the Dirac–Hartree–Fock (DHF) method shows good agreement. Our results also show that inclusion of partial triple excitations in the perturbative approach (RCCSD(T) method) through energy derivation lessens accuracy, but these results can be improved when triple excitations are included in the wave function that determines the RCC equations. The differences between the RCCSD and RCCSD(T) results demonstrate the importance of triple excitations in evaluating energies and IS constants for Ca II. Finally, we also present ab initio values of IS’s between the S–P, S–D, and D–P transitions in the DHF, and RCCSD and RCCSD(T) approximations and this is compared to the previously reported values (theoretical as well as experimental).

Dynamic polarizability measurements with Lu+176

We measure the differential polarizability of the $^{176}$Lu$^+$ $^1S_0$ -to- ${^3}D_1$ clock transition at multiple wavelengths. This experimentally characterizes the differential dynamic polarizability for frequencies up to 372 THz and allows an experimental determination of the dynamic correction to the blackbody radiation shift for the clock transition. In addition, measurements at the near resonant wavelengths of 598 and 646 nm determine the two dominant contributions to the differential dynamic polarizability below 372 THz. These additional measurements are carried out by two independent methods to verify the validity of our methodology. We also carry out a theoretical calculation of the polarizabilities using the hybrid method that combines the configuration interaction (CI) and the coupled-cluster approaches, incorporating for the first time quadratic non-linear terms and partial triple excitations in the coupled-cluster calculations. The experimental measurements of the $|\langle ^3D_1|| r || ^3P_J\rangle|$ matrix elements provide high-precision benchmarks for this theoretical approach.

Relativistic many-body calculation of energies, lifetimes, polarizabilities, blackbody radiative shift, and hyperfine constants inLu2+

Energy levels of 30 low-lying states of Lu2+ and allowed electric-dipole matrix elements between these states are evaluated using a relativistic all-order method in which all single, double and partial triple excitations of Dirac-Fock wave functions are included to all orders of perturbation theory. Matrix elements are critically evaluated for their accuracy and recommended values of the matrix elements are given together with uncertainty estimates. Line strengths, transition rates and lifetimes of the metastable 5d(3/2) and 5d(5/2) states are calculated. Recommended values are given for static polarizabilities of the 6s, 5d and 6p states and tensor polarizabilities of the 5d and 6p(3/2) states. Uncertainties of the polarizability values are estimated in all cases. The blackbody radiation shift of the 6s(1/2)-5d(5/2) transition frequency of the Lu2+ ion is calculated with the aid of the recommended scalar polarizabilities of the 6s(1/2) and 5d(5/2) states. Finally, A and B hyperfine constants are determined for states of 175Lu2+ with n <= 9. This work provides recommended values of transition matrix elements, polarizabilities and hyperfine constants of Lu2+, critically evaluated for accuracy, for benchmark tests of high-precision theoretical methodology and planning of future experiments.

Relativistic many-body calculation of energies, transition rates, lifetimes, and multipole polarizabilities in Cs-like La iii

Excitation energies of the [Xe]$nd$ ($n=5\ensuremath{-}9$), [Xe]$ns$ ($n=6\ensuremath{-}10$), [Xe]$np$ ($n=6\ensuremath{-}9$), [Xe]$nf$ ($n=4\ensuremath{-}8$), and [Xe]$ng$ ($n=5\ensuremath{-}8$) states in La iii, where [Xe] = $1{s}^{2}2{s}^{2}2{p}^{6}3{s}^{2}3{p}^{6}3{d}^{10}4{s}^{2}4{p}^{6}4{d}^{10}5{s}^{2}5{p}^{6}$, are evaluated. Electric dipole matrix elements for the allowed transitions between the low-lying [Xe]$nd$, [Xe]$ns$, [Xe]$np$, [Xe]$nf$, and [Xe]$ng$ states in the La iii ion are calculated using the high-precision relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of electric dipole matrix elements, oscillator strengths, transition rates, and lifetimes. Scalar and tensor polarizabilities of the states listed above are evaluated. The uncertainties of the recommended values are estimated. Electric quadrupole and magnetic dipole matrix elements are calculated to determine lifetimes of the $5{d}_{5/2}$ and $6s$ metastable levels. The ground-state $E1$, $E2$, and $E3$ static polarizabilities are calculated. This work provides recommended values critically evaluated for their accuracy for a number of La iii atomic properties for use in planning and analysis of various experiments as well as theoretical modeling.

Relativistic many-body calculation of energies, oscillator strengths, transition rates, lifetimes, polarizabilities, and quadrupole moment of a Fr-like Thiv ion

Atomic properties of the 24 low-lying ns, np, nd, nf, and ng states in Th IV ion are calculated using the high-precision relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of electric-dipole matrix elements, oscillator strengths, transition rates, and lifetimes. Scalar polarizabilities of the ground and six excited states (5f_j, 6d_j, 7p_j, and 7s), and tensor polarizabilities of the 5f_j, 6d_j, 7p_{3/2} states of Th IV are evaluated. The uncertainties of the recommended values are estimated. These calculations provide recommended values critically evaluated for their accuracy for a number of Th IV atomic properties for use in theoretical modeling as well as planning and analysis of various experiments including development of ultra precise nuclear clock and RESIS studies of actinide ions

Magic wavelengths for optical cooling and trapping of potassium

We carry out a systematic study of the static and dynamic polarizabilities of the potassium atom using a first-principles high-precision relativistic all-order method in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values and uncertainties are provided for the relevant electric-dipole matrix elements. Polarizabilities of the $4s$, $4{p}_{j}$, $5s$, $5{p}_{j}$, and $3{d}_{j}$ states are compared with other theoretical and experimental values when possible. We identify magic wavelengths for the $4s\ensuremath{-}np$ transitions for $n=4,5$, i.e., those wavelengths for which the two levels have the same ac Stark shifts. The magic wavelengths for the $4s\ensuremath{-}5p$ transitions are of particular interest for attaining a quantum gas of potassium at high phase-space density. We find 20 such wavelengths in the technically interesting region of $1050--1130$ nm.

Polarizabilities, Stark shifts, and lifetimes of the In atom

We evaluate the polarizabilities of the $5{p}_{1/2}$, $6s$, $6{p}_{1/2}$, and $6{p}_{3/2}$ states of In using two high-precision relativistic methods: the linearized coupled-cluster approach, where single, double, and partial triple excitations of the Dirac-Fock wave function are included to all orders of perturbation theory, and an approach that combines the configuration interaction and the coupled-cluster method. An extensive comparison of the accuracy of these methods is carried out. The uncertainties of all recommended values are evaluated. Our result for the $6s$-$5{p}_{1/2}$ Stark shift is in excellent agreement with a recent measurement [Ranjit et al., Phys. Rev. A 87, 032506 (2013)]. Combining our calculation with this precision measurement allows us to infer the values of the $6{p}_{1/2}$ and $6{p}_{3/2}$ lifetimes in In with 0.8$%$ accuracy. Our predictions for the $6{p}_{3/2}$ scalar and tensor polarizabilities may be combined with the future measurement of the $6s$-$6{p}_{3/2}$ Stark shift to accurately determine the $5{d}_{j}$-$6{p}_{{j}^{\ensuremath{'}}}$ matrix elements.

Magic wavelengths for optical cooling and trapping of lithium

Using first-principles calculations, we identify magic wavelengths for the 2s-2p and 2s-3p transitions in lithium. The ns and np atomic levels have the same ac Stark shifts at the corresponding magic wavelength, which facilitates state-insensitive optical cooling and trapping. Tune-out wavelengths for which the ground-state frequency-dependent polarizability vanishes are also calculated. Differences of these wavelengths between 6Li and 7Li are reported. Our approach uses high-precision, relativistic all-order methods in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of Li electric-dipole matrix elements. Static polarizabilities for the 2s, 2p, 3s, 3p, and 3d levels are compared with other theory and experiment where available. Uncertainties of all recommended values are estimated. The magic wavelengths for the uv 2s-3p transition are of particular interest for the production of a quantum gas of lithium [Duarte et al., Phys. Rev. A 84, 061406R (2011)].

Diagnosis of the performance of the state-specific multireference coupled-cluster method with different truncation schemes

We have tested the linked version of a iterative (partial) triples correction for the Jeziorski-Monkhorst ansatz based state-specific multireference coupled cluster (SS-MRCC) approach with singles and doubles (SD) excitations [abbreviated as SS-MRCCSDT-1a and SS-MRCCSDT-1a+d]. The assessments of SS-MRCCSDT-1a and SS-MRCCSDT-1a+d schemes have been performed on the ground potential energy surface (PES) of P4, Li(2),Be(2) systems which demand the MR description, and on study of the excitation energy between the ground and first excited state for P4 system. Illustrations in the isomerization of cyclobutadiene also show the power of the schemes. One of the designed features of the SS-MRCCSDT-n methods introduced here is that they do not require storage of the triples amplitudes. In the entire range of geometries, we found a definite improvement provided by SS-MRCC with SDT-1a and SDT-1a+d schemes over the standard SD one. In the nondegenerate regions of PES, the closeness of the performance of the single-reference CC to the SS-MRCC methods increases after inclusion of even partial triple excitations. Generally, the performance of the SS-MRCCSDT-1a+d approach is closer to the corresponding full configuration interaction (FCI) one than to the SS-MRCCSDT-1a specially in the degenerate geometries (as is evident from nonparallelism error). The deviation from FCI for the first excited state of the P4 model using various SS-MRCC theories with different truncation schemes obtained by converging on the second root of the effective Hamiltonian has also been reported. We also compare our results with the current generation state-of-the-art single and multireference CC calculations to envisage the usefulness of the present approach. Initial implementation indicates that the SS-MRCCSDT-n formalism can provide not only reliable excitation energies and barrier height even when used in a relatively small model space, but also offers a considerable promise in generating the entire energy surface with low nonparallelity error.

Relativistic many-body calculation of energies, oscillator strengths, transition rates, and lifetimes of Sc III ion

A systematic study of Sc iii atomic properties is carried out using a high-precision relativistic all-order method where all single, double, and partial-triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the $ns$, $n{p}_{j}$, $n{d}_{j}$, $n{f}_{j}$, and $n{g}_{j}$ levels with $n\ensuremath{\leqslant}7$. Recommended values and estimates of their uncertainties are provided for a large number of electric-dipole transitions. Electric-quadrupole and magnetic-dipole matrix elements are evaluated to determine lifetimes of the $3{d}_{5/2}$ and $4s$ metastable levels. These calculations provide recommended values critically evaluated for their accuracy for a number of Sc iii atomic properties for use in theoretical modeling as well as planning and analysis of various experiments. We hope that the present study will stimulate further exploration of Sc iii for various applications owing to its interesting structure of different low-lying metastable levels.

Tune-out wavelengths of alkali-metal atoms and their applications

Using first-principles calculations, we identify ``tune-out'' optical wavelengths, ${\ensuremath{\lambda}}_{\mathrm{zero}}$, for which the ground-state frequency-dependent polarizabilities of alkali-metal atoms vanish. Our approach uses high-precision, relativistic all-order method in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. We discuss the use of tune-out wavelengths for sympathetic cooling in two-species mixtures of alkali metals with group II and other elements of interest. Special cases in which these wavelengths coincide with strong resonance transitions in a target system are identified.

Resolving all-order method convergence problems for atomic physics applications

The development of the relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Hartree-Fock wave function are included to all orders of perturbation theory led to many important results for the study of fundamental symmetries, development of atomic clocks, ultracold atom physics, and others, as well as provided recommended values of many atomic properties critically evaluated for their accuracy for a large number of monovalent systems. This approach requires iterative solutions of the linearized coupled-cluster equations leading to convergence issues in some cases where correlation corrections are particularly large or lead to an oscillating pattern. Moreover, these issues also lead to similar problems in the configuration-interaction (CI)$+$all-order method for many-particle systems. In this work, we have resolved most of the known convergence problems by applying two different convergence stabilizer methods, namely, reduced linear equation and direct inversion of iterative subspace. Examples are presented for B, Al, Zn${}^{+}$, and Yb${}^{+}$. Solving these convergence problems greatly expands the number of atomic species that can be treated with the all-order methods and is anticipated to facilitate many interesting future applications.

Blackbody radiation shift, multipole polarizabilities, oscillator strengths, lifetimes, hyperfine constants, and excitation energies in Ca+

A systematic study of Ca${}^{+}$ atomic properties is carried out using a high-precision relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the levels up to $n=7$. Recommended values and estimates of their uncertainties are provided for a large number of electric-dipole transitions. Electric-dipole scalar polarizabilities for the $5s$, $6s$, $7s$, $8s$, $4{p}_{j}$, $5{p}_{j}$, $3{d}_{j}$, and $4{d}_{j}$ states and tensor polarizabilities for the $4{p}_{3/2}$, $5{p}_{3/2}$, $3{d}_{j}$, and $4{d}_{j}$ states in Ca${}^{+}$ are calculated. Methods are developed to accurately treat the contributions from highly excited states, resulting in significant (factor of 3) improvement in the accuracy of the $3{d}_{5/2}$ static polarizability value, $31.8(3){a}_{0}^{3}$, in comparison with the previous calculation [Arora et al., Phys. Rev. A 76, 064501 (2007).]. The blackbody radiation shift of the $4s--3{d}_{5/2}$ clock transition in Ca${}^{+}$ is calculated to be $0.381(4)$ Hz at room temperature, $T=300$ K. Electric-quadrupole $4s--\mathit{nd}$ and electric-octupole $4s--\mathit{nf}$ matrix elements are calculated to obtain the ground-state multipole $E2$ and $E3$ static polarizabilities. Excitation energies of the $\mathit{ns}$, $\mathit{np}$, $\mathit{nd}$, $\mathit{nf}$, and $\mathit{ng}$ states with $n\ensuremath{\leqslant}$ 7 in are evaluated and compared with experiment. Recommended values are provided for the $7{p}_{1/2}$, $7{p}_{3/2}$, $8{p}_{1/2}$, and $8{p}_{3/2}$ removal energies for which experimental measurements are not available. The hyperfine constants $A$ are determined for the low-lying levels up to $n=7$. The quadratic Stark effect on hyperfine structure levels of $^{43}\mathrm{Ca}$${}^{+}$ ground state is investigated. These calculations provide recommended values critically evaluated for their accuracy for a number of Ca${}^{+}$ atomic properties for use in planning and analysis of various experiments as well as theoretical modeling.

Insights into the orbital invariance problem in state-specific multireference coupled cluster theory

In this communication we report the results of our studies on the orbital invariance properties of the state-specific multireference coupled cluster approach suggested by Mukherjee and co-workers (Mk-MRCC). In particular, we have gathered numerical evidence to show that even when the linear excitation manifold is modified in order to span the same space for each reference, the resulting method is not orbital invariant. In order to test this conjecture we have proposed a new truncation scheme (Mk-MRCCSDtq) which, in addition to full single and double excitations, contains partial triple and quadruple excitations. For a reference space generated by all possible combinations of two electrons in two orbitals, the linear excitation manifold of Mk-MRCCSDtq spans the same set for each reference determinant. Mk-MRCCSDtq is found to lack energy invariance for rotations among active molecular orbitals but it is less sensitive to orbital rotations than the conventional scheme which includes only singles and doubles (Mk-MRCCSD). Nevertheless, Mk-MRCCSDtq is a very accurate method, superior with respect to multireference configuration interaction approaches, and competitive with the active-space coupled cluster method and the MRexpT ansatz.

Electric quadrupole moments of metastable states ofCa+,Sr+, andBa+

The electric quadrupole moments of the metastable $n{d}_{3∕2}$ and $n{d}_{5∕2}$ states of ${\mathrm{Ca}}^{+}$, ${\mathrm{Sr}}^{+}$, and ${\mathrm{Ba}}^{+}$ are calculated using the relativistic all-order method including all single, double, and partial triple excitations of the Dirac-Hartree-Fock wave function to provide recommended values for the cases where no experimental data are available. The contributions of all nonlinear single and double terms are also calculated for the case of ${\mathrm{Ca}}^{+}$ for comparison of our approach with results of the coupled-cluster method with singles, doubles, and perturbative triples. Third-order many-body perturbation theory is used to evaluate the contributions of high partial waves and the Breit interaction. The remaining omitted correlation corrections are estimated as well. An extensive study of the uncertainty of our calculations is carried out to establish the accuracy of our recommended values as 0.5--1 % depending on the particular ion. A comprehensive comparison of our results with other theoretical values and experimental results is carried out. Our result for the quadrupole moment of the $3{d}_{5∕2}$ state of the ${\mathrm{Ca}}^{+}$ ion, $1.849(17)e{a}_{0}^{2}$, is in agreement with the most precise recent measurement $1.83(1)e{a}_{0}^{2}$ by Roos et al. [Nature (London) 443, 316 (2006)].

Effects of partial triple excitations in atomic coupled cluster calculations

In this Letter, we study the effects of higher body excitations in the relativistic CC calculations for atoms and ions with one valence electron using Fock-space CCSD, CCSD(T) and its unitary variants. The present study demonstrates that CCSD(T) estimates the ionization potentials (IPs) and the valence electron removal energies quite accurately for alkali atoms and singly ionized alkaline earth ions, but yields unphysical energy levels for atoms and/or ions with partially filled sub-shell like C II. We further demonstrate that the higher body excitation effects can be incorporated more effectively through the unitary coupled cluster theory (UCC) compared to the CCSD(T) method.

Renner−Teller Bending Frequencies of the à 2Π State of OCS+

There are inconsistencies among previously reported Renner-Teller bending frequencies for the approximately A 2Pi state of OCS+. To resolve these controversies, we have computed vibrational frequencies using high-level excited electronic state ab initio equation-of-motion coupled cluster methods. On the basis of equation-of-motion coupled cluster theory including single, double, and iterative inclusion of partial triple excitations (EOM-CC3) paired with the correlation-consistent polarized valence quadruple-zeta basis set (cc-pVQZ), we predict harmonic bending frequencies of 364 and 401 cm-1 for the A' and A" components of approximately A 2Pi OCS+, respectively. Particularly for the upper Renner-Teller component, these results are lower than the theoretical predictions of 370 and 459 cm-1 reported by Chen, Hochlaf, Rosmus, He, and Ng [J. Chem. Phys. 2002, 116, 5612]. Instead, the presently computed bending frequencies are more consistent with the experimentally derived average value of 357 +/- 5 cm-1 recently reported by Sommavilla and Merkt [J. Phys. Chem. A 2004, 108, 9970], lending credence to the spectral assignments made in this later work. The two components of the Renner-Teller bending frequencies of approximately X 2Pi OCS+ are similarly predicted to be 396 and 453 cm-1. Anharmonicity constants arising from a quartic force field computed at the cc-pVQZ EOM-CC3 level of theory are given, to provide a more complete characterization of the potential energy surface of the approximately A 2Pi state of OCS+.

Characterization of singlet ground and low-lying electronic excited states of phosphaethyne and isophosphaethyne

The singlet ground ((approximate)X(1)Sigma1+) and excited (1Sigma-,1Delta) states of HCP and HPC have been systematically investigated using ab initio molecular electronic structure theory. For the ground state, geometries of the two linear stationary points have been optimized and physical properties have been predicted utilizing restricted self-consistent field theory, coupled cluster theory with single and double excitations (CCSD), CCSD with perturbative triple corrections [CCSD(T)], and CCSD with partial iterative triple excitations (CCSDT-3 and CC3). Physical properties computed for the global minimum ((approximate)X(1)Sigma+HCP) include harmonic vibrational frequencies with the cc-pV5Z CCSD(T) method of omega1=3344 cm(-1), omega2=689 cm(-1), and omega3=1298 cm(-1). Linear HPC, a stationary point of Hessian index 2, is predicted to lie 75.2 kcal mol(-1) above the global minimum HCP. The dissociation energy D0[HCP((approximate)X(1)Sigma+)-->H(2S)+CP(X2Sigma+)] of HCP is predicted to be 119.0 kcal mol(-1), which is very close to the experimental lower limit of 119.1 kcal mol(-1). Eight singlet excited states were examined and their physical properties were determined employing three equation-of-motion coupled cluster methods (EOM-CCSD, EOM-CCSDT-3, and EOM-CC3). Four stationary points were located on the lowest-lying excited state potential energy surface, 1Sigma- -->1A", with excitation energies Te of 101.4 kcal mol(-1) (1A"HCP), 104.6 kcal mol(-1)(1Sigma-HCP), 122.3 kcal mol(-1)(1A" HPC), and 171.6 kcal mol(-1)(1Sigma-HPC) at the cc-pVQZ EOM-CCSDT-3 level of theory. The physical properties of the 1A" state with a predicted bond angle of 129.5 degrees compare well with the experimentally reported first singlet state ((approximate)A1A"). The excitation energy predicted for this excitation is T0=99.4 kcal mol(-1) (34 800 cm(-1),4.31 eV), in essentially perfect agreement with the experimental value of T0=99.3 kcal mol(-1)(34 746 cm(-1),4.308 eV). For the second lowest-lying excited singlet surface, 1Delta-->1A', four stationary points were found with Te values of 111.2 kcal mol(-1) (2(1)A' HCP), 112.4 kcal mol(-1) (1Delta HPC), 125.6 kcal mol(-1)(2(1)A' HCP), and 177.8 kcal mol(-1)(1Delta HPC). The predicted CP bond length and frequencies of the 2(1)A' state with a bond angle of 89.8 degrees (1.707 A, 666 and 979 cm(-1)) compare reasonably well with those for the experimentally reported (approximate)C(1)A' state (1.69 A, 615 and 969 cm(-1)). However, the excitation energy and bond angle do not agree well: theoretical values of 108.7 kcal mol(-1) and 89.8 degrees versus experimental values of 115.1 kcal mol(-1) and 113 degrees. of 115.1 kcal mol(-1) and 113 degrees.

Relativistic Coupled-Cluster Theory of Atomic Parity Nonconservation: Application toBa+137

We report the result of our ab initio calculation of the 6s2S1/2-->5d2D3/2 parity nonconserving electric dipole transition amplitude in 137Ba+ based on relativistic coupled-cluster theory. Considering single, double, and partial triple excitations, we have achieved an accuracy of less than 1%. If the accuracy of our calculation can be matched by the proposed parity nonconservation experiment in Ba+ for the above transition, then the combination of the two results would provide an independent nonaccelerator test of the standard model of particle physics.

Application of equation-of-motion coupled-cluster methods to low-lying singlet and triplet electronic states of HBO and BOH

The equilibrium structures and physical properties of the X (1)sigma(+) linear electronic states, linear excited singlet and triplet electronic states of hydroboron monoxide (HBO) (A (1)sigma(-), B (1)delta, a (3)sigma(+), and b (3)delta) and boron hydroxide (BOH) (A (1)sigma(+), B (1)Pi, and b (3)Pi), and their bent counterparts (HBO a (3)A('), b (3)A("), A (1)A("), B (1)A(') and BOH X (1)A('), b (3)A('), c (3)A("), A (1)A('), B (1)A('), C (1)A(")) are investigated using excited electronic state ab initio equation-of-motion coupled-cluster (EOM-CC) methods. A new implementation of open-shell EOM-CC including iterative partial triple excitations (EOM-CC3) was tested. Coupled-cluster wave functions with single and double excitations (CCSD), single, double, and iterative partial triple excitations (CC3), and single, double, and full triple excitations (CCSDT) are employed with the correlation-consistent quadruple and quintuple zeta basis sets. The linear HBO X (1)sigma(+) state is predicted to lie 48.3 kcal mol(-1) (2.09 eV) lower in energy than the BOH X (1)sigma(+) linear stationary point at the CCSDT level of theory. The CCSDT BOH barrier to linearity is predicted to lie 3.7 kcal mol(-1) (0.16 eV). With a harmonic zero-point vibrational energy correction, the HBO X (1)sigma(+)-BOH X (1)A(') energy difference is 45.2 kcal mol(-1) (1.96 eV). The lowest triplet excited electronic state of HBO, a (3)A('), has a predicted excitation energy (T(e)) of 115 kcal mol(-1) (4.97 eV) from the HBO ground state minimum, while the lowest-bound BOH excited electronic state, b (3)A('), has a T(e) of 70.2 kcal mol(-1) (3.04 eV) with respect to BOH X (1)A('). The T(e) values predicted for the lowest singlet excited states are A (1)A(")<--X (1)sigma(+)=139 kcal mol(-1) (6.01 eV) for HBO and A (1)A(')<--X (1)A(')=102 kcal mol(-1) (4.42 eV) for BOH. Also for BOH, the triplet vertical transition energies are b (3)A(')<--X (1)A(')=71.4 kcal mol(-1) (3.10 eV) and c (3)A(")<--X (1)A(')=87.2 kcal mol(-1) (3.78 eV).