One-particle Basis Set Research Articles

Accurate Infrared Line Lists for 20 Isotopologues of CS2 at Room Temperature

To facilitate atmospheric and spectroscopic studies of carbon disulfide, or CS2, in both planetary and exoplanetary atmospheres, we adopt the “Best Theory + Reliable High-resolution Experiment” algorithm to generate semiempirical IR line lists for the 20 most abundant CS2 isotopologues, denoted as Ames-296K. The IR lists are computed using the Ames-1 potential energy surface, refined using the experimental transition set and an ab initio dipole moment surface fitted from CCSD(T)/aug-cc-pV(T/Q/5+d)Z dipoles extrapolated to a one-particle basis set limit. The IR lists cover the range of 0–10,000 cm−1, with an S 296K cutoff at 10−31 cm−1/molecule·cm−2 (abundance included). A “natural” IR line list at 296 K includes about 10 million lines of the 20 isotopologues, with their intensities scaled by the corresponding abundances. The zero-point energy, partition functions, and abundances are reported for each isotopologue. The energy levels in the global effective Hamiltonian model for 12C32S2 are adopted to improve the line position accuracy. This new IR list for the main isotopologue is denoted as A+I.296K. Reliable HITRAN2020 line positions are also utilized to improve the accuracy of the 32S12C34S, 32S12C33S, and 32S13C32S isotopologue line lists. The final composite line list is validated against Pacific Northwest National Laboratory experimental cross sections, showing excellent agreement. The agreement supports the quality of the composite line list and the power of synergy between experiment and theory. The new data are proposed for use in updating and expanding the CS2 data in HITRAN and other high-resolution IR databases. Supplementary files are available in Zenodo and AHED.

Combining low-cost electronic structure theory and low-cost parallel computing architecture.

The computational efficiency of low-cost electronic structure methods can be further improved by leveraging heterogenous computing architectures. The software package TeraChem has been developed since 2008 to make use of graphical processing units (GPUs), particularly their strong single-precision performance, for the acceleration of quantum chemical calculations. Here, we present the implementation of three low-cost methods, namely HF-3c, PBEh-3c, and the recently introduced ωB97X-3c. We show that these can benefit in terms of performance when combined with "consumer grade" GPUs by leveraging the mixed precision integral handling in TeraChem. The current limitation of the latter's GPU integral library is that Gaussian integrals only for functions with angular momentum l < 3 can be computed, which generally restricts the achievable accuracy in terms of the one-particle basis set. Particularly, the implementation of the ωB97X-3c method now enables higher accuracy with this setting which, in turn, provides the most efficient implementation accessible with consumer-grade hardware. We furthermore show that the implemented 3c methods can be combined with the hh-TDA formalism. This gives new and efficient low-cost multi-configurational excited states methods, which are benchmarked for the description of lowest vertical excitation energies in this work. All in all, the combination of these efficient electronic structure theory methods with affordable highly parallelized computing hardware provides an optimal computational and monetary cost to accuracy ratio.

Hydrogen-Atom Electronic Basis Sets for Multicomponent Quantum Chemistry.

Multicomponent methods are a conceptually simple way to include nuclear quantum effects into quantum chemistry calculations. In multicomponent methods, the electronic molecular orbitals are described using the linear combination of atomic orbitals approximation. This requires the selection of a one-particle electronic basis set which, in practice, is commonly a correlation-consistent basis set. In multicomponent method studies, it has been demonstrated that large electronic basis sets are required for quantum hydrogen nuclei to accurately describe electron-nuclear correlation. However, as we show in this study, much of the need for large electronic basis sets is due to the correlation-consistent electronic basis sets not being optimized to describe nuclear properties and electron-nuclear correlation. Herein, we introduce a series of correlation-consistent electronic basis sets for hydrogen atoms called cc-pVnZ-mc with additional basis functions optimized to reproduce multicomponent density functional theory protonic densities. These new electronic basis sets are shown to yield better protonic densities with fewer electronic basis functions than the standard correlation-consistent basis sets and reproduce other protonic properties such as proton affinities and protonic excitation energies, even though they were not optimized for these purposes. The cc-pVnZ-mc basis sets should enable multicomponent many-body calculations on larger systems due to the improved computational efficiency they provide for a given level of accuracy.

Energy Landscape and Structural and Spectroscopic Characterization of Diazirine and Its Cyclic Isomers

Identifying new nitrogenated hydrocarbon molecules in the interstellar medium (ISM) is challenging because of the lack of comprehensive spectroscopic data from experiments. In this computational work, we focus on investigating the structures, relative energies, spectroscopic constants, and energy landscape of the cyclic isomers of diazirine (c-CH2N2) using ab initio quantum chemical methods. Density functional theory (DFT) methods and coupled cluster theory with singles and doubles including perturbative triples [CCSD(T)] and CCSD(T) with the explicitly correlated F12b correction [CCSD(T)-F12b] were employed for this purpose along with large correlation consistent cc-pVTZ, cc-pVQZ, and cc-pV5Z basis sets. Harmonic vibrational frequencies, infrared vibrational intensities, rotational constants, and dipole moments are reported. Anharmonic vibrational fundamentals along with centrifugal distortion constants, and vibration-rotation interaction constants are also reported for all the cyclic isomers. The energies computed with the CCSD(T) and CCSD(T)-F12b methods were extrapolated to the one-particle complete basis set (CBS) limit following a three-point formula. At the CCSD(T)-F12b/CBS level of theory, the 3,3H-diazirine (c-CH2N2) is the lowest energy cyclic isomer followed by 1,3H-diazirine, (E)-1,2H-diazirine, and (Z)-1,2H-diazirine, which are 20.1, 47.8, and 51.3 kcal mol-1 above the 3,3H-diazirine, respectively. Accurate structures and spectroscopic constants that are reported here could be useful for future identification of these cyclic nitrogenated organic molecules in the interstellar medium or circumstellar disks.

Multicomponent heat-bath configuration interaction with the perturbative correction for the calculation of protonic excited states.

In this study, we extend the multicomponent heat-bath configuration interaction (HCI) method to excited states. Previous multicomponent HCI studies have been performed using only the variational stage of the HCI algorithm as they have largely focused on the calculation of protonic densities. Because this study focuses on energetic quantities, a second-order perturbative correction after the variational stage is essential. Therefore, this study implements the second-order Epstein-Nesbet correction to the variational stage of multicomponent HCI for the first time. Additionally, this study introduces a new procedure for calculating reference excitation energies for multicomponent methods using the Fourier-grid Hamiltonian (FGH) method, which should allow the one-particle electronic basis set errors to be better isolated from errors arising from an incomplete description of electron-proton correlation. The excited-state multicomponent HCI method is benchmarked by computing protonic excitations of the HCN and FHF- molecules and is shown to be of similar accuracy to previous excited-state multicomponent methods such as the multicomponent time-dependent density-functional theory and equation-of-motion coupled-cluster theory relative to the new FGH reference values.

Vibronic resonance is inadequately described by one-particle basis sets

Vibrational-electronic (vibronic) resonance and its possible role in energy and charge transfer have been experimentally and theoretically investigated in several photosynthetic proteins. Using a dimer modeled on a typical photosynthetic protein, we contrast the description of such excitons provided by an exact basis set description, as opposed to a basis set with reduced vibrational dimensionality. Using a reduced analytical description of the full Hamiltonian, we show that in the presence of vibrational excitation both on electronically excited as well as unexcited sites, constructive interference between such basis states causes vibronic coupling between excitons to become progressively stronger with increasing quanta of vibrational excitation. This effect leads to three distinguishing features of excitons coupled through a vibronic resonance, which are not captured in basis sets that restrict ground state vibrations: (1) the vibronic resonance criterion itself, (2) vibronically assisted perfect delocalization between sites even though purely electronic mixing between the sites is imperfect due to energetic disorder, and (3) the nuclear distortion accompanying vibronic excitons becoming increasingly larger for resonant vibronic coupling involving higher vibrational quanta. In terms of spectroscopically observable limitations of reduced basis set descriptions of vibronic resonance, several differences are seen in absorption and emission spectra but may be obscured on account of overwhelming line broadening. However, we show that several features such as vibronic exciton delocalization and vibrational distortions associated with electronic excitations, which ultimately dictate the excited state wavepacket motions and relaxation processes, are fundamentally not described by basis sets that restrict ground state vibrations.

Cope rearrangements in shapeshifting molecules re-examined by means of high-level CCSDT(Q) composite ab initio methods

Benchmark reaction barrier heights for the degenerate Cope rearrangements in the highly fluxional bullvalene and semibullvalene hydrocarbon cages are obtained at the CCSDT(Q) level close to the one-particle basis set limit and include inner-shell, scalar-relativistic, and Born–Oppenheimer corrections. Our best theoretical CCSDT(Q) Gibbs free reaction barrier height for semibullvalene (ΔG298‡ = 27.9 kJ mol−1) is in good agreement with the most recent experimental value of 25.9 kJ mol−1. However, our CCSDT(Q) reaction barrier height for bullvalene (ΔG298‡ = 62.2 kJ mol−1) indicates that the most recent gas-phase experimental value of 54.8 ± 0.8 should be revised upward.

Highly Accurate Quartic Force Field and Rovibrational Spectroscopic Constants for the Azirinyl Cation (c-C2NH2+) and Its Isomers.

The azirinyl cation is an aromatic cyclic molecule that is isoelectronic with cyclopropenylidene, c-C3H2, and c-C3H3+. Cyclopropenylidene has been shown to be ubiquitous, existing in many different astrophysical environments. Given the similar chemistry between C and N, and the relative abundances between C and N in astrophysical environments, it is expected that there should be aromatic ringed molecules that incorporate N in the ring, but as yet, no such molecule has been identified. To address this issue, the present study uses high levels of electronic structure theory to compute a highly accurate quartic force field (QFF) for the azirinyl cation and its two lowest lying isomers, the cyanomethyl and isocyanomethyl cations. The theoretical approach uses the singles and doubles coupled-cluster method that includes a perturbative correction for connected triple excitations, CCSD(T), together with extrapolation to the one-particle basis set limit and corrections for scalar relativity and core-correlation. The QFF is then used in a second-order vibrational perturbation theory analysis (VPT2) to compute the fundamental vibrational frequencies and rovibrational spectroscopic constants for all three C2NH2+ isomers. The reliability of the VPT2 vibrational frequencies is tested by comparison to vibrational configuration interaction (VCI) calculations, and excellent agreement is found between the two approaches. Fundamental vibrational frequencies and rovibrational spectroscopic constants for all singly substituted 13C, 15N, and D isotopologues are also reported. It is expected that the highly accurate spectroscopic data reported herein will be useful in the identification of these cations in high-resolution experimental or astronomical observations.

Thermochemistry of phosphorus sulfide cages: an extreme challenge for high-level ab initio methods

The enthalpies of formation and isomerization energies of P4Sn molecular cages are not experimentally (or theoretically) well known. We obtain accurate enthalpies of formation and isomerization energies for P4Sn cages (n = 3, 4, 5, 6, and 10) by means of explicitly correlated high-level thermochemical procedures approximating the CCSD(T) and CCSDT(Q) energies at the complete basis set (CBS) limit. The atomization reactions have very significant contribution from post-CCSD(T) correlation effects and, due to the presence of many second-row atoms, the CCSD and (T) correlation energies converge exceedingly slowly with the size of the one-particle basis set. As a result, these cage structures are challenging targets for thermochemical procedures approximating the CCSD(T) energy (e.g., W1-F12 and G4). Our best enthalpies of formation at 298 K (∆fH°298) are obtained from thermochemical cycles in which the P4Sn cages are broken down into P2S2 and S2 fragments for which highly accurate ∆fH°298 values are available from W4 theory. For the smaller P4S3 and P4S4 cages, the reaction energies are calculated at the CCSDT(Q)/CBS level and for the larger P4S5, P4S6, and P4S10 cages, they are obtained at the CCSD(T)/CBS level. Our best ∆fH°298 values are − 94.5 (P4S3), − 108.4 (α-P4S4), − 98.7 (β-P4S4), − 126.2 (α-P4S5), − 126.1 (β-P4S5), − 112.7 (γ-P4S5), − 144.7 (α-P4S6), − 153.9 (β-P4S6), − 134.4 (γ-P4S6), − 136.3 (δ-P4S6), − 118.7 (e-P4S6), and − 215.4 (P4S10) kJ mol−1. Interestingly, we find a linear correlation (R2 = 0.992) between the enthalpies of formation of the most stable isomers of each molecular formula and the number of atoms in the P4Sn cages. We use our best ∆fH°298 values to assess the performance of a number of lower-cost composite ab initio methods. For absolute enthalpies of formation, G4(MP2) and G3(MP2)B3 result in the best overall performance with root-mean-square deviations (RMSDs) of 10.6 and 12.9 kJ mol−1, respectively, whereas G3, G3B3, and CBS-QB3 result in the worst performance with RMSDs of 27.0–38.8 kJ mol−1. In contrast to absolute enthalpies of formation, all of the considered composite procedures give a good-to-excellent performance for the isomerization energies with RMSDs below the 5 kJ mol−1 mark.

Curing basis-set convergence of wave-function theory using density-functional theory: A systematically improvable approach.

The present work proposes to use density-functional theory (DFT) to correct for the basis-set error of wave-function theory (WFT). One of the key ideas developed here is to define a range-separation parameter which automatically adapts to a given basis set. The derivation of the exact equations are based on the Levy-Lieb formulation of DFT, which helps us to define a complementary functional which corrects uniquely for the basis-set error of WFT. The coupling of DFT and WFT is done through the definition of a real-space representation of the electron-electron Coulomb operator projected on a one-particle basis set. Such an effective interaction has the particularity to coincide with the exact electron-electron interaction in the limit of a complete basis set, and to be finite at the electron-electron coalescence point when the basis set is incomplete. The non-diverging character of the effective interaction allows one to define a mapping with the long-range interaction used in the context of range-separated DFT and to design practical approximations for the unknown complementary functional. Here, a local-density approximation is proposed for both full-configuration-interaction (FCI) and selected configuration-interaction approaches. Our theory is numerically tested to compute total energies and ionization potentials for a series of atomic systems. The results clearly show that the DFT correction drastically improves the basis-set convergence of both the total energies and the energy differences. For instance, a sub kcal/mol accuracy is obtained from the aug-cc-pVTZ basis set with the method proposed here when an aug-cc-pV5Z basis set barely reaches such a level of accuracy at the near FCI level.

Do CCSD and approximate CCSD-F12 variants converge to the same basis set limits? The case of atomization energies.

While the title question is a clear "yes" from purely theoretical arguments, the case is less clear for practical calculations with finite (one-particle) basis sets. To shed further light on this issue, the convergence to the basis set limit of CCSD (coupled cluster theory with all single and double excitations) and of different approximate implementations of CCSD-F12 (explicitly correlated CCSD) has been investigated in detail for the W4-17 thermochemical benchmark. Near the CBS ([1-particle] complete basis set) limit, CCSD and CCSD(F12*) agree to within their respective uncertainties (about ±0.04 kcal/mol) due to residual basis set incompleteness error, but a nontrivial difference remains between CCSD-F12b and CCSD(F12*), which is roughly proportional to the degree of static correlation. The observed basis set convergence behavior results from the superposition of a rapidly converging, attractive, CCSD[F12]-CCSD-F12b difference (consisting mostly of third-order terms) and a more slowly converging, repulsive, fourth-order difference between CCSD(F12*) and CCSD[F12]. For accurate thermochemistry, we recommend CCSD(F12*) over CCSD-F12b if at all possible. There are some indications that the nZaPa family of basis sets exhibits somewhat smoother convergence than the correlation consistent family.

On the Choice of a Distributed Basis Set in Calculations of Transition-Dipole Moments in the One-Determinant Approximation

The so-called “asymptotic projection technique” developed in previous papers of the authors is applied to the calculation of electronic transition-dipole moments (TDMs) in the one-determinant approximation between states of the same spin and spatial symmetry. The basic equations of the method and specific features of their application to a TDM calculation are briefly discussed. The attention focusses on the choice of a finite one-particle basis set. For this purpose, two possible algorithms for constructing distributed basis sets are proposed. In the first of them, the construction is based on minimization of the Hartree–Fock energy (EHF) with respect to nonlinear basis set parameters. In the second case, the parameters are determined by minimizing the functional E = EHF + EMP2, which includes the electron correlation through the second order of Moller–Plesset perturbation theory (ЕМР2). On the whole, the results of calculations in both basis sets are in agreement with high-accuracy calculations performed by configuration interaction methods. The basis set adapted for E = EHF + EMP2 significantly improves the accuracy as compared to the basis set of the first type.

Automatic Differentiation in Quantum Chemistry with Applications to Fully Variational Hartree-Fock.

Automatic differentiation (AD) is a powerful tool that allows calculating derivatives of implemented algorithms with respect to all of their parameters up to machine precision, without the need to explicitly add any additional functions. Thus, AD has great potential in quantum chemistry, where gradients are omnipresent but also difficult to obtain, and researchers typically spend a considerable amount of time finding suitable analytical forms when implementing derivatives. Here, we demonstrate that AD can be used to compute gradients with respect to any parameter throughout a complete quantum chemistry method. We present DiffiQult, a Hartree–Fock implementation, entirely differentiated with the use of AD tools. DiffiQult is a software package written in plain Python with minimal deviation from standard code which illustrates the capability of AD to save human effort and time in implementations of exact gradients in quantum chemistry. We leverage the obtained gradients to optimize the parameters of one-particle basis sets in the context of the floating Gaussian framework.

The S66 Non-Covalent Interactions Benchmark Reconsidered Using Explicitly Correlated Methods Near the Basis Set Limit

The S66 benchmark for non-covalent interactions has been re-evaluated using explicitly correlated methods with basis sets near the one-particle basis set limit. It is found that post-MP2 ‘high-level corrections’ are treated adequately well using a combination of CCSD(F12*) with (aug-)cc-pVTZ-F12 basis sets on the one hand, and (T) extrapolated from conventional CCSD(T)/heavy-aug-cc-pV{D,T}Z on the other hand. Implications for earlier benchmarks on the larger S66×8 problem set in particular, and for accurate calculations on non-covalent interactions in general, are discussed. At a slight cost in accuracy, (T) can be considerably accelerated by using sano-V{D,T}Z+ basis sets, whereas half-counterpoise CCSD(F12*)(T)/cc-pVDZ-F12 offers the best compromise between accuracy and computational cost.

Communication: The failure of correlation to describe carbon=carbon bonding in out-of-plane bends.

Carbon-carbon multiply bonded systems are improperly described with standard, wave function-based correlation methods and Gaussian one-particle basis sets implying that thermochemical, spectroscopic, and potential energy surface computations are consistently erroneous. For computations of vibrational modes, the out-of-plane bends can be reported as imaginary at worst or simply too low at best. Utilizing the simplest of aromatic structures (cyclopropenylidene) and various levels of theory, this work diagnoses this known behavior as a combined one-particle and n-particle basis set effect for the first time. In essence, standard carbon basis sets do not describe equally well sp, sp2, and sp3 hybridized orbitals, and this effect is exacerbated post-Hartree-Fock by correlation methods. The latter allow for occupation of the π and π* orbitals in the expanded wave function that combine with the hydrogen s orbitals. As a result, the improperly described space is non-physically stabilized by post-Hartree-Fock correlation. This represents a fundamental problem in wavefunction theory for describing carbon.

Embedded Mean-Field Theory with Block-Orthogonalized Partitioning.

Embedded mean-field theory (EMFT) provides a simple, flexible framework for describing subsystems at different levels of mean-field theory. Subsystems are defined by partitioning a one-particle basis set, with a natural choice being the atomic orbital (AO) basis. Although generally well behaved, EMFT with AO partitioning can exhibit unphysical collapse of the self-consistent solution. To avoid this issue, we introduce subsystem partitioning of a block-orthogonalized (BO) basis set; this eliminates the unphysical collapse without significantly increasing computational cost. We also investigate a non-self-consistent implementation of EMFT, in which the density matrix is obtained using BO partitioning and the final energy evaluated using AO partitioning; this density-corrected EMFT approach is found to yield more accurate energies than BO partitioning while also avoiding issues of the unphysical collapse. Using these refined implementations of EMFT, previously proposed descriptions of the exact-exchange coupling between subsystems are compared: although the EX1 coupling scheme is slightly more accurate than EX0, the small improvement does not merit its substantially greater computational cost.

Decomposition of Intermolecular Interaction Energies within the Local Pair Natural Orbital Coupled Cluster Framework.

The local coupled cluster method DLPNO-CCSD(T) allows calculations on systems containing hundreds of atoms to be performed while typically reproducing canonical CCSD(T) energies with chemical accuracy. In this work, we present a scheme for decomposing the DLPNO-CCSD(T) interaction energy between two molecules into physical meaningful contributions, providing a quantification of the most important components of the chemical interaction. The method, called Local Energy Decomposition (LED), is straightforward and requires negligible additional computing time. Both the Hartree-Fock and the correlation energy are decomposed into contributions from localized or pairs of localized occupied orbitals. Assigning these localized orbitals to fragments allows one to differentiate between intra- and intermolecular contributions to the interaction energy. Accordingly, the interaction energy can be decomposed into electronic promotion, electrostatic, exchange, dynamic charge polarization, and dispersion contributions. The LED scheme is applied to a number of test cases ranging from weakly, dispersively bound complexes to systems with strong ionic interactions. The dependence of the results on the one-particle basis set and various technical aspects, such as the localization scheme, are carefully studied in order to ensure that the results do not suffer from technical artifacts. A numerical comparison between the DLPNO-CCSD(T)/LED and the popular symmetry adapted perturbation theory (DFT-SAPT) is made, and the limitations of the proposed scheme are discussed.

Many interacting fermions in a one-dimensional harmonic trap: a quantum-chemical treatment

We employ ab initio methods of quantum chemistry to investigate spin-1/2 fermions interacting via a two-body contact potential in a one-dimensional harmonic trap. The convergence of the total energy with the size of the one-particle basis set is analytically investigated for the two-body problem and the same form of the convergence formula is numerically confirmed to be valid for the many-body case. Benchmark calculations for two to six fermions with the full configuration interaction method equivalent to the exact diagonalization approach, and the coupled cluster (CC) method including single, double, triple, and quadruple excitations are presented. The convergence of the correlation energy with the level of excitations included in the CC model is analyzed. The range of the interaction strength for which single-reference CC methods work is examined. Next, the CC method restricted to single, double, and noniterative triple excitations, CCSD(T), is employed to study a two-component Fermi gas composed of 6–80 atoms in a one-dimensional harmonic trap. The density profiles of trapped atomic clouds are also reported. Finally, a comparison with experimental results for few-fermion systems is presented. Upcoming possible applications and extensions of the presented approach are discussed.

Estimating the CCSD basis-set limit energy from small basis sets: basis-set extrapolations vs additivity schemes

Coupled cluster calculations with all single and double excitations (CCSD) converge exceedingly slowly with the size of the one-particle basis set. We assess the performance of a number of approaches for obtaining CCSD correlation energies close to the complete basis-set limit in conjunction with relatively small DZ and TZ basis sets. These include global and system-dependent extrapolations based on the A + B/Lα two-point extrapolation formula, and the well-known additivity approach that uses an MP2-based basis-set-correction term. We show that the basis set convergence rate can change dramatically between different systems(e.g.it is slower for molecules with polar bonds and/or second-row elements). The system-dependent basis-set extrapolation scheme, in which unique basis-set extrapolation exponents for each system are obtained from lower-cost MP2 calculations, significantly accelerates the basis-set convergence relative to the global extrapolations. Nevertheless, we find that the simple MP2-based basis-set additivity scheme outperforms the extrapolation approaches. For example, the following root-mean-squared deviations are obtained for the 140 basis-set limit CCSD atomization energies in the W4-11 database: 9.1 (global extrapolation), 3.7 (system-dependent extrapolation), and 2.4 (additivity scheme) kJ mol–1. The CCSD energy in these approximations is obtained from basis sets of up to TZ quality and the latter two approaches require additional MP2 calculations with basis sets of up to QZ quality. We also assess the performance of the basis-set extrapolations and additivity schemes for a set of 20 basis-set limit CCSD atomization energies of larger molecules including amino acids, DNA/RNA bases, aromatic compounds, and platonic hydrocarbon cages. We obtain the following RMSDs for the above methods: 10.2 (global extrapolation), 5.7 (system-dependent extrapolation), and 2.9 (additivity scheme) kJ mol–1.

Ab initio ground-state potential energy function and vibration-rotation energy levels of imidogen, NH.

The accurate ground-state potential energy function of imidogen, NH, has been determined from ab initio calculations using the multireference averaged coupled-pair functional (MR-ACPF) method in conjunction with the correlation-consistent core-valence basis sets up to octuple-zeta quality. The importance of several effects, including electron correlation beyond the MR-ACPF level of approximation, the scalar relativistic, adiabatic, and nonadiabatic corrections were discussed. Along with the large one-particle basis set, all of these effects were found to be crucial to attain "spectroscopic" accuracy of the theoretical predictions of vibration-rotation energy levels of NH.