The formation of plutonium (III–VI) complexes in nitric and hydrochloric acid solutions was simulated using DMol 3 and Relativistic Discrete-Variational (RDV) methods. Both explicit and explicit-plus-implicit approaches for the modeling of solution boundary conditions were used. For the explicit modeling of molecular environment of plutonium ions we used 22 and 32 water molecules and the counter ions NO 3 − or Cl − randomly distributed around actinide atom. For the additional implicit modeling of solvent environment, COSMO potential (Conductor-like Screening Model) for water ( ε = 78.54) was used. The original method for the calculation of interaction energies between selected parts of the large multi-atomic systems provides the quantitative comparison of the stability of plutonium complexes with various compositions and the estimation of the roles of NO 3 − , Cl − and water molecules of the nearest and next-nearest solution layers. We obtained that the average interaction energies between Pu Z+ ion and each nearest H 2 O molecule were slightly dependent on the size and composition of optimized plutonium complex.

Релятивистским методом дискретного варьирования выполнен расчет электронного строения NoO2 и спектра РФЭС (рентгеновской фотоэлектронной спектроскопии) валентных электронов в диапазоне энергий связи от 0 до ~40 эВ. Наблюдаются значительные эффекты ковалентности в NoO2, обусловленные существенным перекрыванием не только No 6d АО, но и No 6p и No 5f АО с орбиталями кислорода. Построены гистограмма и схема МО, позволяющие понять особенности природы химической связи и структуру спектра РФЭС валентных электронов в NoO2.

The electronic structure of NoO2 and the valence-band X-ray photoelectron spectrum (XPS) in the energy range from 0 eV to 40 eV are calculated by the relativistic discrete variation method. Significant covalency effects are observed in NoO2, which are due to a considerable overlap of not only No 6d AO but also No 6p and No 5f AOs with oxygen orbitals. The MO histogram and scheme are derived, which enable the comprehension of features of the chemical bond nature and the structure of the XPS spectrum of valence electrons in NoO2.

The electronic structure of AnO2 (An = Th‒Lr) and the structure of X-ray photoelectron spectra of their valence electrons were calculated by the relativistic discrete variation method in the MO LCAO cluster approximation (molecular orbitals as linear combinations of atomic orbitals). This structure is in satisfactory agreement with the available experimental spectra. The effective charges QAn of the An ions in AnO2 were determined as the difference between the number of electrons in the neutral An atom and the number of electrons in the actinide ion in the AnO8 cluster. The dependence of the effective charges QAn in AnO2 on the atomic number Z was obtained. The estimated values in the range 0.42 e < QAn < 1.04 e differ significantly from QAn(IV) = 4 e, found in the ionic approximation. This is attributed to the significant covalence effects in AnO2, associated with the overlap of not only An6d, but also of An6p and An5f AOs with the oxygen orbitals. There is qualitative agreement between the obtained QAn values and the values of the chemical shifts (several electron-volts) of the lines of the actinide 4f core electrons in the XP spectra of dioxides relative to the metals.

Релятивистским методом дискретного варьирования (РДВ) рассчитана плотность состояний валентных электронов диоксида EsO2. Построена схема молекулярных орбиталей (МО) валентных электронов и с учетом сечений фотоэффекта валентных электронов построена гистограмма спектра РФЭС (рентгеновской фотоэлектронной спектроскопии) в диапазоне энергий связи электронов от 0 до ~40 эВ. Показано, что в структуру этого спектра вносят вклад электроны внешних валентных (ВМО, от 0 до ~15 эВ) и внутренних валентных (ВВМО, от ~15 до ~50 эВ) МО. Установлено участие Es 5f- и Es 6p-электронов в химической связи. Наблюдается значительное перекрывание не только Es 6d АО, но и Es 6p и Es 5f АО с орбиталями лигандов, что обусловливает высокий вклад ковалентной составляющей в химическую связь в этом диоксиде. Отмечается, что схема МО позволяет понять природу химической связи и структуру спектра РФЭС валентных электронов в EsO2. Показано, что электроны ВВМО на треть ослабляют химическую связь, обусловленную электронами ВМО.

The density of electronic states and the XPS spectrum of FmO2 valence electrons in the binding energy range from 0 to ∼40 eV have been calculated by the fully relativistic method of discrete variation. It is shown that the electrons of the outer and inner valence molecular orbitals (MOs) with binding energies from 0 to ∼15 eV and from ∼15 to ∼40 eV, respectively, contribute to the complex structure of the XPS spectrum of FmO2. The FmO2 MO diagram was constructed and the contribution of the electrons of the outer and inner valence MOs to the chemical bond was estimated.

The density of states of valence electrons of the EsO 2 dioxide is calculated by the relativistic discrete variational method. The scheme of valence molecular orbitals (MOs) is constructed taking into account the photoelectric effect cross sections of valence electrons. The histogram of X-ray photoelectron spectra (XPS) is built for the electron binding energies from 0 eV to ~40 eV. It is shown that the structure of this spectrum contains contributions of outer valence orbitals (OVMOs, from 0 eV to ~15 eV) and inner valence orbitals (IVMOs, from ~15 eV to ~50 eV) molecular orbitals. It is established that Es 5 f and Es 6 p electrons participate in the chemical bonding. It is established that not only Es 6 d , but also Es 6 p and Es 5 f orbitals overlap significantly with ligand orbitals, resulting in a highly covalent chemical bonding in this dioxide. The nature of chemical bonding and the structure of the XPS spectrum of valence electrons in EsO 2 is clarified using the scheme of MOs. It is shown that the chemical bonding formed by OVMO electrons is weaken by one third due to IVMO electrons.

The complex structure of precision X-ray photoelectron spectra (XPS) of valence and core electrons of a ThO2(001) crystal film on Si(100) was obtained and analyzed, and the electronic structure of ThO8, Th13O56, and Th63O216 clusters was calculated. A histogram of the calculated XPS spectrum of electrons of the outer (from 0 to ~15 eV, OVMO) and inner (from ~15 to ~35 eV, IVMO) valence MOs was plotted. The calculated spectrum was in good agreement with the experimental one. Significant overlap of Th 6d atomic orbitals (AO) as well as Th 6p, 5f AO with oxygen orbitals is noted, which brings about the covalent nature of the bond in this dioxide. The contribution of the OVMO and IVMO electrons to the chemical bond was estimated based on the values of the bond populations. It was shown that the IVMO electrons weaken the chemical bond caused by OVMO electrons. It is assumed that the complex structure in the spectra of the Th 5s and Th 5p electrons is largely due to the dynamic effect, which does not allow observing the structure in the spectrum of the Th 5s electrons in ThO2.

The relativistic method of discrete variation has been used to calculate the density of states and the X-ray photoelectron spectroscopy spectrum of valence electrons in the range of electron binding energies from 0 to ~50 eV in PaO2. A scheme of molecular orbitals has been constructed. Significant covalence effects are observed in PaO2, which are associated with the overlap of not only Pa6d atomic orbitals but also Pa6p and Pa5f atomic orbitals with oxygen orbitals. It has been found that the electrons of the inner valence molecular orbitals weaken the chemical bond formed by the electrons of the outer valence molecular orbitals.

A study was made of glass samples obtained from highly purified natural quartz, synthetic silica, and glass grit made of synthetic quartz crystals smelted according to a technology that included elements of the KS-4V technology. It was determined that the transmission spectra of the glasses smelted from various materials have differences in the UV and IR regions.

In the approximation of the relativistic discrete variation method, the valence X-ray photoelectron spectrum of CmO2 was calculated, and satisfactory agreement with the structure of the experimental spectrum was found. It was shown that the structure of the spectrum is due to the electrons of the outer (from 0 to ~15 eV) and inner (from ~15 to ~35 eV) valence molecular orbitals, which leads to an increase in the covalency of the chemical bond in CmO2. The effective charge of curium in CmO2 was determined, and the contribution of various electrons to the chemical bond was evaluated. A semiempirical scheme of molecular orbitals for CmO2 was constructed.

The electronic structure of CfO 2 is calculated in the fully relativistic cluster approximation of the discrete variation method (RDV). Theoretical X-ray photoelectron spectroscopy (XPS) spectrum of valence electrons is obtained in the range of electron binding energies 0 -…~40 eV. It is shown that outer valence molecular orbitals (OVMOs) in the energy range 0 -…~15 eV are formed by atomic orbitals Cf 5 f and Cf 6 p . The inner valence molecular orbitals (IVMOs) in the energy range ~15 -…~40 eV are formed mainly by Cf 6 p 3/2 and O 2 s AOs. Significant covalent effects in CfO 2 are due to the strong overlap of AOs with the ligand′s orbitals such as Cf 6 d as well as Cf 5 f and Cf 6 p . The structure of MOs formed by Cf 6 d , 7 s , and 7 p AOs differs only slightly from those of dioxides of lighter actinides. These MOs, together with those containing O 2 s and O 2 p AOs, form a “rigid framework” where MOs containing An 5 f AOs move. We suggest a theoretical scheme of MOs that allows understanding the nature of chemical bonding and the structure of the XPS spectrum of valence electrons in CfO 2 .

The first calculations of the electronic structure and X-ray photoelectron spectrum (XPS) of valence electrons of BkO2 in the 0 to ~50 eV range of binding energies are made via relativistic discrete-variational method (RDV). Satisfactory agreement is established between the calculated and experimental spectra of this dioxide, obtained in the works of other authors. A quantitative molecular orbitals (MO) scheme is constructed that allows us to understand the nature of the chemical bonds and the structure of the XPS of valence electrons in BkO2. In contrast to the concepts of the crystal field theory, the effects of covalence in BkO2 are considerable and result in strong overlapping not only of the Bk6d, but of Bk6p, 5f atomic orbitals (AO) with ligand orbitals as well. It is found that the electrons of inner valence molecular orbitals (IVMO) weaken the chemical bonds caused by the electrons of outer valence molecular orbitals (OVMO) by 28%.

Abstract Geometry optimization and the electronic structure calculations of Pu Z+ complexes (Z = 3–6) in water solution have been performed, within the framework of the DMol3 and Relativistic Discrete-Variational (RDV) methods. For the simulation of Pu Z+ molecular environment in aqueous solution we used 22 and 32 water molecules randomly distributed around cation. To model the effect of bulk solvent environment we used COSMO (Conductor-like Screening Model) potential for water (ε = 78.54). The obtained results showed that this approach allows the modeling of water dissociation and the formation of hydrolysis products. Our previously suggested scheme for the calculation of interaction energies between selected fragments of multi-molecular systems provides the quantitative estimation of the interaction strengths between plutonium in various oxidation states and each ligand in the first and second coordination shells in water solution.

Theoretical study of the formation of PuZ+ (Z = 3, 4, 5, 6) complexes with the two types of diamide molecules C8N2H10O2(CH3)(2) (dimethylbicyclicdiamide-DMDA) with bicyclic structure and C3N2H2O2(CH3)(4) (tetramethylmalonamide-TMMA) with acyclic structure was carried out using ab initio DFT based DMol(3) and relativistic discrete variational methods. The results of gas phase modeling showed that the appropriate positions of the oxygen atoms in DMDA in comparison with TMMA cannot explain the considerable difference in sorption affinity of these molecules. For the modeling of solutions, the implicit (COSMO) and explicit methods were used. In the latter approach, we included 40 water molecules, 16NO(3)(-) or 16Cl(-) and 16H(+) ions into the systems under investigation. The obtained results showed the principle role of solution in the weakening of actinide bonding with TMMA and DMDA molecules due to interaction with H2O and NO3- or Cl- ions.

Проведен расчет электронной структуры CfO2 в полностью релятивистском кластерном приближении метода дискретного варьирования (РДВ). Получен теоретический спектр рентгеновский фотоэлектронный спектроскопии (РФЭС) валентных электронов в диапазоне энергий связи электронов 0…~40 эВ. Показано, что в образовании внешних валентных молекулярных орбиталей в диапазоне энергий 0…~15 эВ принимают участие атомные орбитали Cf 5f и Cf 6p. Основной вклад в образование внутренних валентных молекулярных орбиталей в диапазоне энергий ~15…~40 эВ вносят АО Cf 6p3/2 и O 2s. Значительные эффекты ковалентности в CfO2 связаны с сильным перекрыванием АО с орбиталями лигандов не только Cf 6d, но и Cf 5f, а также Cf 6p. Структура МО с участием АО Cf 6d, 7s и 7р мало меняется по сравнению с таковой диоксидов более легких актиноидов. Эти МО вместе с содержащими O 2s и О 2р АО образуют «жесткий каркас», в котором перемещаются МО, включающие An 5f АО. Построена теоретическая схема МО, позволяющая понять природу химической связи и структуру спектра РФЭС валентных электронов в CfO2.

The ab initio calculations on electronic structure of the large fragments of UO2 crystal lattice was performed using Molecular Dynamics and fully relativistic Discrete Variational method. The four types of clusters corresponding to stoichiometric crystal and to the crystals with isolated uranium vacancy and uranium interstitial impurity were considered. We investigated the transformation of valence and vacant bands and the nature of chemical bonding. The estimation of electron density redistribution among atoms of several coordination spheres around defects was performed. In contrast to previous ab initio and semi-empirical calculations, our model included the point symmetry of defects and the possibility of charge transfer between defects and all nearest and next nearest neighbors. We obtained that the deformation of crystal structure and the covalent interactions minimizes (or completely prevent) the electron density transfer between atoms in the vicinity of defects.

The computer modeling of electronic structure and electron density distribution in the large fragments of crystal lattices of uranium dioxide was carried out using Molecular Dynamics and ab initio Relativistic Discrete Variational method (RDV). The five types of clusters with oxygen vacancy and metal and oxygen atoms in the center were considered. At the first step of simulation, the geometry of clusters corresponded to the regular crystals, and at the second step, the distorted structures around one oxygen vacancy and one oxygen interstitial point defects were considered. In each case, the transformation of electronic states and chemical bonding were investigated, as well the estimation of effective charges on atoms of several coordination spheres around defects was performed. For the calculations of atomic charges we used the original procedure based on spatial integration of electron density. Unlike previous simulations ignoring point symmetry of isolated defects, our model included the charge transfer between defects and all nearest and next nearest neighbors. Our study showed that the transfer of electron density between atoms around defects is more complex than that predicted in previous calculations using ab initio and pair-potential models.

The nature of the chemical bond in UO 2 was analyzed taking into account the X-ray photoelectron spectroscopy (XPS) structure parameters of the valence and core electrons, as well as the relativistic discrete variation electronic structure calculation results for this oxide. The ionic/covalent nature of the chemical bond was determined for the UO 8 (D 4h ) cluster, reflecting uranium's close environment in UO 2 , and the U 13 O 56 and U 63 O 216 clusters, reflecting the bulk of solid uranium dioxide. The bar graph of the theoretical valence band (from 0 to ~35 eV) of XPS spectrum was built such that it was in satisfactory agreement with the experimental spectrum of a UO 2 single crystalline thin film. It was shown that unlike the crystal field theory results, the covalence effects in UO 2 are significant due to the strong overlap of the U 6p and U 5f atomic orbitals with the ligand orbitals, in addition to the U 6d atomic orbital (AO). A quantitative molecular orbital (MO) scheme for UO 2 was built. The contribution of the MO electrons to the chemical bond covalence component was evaluated on the basis of the bond population values. It was found that the electrons of inner valence molecular orbitals (IVMO) weaken the chemical bond formed by the electrons of outer valence molecular orbitals (OVMO) by 32% in UO 8 and by 25% in U 63 O 216 .